A Review of Melting and Freezing Processes of PCMnano-PCM and

Energy 211 (2020) 118698
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Energy
journal homepage: www.elsevier.com/locate/energy
A review of melting and freezing processes of PCM/nano-PCM and

their application in energy storage
Sara Rostami a, b, Masoud Afrand c, d, *, Amin Shahsavar e, M. Sheikholeslami f, g,
Rasool Kalbasi h, Saeed Aghakhani h, Mostafa Safdari Shadloo i, Hakan F. Oztop j
a
Laboratory of Magnetism and Magnetic Materials, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
b
Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam
c
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
d
Faculty of Electrical e Electronic Engineering, Duy Tan University, Da Nang 550000, Vietnam
e
Department of Mechanical Engineering, Kermanshah University of Technology, Kermanshah, Iran
f
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran
g
Renewable Energy Systems and Nanofluid Applications in Heat Transfer Laboratory, Babol Noshirvani University of Technology, Babol, Iran
h
Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
i
CORIA-UMR 6614, Normandie University, CNRS-University & INSA, 76000, Rouen, France
j
Department of Mechanical Engineering, Technology Faculty, Fırat University, Elazig, Turkey
a r t i c l e i n f o a b s t r a c t
Article history: Phase change materials (PCMs) are capable of storing energy as latent energy by changing the phase and
Received 15 June 2020 provide the stored energy when they are returned to their initial phase at a desired time. Due to the
Received in revised form varying melting temperature of these materials, their application in air conditions of buildings, as well as
6 August 2020
the provision of hygienic hot water has received much attention, recently. This paper first provides a
Accepted 21 August 2020
Available online 27 August 2020
detailed illustration of phase change materials and their working principle, different types, and prop-
erties. Then a characteristic example of PCMs in solar energy storage and the design of PCMs are
reviewed and analyzed. Next, this paper focuses on the heat transfer, melting and freezing processes of
Keywords:
Phase change materials
PCM/nano-PCMS including different models and experimental research on the natural convection and
Natural convection thermal energy storage. Finally, some challenges and suggestions are presented following the conclusion
Solar energy of this article. It is found that these materials generally improve system efficiency. Without using me-
Energy storage chanical equipment, these materials are naturally adapted to the temperature fluctuations of the envi-
Energy management ronment, leading to a reduction in energy consumption and subsequently energy management.
© 2020 Elsevier Ltd. All rights reserved.
1. Introduction consumption in the two centuries before [1,2]. The US Energy In-
formation Agency forecasts world energy consumption to grow by
Nowadays, the importance of energy is so much that it is 57% by 2030. Due to the problems of fossil fuels (environmental
interpreted as an energy crisis. The energy crisis means the gradual pollution, limited and endless resources, renewability and direct
shutdown of factories and power plants, disruptions in trans- policy influence), the world has shown a tendency for renewable
portation, reduction of gasoline for vehicles, the closure of schools energies including solar, wind (for wind machines), biomass [3],
in the winter, no airplanes flying, etc. In the last hundred years, geothermal, hydrogen [4e6], nuclear energy [7], etc. Solar power
energy dependency has increased dramatically, and we are heavily comes from nature, and because humans do not interfere with its
dependent on fossil fuels that are running out. Coal, gas, and oil production, it does not cause pollution [8,9].
constitute about 80% of the world’s energy consumption. Energy Simple technology, reducing air pollution and the environment,
consumption in the last fifty years has been higher than energy and most importantly saving fossil fuels for the future by con-
verting them to essential living materials using petrochemical
techniques, are the reasons for the need for solar energy [10e14].
* Corresponding author. Duy Tan University, Da Nang 550000, Vietnam. The sun not only is a great source of energy, but it is also the
E-mail addresses: sara.rostami@tdtu.edu.vn (S. Rostami), masoudafrand@ beginning of life and the source of all other energies. According to
duytan.edu.vn (M. Afrand).
https://doi.org/10.1016/j.energy.2020.118698
0360-5442/© 2020 Elsevier Ltd. All rights reserved.
2 S. Rostami et al. / Energy 211 (2020) 118698
scientific estimations, it has born from about 6000 million years forms. Thermal energy storage (TES) is carried out in sensible
ago, producing 4.2 million tons of energy per second as a result of (through specific heat of materials such as water, earth, etc.) and
nuclear fusion [15]. Due to the sun’s weight, which is about 333 000 latent (through phase change of materials such as paraffin, hy-
times the Earth’s weight, it could be a huge source of energy for the drated salt, etc.) [34,35]. PCMs are widely used in various industries
next 5 billion years. The diameter of the sun is 1.39 109 m, the including textiles, satellites, telecommunications and medicine due
temperature in the center of the sun is about 10e14 million C. The to the change in their states. Materials with the melting tempera-
radiation is emitted from its surface at a temperature of about ture of less than 15 C are used for air conditioning and extreme
5600 C by electromagnetic waves into space [16e18]. By cooling in phenomena that do not undergo regular temperature
measuring the solar radiation flux above the Earth’s atmosphere, changes, while those with the melting temperature higher than
we can calculate the total power received from the sun, which is 90 C are used to prevent fires where temperatures may suddenly
about 1.8 1011 MW [19,20]. Of course, almost half of the total solar rise [36e38]. Fig. 2 shows melting enthalpy and its temperature for
energy is absorbed by the atmosphere and just less than half of it is some PCMs.
absorbed by the earth’s surface [21e23]. The energy thus obtained PCMs are used in residential buildings (with 40% energy con-
in the form of visible, infrared, and ultraviolet light is about 1 kWh/ sumption) and industrial silos and factories (with 55% energy
m2 [24]. Fig. 1 shows the amount of primary energy produced from consumption). Their importance will be doubled when we look at
various sources in the US in 2009. It can be seen that the share of the role of recycling and optimization of energy consumption in
new energies is not significant [25,26]. energy management [41,42]. For example, the use of these mate-
The most important issue in solar energy is its absorption and rials in the eastern and western walls leas to the energy-saving
storage. Solar energy is absorbed by different collectors for different about 29% and the northern and southern walls of a residential
purposes such as electricity generation, water heating, space home result in energy-saving about 19% [43]. In Fig. 3, heat transfer
heating, etc. [29]. The abundance and cheapness of energy at is plotted for buildings.
certain times of the day are important reasons for energy storage. The main purposes of using PCMs in buildings are: using the
Solar energy is abundant in the daytime, but one of the major sun’s natural heat for cooling and heating and using the heat stored
drawbacks of this energy is its inaccessibility at night. Energy by the heating and cooling systems. There are three general ways to
storage can also be used in the absence of the sun [30,31]. In some use PCMs to research these goals: using PCMs on the building wall,
countries, such as China, where electricity is mostly used for home using PCMs on ceilings and floors, using them in cold and hot
heating, due to the low cost of electricity per day and its high costs storage tanks, reduce indoor temperature fluctuations, using PCMs
at night (due to peak hours of consumption), energy storage is an in solar systems, and their application in textiles.
important solution [32,33]. The use of PCM in the building (Fig. 4) can include PCM shutters,
Energy storage is done in mechanical, electrical and thermal PCM layer in facing walls, floor heating systems and PCM roof
Fig. 1. Primary production of energies from various sources in the US in 2009 [27,28].
S. Rostami et al. / Energy 211 (2020) 118698 3
Fig. 2. Melting temperature and enthalpy for some PCMs [39,40].
Fig. 3. Schematic of heat transfer in buildings [44,45].

Fig. 4. Energy storage methods in buildings.
boards. By placing the PCM on the suspended ceiling, they are used process, the PCMs behave like a thermal battery with the capacity
as part of air conditioning systems. The use of PCM in walls not only of latent heat and store the heat energy and release it during
makes them lighter but also saves energy by reducing thermal freezing. Considering the breadth and importance of PCMs in
loads [46,47]. These materials are usually made from hydrocarbons renewable and sustainable energy, this paper first provides a
or hydrated salts that are used in combination with ferrous addi- detailed illustration of phase change materials and their working
tives to increase the thermal conductivity [48,49]. principle, different types, and properties. Then a characteristic
Radiation heat transfer from the floor is better than convection example of PCMs in solar energy storage and the design of PCMs are
heat transfer because of providing more appropriate heating and reviewed and analyzed. Next, this paper focuses on the heat
less space occupancy. By utilizing PCM in the floor materials and by transfer, melting and freezing processes of PCM/nano-PCMS
assuming electrical heating, the electrical energy consumption can including different models and experimental research on the nat-
be reduced. In this way, at night when power consumption is less, ural convection and thermal energy storage. Finally, some chal-
the PCM material is melted and stores the heat as the electrical lenges and suggestions are presented following the conclusion of
system is turned on. The heat is returned to the environment this article.
during the day leads to savings in power consumption and the
creation of balance in power generation of power plants [50].
2. Aim of the present study
The increasing demand for energy consumption and the limi-
tation of fossil fuels as running out of resources and increasing
The most prominent feature of PCMs is the potential for thermal
environmental pollutants make the issue of energy storage is of
energy storage, as these materials, like a heat sink absorbs lot of
paramount importance. About 40% of all energy is consumed in the
energy at a constant temperature. Thermal conductivity is a prop-
buildings such that 14% of which is consumed in space heating and
erty attributed to thermal energy transfer capability, and its low
cooling. The first reports of the use of these materials in the
content will reduce the storage potential. Therefore, researchers
building emerged from the 1940s. Then, the use of these materials
have always sought to apply techniques to improve heat transfer
in buildings has been extensively studied since the 1980s, and
rates inside PCMs. Installing fins, loading metal foams and using
today their use in the building industry has been increased
pin-fins are some of the techniques that have received a lot of
considerably [51]. The use of PCMs is an effective energy-saving
thoughtfulness. On the other hand, today’s technology has led to
approach sorted as renewable energy sources. During the melting
more nanoparticles (these materials have very high thermal
conductivity) being produced at a lower cost. Adding nanoparticles although the ambient temperature continues to increase, the
can improve the heat transfer rate within the PCMs. Because these temperature of the materials and their surrounding environment
materials have very low thermal resistance and can be used as a remain constant and resist temperature rise due to the changing
path with low thermal resistance to transfer thermal energy. phase [66]. During this period, which usually lasts several hours,
However, these substances also affect the viscosity and exacerbate PCMs absorb large amounts of ambient heat but do not spend it for
the viscous force. On the other hand, convection in the liquid PCM increasing their temperature [67,68]. During the phase change
depends on the buoyancy as well as viscous forces. Adding nano- process (Fig. 7), they maintain their and surrounding temperature
particles intensifies buoyancy force while also exacerbating viscous (see Fig. 8).
force. Therefore, adding nanoparticles has a positive effect and a Most common PCMs in industries have low thermal conduc-
negative effect. In this paper, the competition between positive/ tivity, leading to a reduction in the efficiency of some systems that
negative effects is analyzed in different applications. In other use these materials for energy storage. As a result, such systems
studies [52], researchers have focused more on changes in ther- face inappropriate economic justification. Various techniques are
mophysical properties caused by the presence of nanoparticles. But used for the improvement of such energy storage systems. These
in this study, the main focus is on the analysis of the melting and techniques are: using extended surfaces (fins) [71,72], using a
freezing phenomena in the presence of nanoparticles. Moreover, network of PCMs with several materials [72e74], microcapsules
more comprehensive study is conducted to assess the nano-PCM PCMs [75e77], and increasing thermal conductivity of PCMs [78].
applications. Because of their higher thermal conductivity and lower density,
fiber filters and carbon nanomaterials are the two most common
3. PCMs and their different types components used to improve their thermal conductivity [79,80].
Carbon materials have high resistance against chemical reactions
PCMs are organic or inorganic compounds that absorb large and corrosion, making them compatible in every situation. By and
amounts of heat energy. Thermal energy storage in these materials large, fibers or carbon fibers can be added to the PCMs by melting
occurs during the phase change process. These materials absorb and shear mixing techniques [81].
and give back the thermal energy to the environment when the
solid to liquid and liquid to solid phase change occurs, respectively. 4. Types of PCMs
The PCMs have the potential to retain latent heat energy without
any change even after thousands of phase change cycles [53]. When PCMs are classified into three categories: organic, inorganic and
they are used indoors, they exchange large amounts of heat with eutectic. In Fig. 6, the temperature ranges of the PCMs and their
the environment through consecutive cycles of melting and thermal conductivity are given.
freezing due to extreme changes in air temperature (e.g. between
night and day), providing a more balanced air temperature for in- 4.1. Organic PCMs
doors [54].
Another application of PCMs is in food transport equipment and Organic materials are divided into two groups of paraffin and
machinery. Food transportation is one of the most difficult tasks in non-Paraffins. Organic materials with homogeneous melting, core-
the freight industry. Foods often cannot last long under normal forming, as well as materials used as coatings are not corrosive. The
conditions due to the possibility of spoilage and deformation. Be- organic PCMs used for heating and cooling of buildings have a
sides, transportation of some foods to distant places is somewhat melting point of 20e32 C.
impossible. On the other hand, the difference between night and Organic PCMs include paraffin and non-paraffins. Paraffin is a
creating of a constant temperature in the cabin of PCMs in different compound of straight chains. Due to availability of Paraffin in a
days and various environments are difficult. Today, a variety of wide range of melting temperatures, it is one of the best choices as
trucks equipped with refrigerators and freezers is produced based a PCM for energy storage. Due to economic considerations, only
on the advancement in the science and achievement of various industrial-purity paraffin can be used as PCM in latent thermal
mechanical and thermodynamic knowledge, including the use of storage systems. Paraffin is safe, reliable, predictable, non-corrosive
PCMs [55,56]. For example, Fig. 5 shows that a system can adjust and cheap. Paraffin is chemically neutral and stable at temperatures
the temperature of food throughout the journey. below 500 C. In addition to the above properties, homogeneous
Numerous studies were conducted to reveal the successive us- melting and core-forming are two important characteristics of
age of PCMs in buildings and the reduction of energy consumption paraffin. Paraffin has drawbacks such as low conductivity, flam-
for heating and cooling as well as providing comfort conditions to mability, and incompatibility with the plastic case, although these
the residents [59,60]. According to the results of the application of drawbacks can be corrected with some changes in paraffin wax and
these materials in the building, the fluctuations of indoor air tem- storage unit [83e89].
perature are significantly reduced and it is easy to maintain the Non-paraffins contain a large number of matters with variable
proper ambient temperature at optimum body temperature [61]. properties. Some researchers have done extensive research on
PCMs are special cases of the solid-liquid state which are solutions organic matter and eventually considered esters, fatty acids,
used to control heat and received the attention of many researchers alcohol, and glycol for energy storage. High latent heat, flamma-
in the last decades because of the latent heat for solid-to-solid or bility, low conductivity, low ignition point, different toxicity and
liquid-to-liquid cases are less than that for solid-to-liquid (melting) incompatibility at high temperatures are among the characteristics
case. As shown in Fig. 6, these materials are categorized in three of non- Paraffins [90e94].
classes of organic, inorganic, and eutectic [62,63].
Once a solid is heated, it absorbs energy to reach its melting 4.2. Inorganic PCMs
point and then changes from solid to liquid. PCMs have the prop-
erty of changing their phase at a given temperature range, in the Inorganic materials are classified into salt and metal hydrates.
sense that they maintain their temperature during the phase Inorganic compounds have a high latent heat per mass and volume,
change [65]. In fact, they are heated in parallel with the environ- they are cost-effective, inexpensive and non-flammable in com-
ment during the heating process until they reach their melting parison with organic compounds. However, these materials have
temperature (phase change). After reaching this temperature, some issues like undercooling and separation (which affect the
Fig. 5. Applications of PCMs in refrigerated vehicle [57,58].
Fig. 6. Heat capacity of different materials compared to PCMs [64].
properties of the phase change). Metal hydrates includes metals with a low melting point and
The general principle of salt hydrates is as follows. The solid- eutectic metals. Due to the weight problem, these metals are not
liquid phase change of salt hydrates is, in fact, the dehydration. widely used. High latent heat per volume and high thermal con-
Salt hydrates are a very important group of PCMs that have the ductivity are among the properties of these materials [100e102].
following characteristics: High latent heat per volume, relatively Eutectics are a minimum-melting of two or more components
high thermal conductivity, Low volume changes during melting, composition, each of which freeze and melts correspondingly
toxicity, homogenous melting, the density difference with water creating a mixture of the component crystals through crystalliza-
(which causes it to be deposited at the end of the case) and the tion (Fig. 7). The coordinates that determine a eutectic point on the
formation of a weak core that causes under cooling [95e99]. phase diagram are the ratio of the eutectic percentage (on the axis
Fig. 7. Temperature changes during the freezing and melting [69,70].
Fig. 8. PCMs classification, stability and cost [82].
of atomic/molecular ratio) and the eutectic temperature (on the especially true in desert cities with hot days and cold nights.
axis of temperature) [103e105]. Using energy-saving systems in buildings is more cost-effective
According to the explanations given above and the types of than purchasing energy-generating equipment such as boilers and
PCMs and based on Fig. 9 in which some PCMs and their thermal chillers. The price of electricity consumed during the peak hours of
conductivity values are given, it can be observed that PCMs are the network is very different from other hours. The amount of
divided into three categories in terms of application in different electricity provided by the network is limited and the addition of
temperature ranges: low temperature, medium temperature and the transformer requires a great deal of cost [113,114]. This is
high temperature, which can be used in the construction industry, especially true in large industrial plants, commercial and residen-
pharmaceutical, textile, electronics, solar collectors, and solar po- tial buildings located in hot and humid regions that their electrical
wer plants, respectively. energy consumption is high enough to supply a cold load.
All human efforts in air conditioning are providing conditions
wherein human comfort in the living environment. These efforts
5. Properties of PCMs are accompanied not only by high costs and the consumption of
fossil fuels but also results in environmental pollution and wiping
According to the performance of PCMs, as shown in Fig. 10, out the energy sources. Energy consumption management in
energy storage systems must have the following attributions: i) buildings is one of the ways to reduce energy consumption and
suitable melting point at optimum temperature range, ii) enough environmental pollutants [65,115e117]. PCMs and energy storage
surface of heat transfer, and iii) suitable enclosure compatible with systems are among the things that have become increasingly
of PCMs. The implementation of energy storage systems is often not important in recent years in energy management in buildings.
economically feasible due to their more complex performance than Storing the energy during unnecessary hours in walls and using
conventional HVAC systems, as well as the need to use specialized them during peak hours is a promising approach. The sun, as an
and skilled personnel in the design and installation process endless source, is of great importance in the field of renewable
[109e112]. Thus, the use of these systems in energy evaluation of energies. The most suitable areas to use this energy are near the
buildings is considered when the following conditions are met in equator, where solar energy is the highest. Due to the great climate
the building: the calculated maximum thermal loads are signifi- change in the world, the use of these systems can greatly save
cantly greater than its averaged value. The building locates in a energy, reduce pollution caused by fossil fuels and decline heating
place with high-temperature differences during a day. This is
Fig. 9. Temperature range of PCMs and their thermal conductivity [106,107].
costs. On the other hand, as most desert regions have high- is defined by the world energy agency as a device, something like a
temperature differences during the day and night, this type of thermal battery, to store thermal energy in a tank for demand in
storage system can be used to absorb cooling energy in buildings another time for heating and cooling or power generation. Half of
and reduce electricity consumption [118e123]. In Fig. 11 a, b, ap- the accumulated energy is consumed as thermal energy. Since heat
plications of PCMs in a cooling system and a building wall, demand may vary throughout the day and from day to day, energy
respectively. storage is used to balance energy demand during the day, week and
The PCMs used in the heat storage scheme must have appro- even a season. Energy storage has a vital effect on reducing the peak
priate chemical, kinetic and thermophysical properties, as illus- of greenhouse gas emissions and has the potential to increase the
trated in Fig. 12. efficiency of energy systems, either. Energy storages are especially
Considering the investigations and properties of PCMs (Fig. 13), useful for power and heat production in-home applications. Figs. 20
the use of organic PCMs is the most commonly used [83,84,88,123]. and 21 illustrate the use of thermal storage for home heating
PCMs can be used in the three forms of raw material, micro, and [138,139]. According to these applications, the storage must have
macro. Since the application of these materials as raw materials can the following properties [140,141] high ratio of volume to cost, high
have disadvantages depending on PCM types and also due to their ratio of absorption to rejection capacity, durability and long life.
probability to flow in the liquid phase, the enclosures are required The results dealing with the application of using PCMs in ther-
for keeping them in the liquid phase (Figs. 14 and 15). Therefore, mal storages shows that energy consumption declines in some
they are usually used as packages of both micro and macro types in cases, even up to 22%, especially during peak hours of energy
different industries [85e87,126]. consumption. The benefits of using these materials in buildings can
To produce both micro and macro types, the PCMs are be related to the increased thermal comfort of residents following
embedded in the enclosures and encapsulated. Hence, the major the reduction of temperature fluctuations. Also, another advantage
difference between the two microcapsules and microcapsules is the of using this method is the reduction of severe temperature fluc-
size of the enclosures or capsules used. In the microcapsule tuations in sensitive cases such as the temperature of greenhouses,
method, the material is embedded in tiny spheres with a diameter solar heaters, and dryers which can affect the desired quality of the
of 1e30 mm. In the microcapsule method (Figs. 16e18), materials finished product [147,148].
are embedded in larger containers in envelopes or containers of
different materials. Most of these containers are made of plastic
bags as well as high-density polyethylene hard panels [128e133]. 7. Design of thermal energy storage
It is easily understood that the liquid-solid phase change

6. Solar energy storage using PCMs problems are more relevant than the liquid-gas and solid-gas phase
changes because they have a higher thermal density. Figure (22)
Along with the growing development of solar power plants, illustrates the preparation stages of the PCMs according to the
thermal systems such as receivers, collectors, and thermal energy work of Qian et al. [123].
storage have developed. Thermal systems are an important part of However, several parameters must be considered by designers.
solar power plants. Fig. 19 shows the components used in a solar In addition to technical features, as shown in Fig. 23, the pro-
power plant and energy storage [136,137]. Thermal energy storage ductions must be affordable, environmental issues should be taken
Fig. 10. The performance of PCMs [108].
into account, also thermal properties such as sensible and latent process such as melting-freezing or distillation-evaporation
heat capacities have an essential impact on the size reduction and [158e164].
efficiency improvement. The heat transfer rate must be as much as Cryogenic energy storage systems are often divided into two
possible to meet the thermal requirements during the absorption categories: full and partial capacity storages. In the former case, the
and rejection cycles [150e153]. On the other hand, the materials of total required cold load is transferred to the non-peak time period
the storage must be chemically and mechanically stable against during peak consumption. In other words, during non-peak hours
successive thermal cycles. Also, the storage must be compatible in which the demand cost decreases, chillers operate at full capacity
with the operating fluid [154e156]. and store the cooling energy generated inside the system in the
The constituent materials of the storage are different because freezing process. During the day and during the time when elec-
the storage method is sensible, latent, and chemical. Sensible heat tricity consumption is maximized and the cost of demand is high,
is the heat that causes temperature changes in the material. In the cooling generating system is switched off and the total cooling
thermal energy storage due to sensible heat, adding or removing load required by the system is obtained by melting the phase
energy from the energy storage material leads to an increase or change materials. It is mostly used when the peak period of con-
decrease in its temperature. Thermal energy storage due to sumption of the electricity distribution network is short or the cost
chemical reaction is another optimal method for storing thermal of electricity consumption at peak times is high [165e169]. It
energy using the heat generated by chemical reactions. Thermal should be noted that this system is also capable of providing
energy Storage due to latent heat includes the addition (or rejec- cooling of the space when emergency power is cut off (Fig. 24).
tion) of thermal energy as latent heat to (or from) the body. As a In partial capacity storage systems, the chiller provides part of
result, the process of phase change occurs in the material. One of the maximum cold load required by the system and the rest is
the features of this storage method is the ability to store energy in a provided by the energy storage system. These types of systems can
volume much lower than the energy storage method due to sen- be implemented in both constant and variable load methods. In the
sible heat, which can be considered the most suitable method of first method, the chiller operates at full capacity for 24 h a day. In
energy storage if the space is limited and the system weight is this case, if the load is greater than the capacity of the chiller, the
maximum. PCMs used as latent storage in heating systems can overload will be provided by storage systems. When the required
absorb or release large amounts of heat during the phase change cooling load is low, the excess cooling generated by chiller is sent to
Fig. 11. a) Application of PCMs in a cooling system and b) their application in a building wall [28,124,125].
storage systems to be stored. In this type of system, the capacity of used in predictions. Nevertheless, all of these researches are
the chiller and the storage system is minimum (Fig. 25). In the restricted to particle suspensions in micro and millimeter di-
second method, the energy storage system provides most of the mensions, and such suspensions result in the following drawbacks
required cooling load. The chiller operates with full capacity during [184e187]: The fast particles settle, making layers on surfaces, and
non-peak hours and the cold produced is stored in the energy decreasing the capacity of heat transfer. Sedimentation decreases
storage system. The partial capacity system is drawn in Fig. 26, as a response to a rise of chaotic fluid motion but corrosion of heat
schematically [141]. transfer devices, pipes, etc. rises speedily. The tendency for clogging
increases along the channel flow path with the particle size. The
8. Nanoparticles and heat transfer enhancement pressure drop in the fluid augments substantially. Therefore, the
path of particle formation in the fluid was well defined but not
Evaluation of the thermal properties of cooling liquids shows generally acceptable for heat transfer applications [188e192]. New
poor heat conductivity (except for liquid metals, which are not material technology has developed the chance to create nano-sized
useable in most temperature ranges). For example, the thermal particles that are completely different in optical, electrical, thermal
conductivity of water is about 30% of copper. It is clear that all and mechanical properties.
works to enhance heat transfer by turbulence, surface enhance- Choi et al. [193] introduced the idea of dispersing nano-sized
ment, etc. are limited by natural limitations of thermal conductivity particles into a liquid. To increase the heat transfer, the re-
[172e174]. It is more than a century that the use of suspended searchers added nanoparticles (particles smaller than 100 nm) to
solids mixtures has been proposed for the thermal conductivity the fluid. This augmentation technique has previously been used
enhancement. Maxwell [175] was the founder of establishing the- with fluid-suspended microparticles to increase heat transfer in
ories in predicting the thermal conductivity of suspended mixtures. micro- and milli-channels. The surface-to-volume ratio of nano-
His attempts were followed up by many empirical studies and particles is 1000 times larger than micro-particles and can transfer
theories such as the works of Zhou [176], Xuan [177], Lee [178], and heat greatly more efficiently. Choi et al. [193] showed that the
Das [179]. Further models presented in Refs. [180e183] were also addition of nano-additives to the common fluids could double the
Fig. 12. Chemical, kinetic and thermophysical properties of PCMs [92e96].
boundary conditions and the presence of SWCNT in the enclosure.

Three different conditions (cold, hot and adiabatic) were used at the
walls. This phenomenon is governed by nonlinear partial differ-
ential equations including continuity, momentum, and energy. The
numerical solution method was the FEM to study the influences of
cylinder conditions (hot, cold and adiabatic), heated zone length
(A LH B), Rayleigh number (104Ra108), nanofluid concen-
tration (0 ¼ ɸ0.2), and the magnetization value (0 ¼ M 500) on
the flow rate, and temperature distribution. The results showed
that as the Ra and ɸ increase, this amount of heat transfer rate in-
creases. Also, the thermal distribution increases as ɸ increases. In
contrast, thermal distribution does not change with the
magnetization.
When particles are dispersed properly, these nanofluid proper-
ties are predictable to have the following advantages.
i) Greater thermal conductivity: The nanoparticles higher surface
area causes more heat transfer. 20% of nanoparticle atoms are on
Fig. 13. Applications of PCMs.
their surface for those smaller than 20 nm. This specification makes
them accessible for heat exchange at any time. One more benefit is
the mobility of the nanoparticles due to their small size, which can
heat transfer rate of those fluids due to the higher thermal con- create micro-displacements and thus increase heat transfer
ductivity of these particles. What makes the nanoparticles attrac- [195e202].
tive as a potential candidate for making a mixture of particles with ii) Stability: Since the particles are small, they have low weight,
fluids is providing a large area for heat transfer, the momentum of leading to a small tendency for settling. This reduction in sedi-
the particles is low, and they have high mobility. mentation overcomes one of the major weaknesses of suspended
Haq et al. [194] investigated thermal management in single- mixtures (particle deposition) and makes nanofluids more stable
walled carbon nanotubes (SWCNTs)/water nanofluid (Fig. 27). In [203e206].
this study, thermal conductivity was improved by heating iii) Micro-channel cooling without blockage: nanofluids are also
Fig. 14. Types of stabilizing materials in PCMs applications [127].
Fig. 15. PCMs application methods [28].
suitable for working in microchannel where they are exposed to toluene provide different nanofluids [212e214].
great heat loads. The grouping of nanofluids and microchannels Although conventional PCMs are usually high in density, their
provides both high conductivity fluid and high heat transfer rate. low melting, and freezing rates reduce the potential of energy
Nanoparticles are much smaller than microchannels and do not storage systems in specific applications. This is because almost all
cause clogging [207e209]. conventional PCMs have low thermal conductivity, although their
iv) Reduced corrosion probability: the size of the nanoparticles is values are increased by the use of high conductivity materials in
very small and consequently their momentum effect on solid walls various methods [215e219]. These methods are.
is very low, resulting in a reduction in the corrosion of pipelines,
heat exchangers and pumps, to name a few [210,211]. i) the saturation/distribution of high thermal conductivity
The nanoparticles are classified into three categories of ce- porous materials/particles within PCMs,
ramics, pure metals, and carbon nanotubes, which will be discussed ii) embedding metal compounds and structures in PCMs, and
in more details. The various combinations of these nanoparticles iii) using low-density high conductivity materials.
and the base fluids including water, ethylene glycol, oils, and
Fig. 16. Synthesis of enhanced and multifunctional microencapsulated and nano encapsulated PCMs [134].
Fig. 17. Schematic summary of future trends in PCMs [135].
Although the use of graphite composite in PCMs improves their weight of the system significantly. In addition, researchers showed
performance, some limitations have led researchers to look for that the compatibility with PCMs is not the intrinsic features for all
other solutions. These limitations correspond to the production metals. For instance, nickel is not compatible with paraffin, while
process of graphite composites which is time-consuming and aluminum particles are. These issues have led researchers to seek
costly. Therefore, some researchers have been looking for a solution for high thermal conductivity, low-density materials which are
to this problem in recent years. They found that by adding high- broadly compatible [220e227].
conductive particles with micro- and nano-scale to the PCM, its Since carbon fiber density is lower than that of metals and its
thermodynamic properties are enhanced, leading to an increase in thermal conductivity is approximately equivalent to that of copper
system efficiency. The embedded metal structure in the PCMs has and aluminum, its use is promising to increase the efficiency of
been proposed as a technique to increase its thermal conductivity. energy storage systems. In addition, carbon fiber has corrosion
In this technique, a metal sphere or a cylindrical tube (or other resistance and is therefore compatible with most PCMs. It is
shapes) is used and placed in the PCM enclosure, which dramati- important to consider the uniform distribution of carbon fiber
cally reduces the phase change time, as a consequence, its effi- particles. Studies showed that systems in which carbon fiber par-
ciency is increased (Fig. 28). High-density metal particles and ticles are uniformly distributed in the PCM exhibit much more ef-
compounds may sediment in the system and also increase the ficiency than that they are distributed randomly and non-
Fig. 18. Various chemical polymerization methods for encapsulating phase change materials: a) suspension, b) dispersion, c) emulsion, d) mini-emulsion, e) in situ polymerization,
and f) interfacial polymerization results in EPCM [56].
uniformly. Previous studies demonstrated that nanoparticles are many other fields in various industries, including aerospace, elec-
most commonly used in paraffin PCMs [228e234]. tronics, medicine, materials, metal coatings, etc. One of the most
important applications is to add nanoparticles to the PCMs
(Figs. 29e31).
9. Nano PCMs
The most important advantage of nanoparticles is improving the 10. Melting and freezing of PCMs
thermal properties provided by the large value of the surface-to-
volume ratio. The reason for this is the increase of heat transfer Since PCMs are mostly used as energy sources, lots of researches
surface and the collision of nanoparticles with their environment. has been conducted to simulate the melting and freezing in
Therefore, numerous researchers are examined the new properties different geometries including rectangular, circular, and spherical.
of nanoparticles in different environments experimentally. One of Rectangular enclosures are widely used because of their simpler
these investigations is nanofluid preparation, which numerous boundary conditions (Fig. 32).
researchers have examined the properties of nanofluids [235].
These properties are viscosity [236e238], thermal conductivity 10.1. Melting and freezing models
[239,240], density, specific heat, etc. [241]. Nanofluids have many
applications in various industries, especially in the heat exchangers During the melting process, the solid material chronologically
[184,242], solar industries [185], refrigeration [243], etc. Another changes its phase to semi-solid, mushy and then to liquid. During
application of nanoparticles is in the field of medicine and drug the freezing process, the reverse trend occurs. Therefore, six steps
delivery [244,245]. Nano drug delivery is the subject of many are required to complete the thermal process. At each particular
medical researchers [246,247]. Nanoparticles are widely used in stage, heat transfer occurs as convection and conduction [251]. In
Fig. 19. Equipment of solar power plant and thermal energy storage [142,143].
this case, predicting the spatial motion of the melting front over great deal of time and expense, ii) the dimensions of the laboratory
time because it is nonlinear and moving; moreover, the heat equipment should be appropriately selected according to the type
transfer involves free convection and conduction. Because of these of experiment. On the other hand, the space in which the equip-
three factors, the governing equations at the interface are ment is located should also be selected according to these di-
nonlinear. Thus, there is an exact solution to some problems. mensions, iii) the equipment needed must be properly assembled,
Alexiades [252] showed that there are many physical phenomena iv) appropriate environmental variables should be considered to
that occur during phase change, including the changes in the spe- simulate actual conditions, v) variation of variables must be accu-
cific heat, volume, thermal conductivity, density, and over-cooling, rately measured by calibrated devices. Further explanation of the
which should be considered in the study of phase change using analytical and numerical methods is presented.
mathematical models. Due to the complexity of the subject, various
methods have been proposed over the years to model and predict
the melting and freezing phase change process. An overview of 10.2. Stefan method
these methods is presented here.
Experimental methods are more accurate to exhibit the actual Stefan method is one of the first and simplest analytical
behavior of the phase change phenomena than numerical studies methods to solve the melting and freezing phase change problems.
since the behavior of the phase change phenomena is examined In this case, heat transfer is considered only in the liquid phase and
directly by observation with no assumptions. However, in many the solid phase remains constant at the melting temperature. The
areas such as large-scale and unsteady environments, experimental melting and freezing rates in a semi-infinite area can be evaluated
methods cannot be used. The properties of the experimental by Stefan number, which is dimensionless and expressed as follows
methods can be categorized as follows [252]: i) they consume a [254,255].
Fig. 20. Schematic of a solar collector and the use of PCMs in them [144,145].
and the liquid density, respectively. It should be noted that the

cðTh Tm Þ relation T0> Tm > Ts is established between the wall, initial, and
Ste ¼ (1)
hl melting temperatures. xt represents the position of the melting
line. Fig. 33 illustrates the two-phase Stefan problem.
where hl and c denote the latent heat of the phase change and the The analytical solution of this problem is obtained by using the
specific heat of the liquid, respectively. Moreover, Th and Tm are the similarity function h.
hot and the melting temperatures, respectively. Most of the solu-
tions presented by Stefan method are one-dimensional with simple x
h ¼ ptffiffiffiffiffi (4)
boundary and initial conditions. 2 al
xt , the position of the melting line is obtained using relation (5):
10.3. The neumann method
pffiffiffiffiffiffi
xt ¼ 2f al t (5)
The development of the Stefan method for two-phase state is
known as the Neumann method, which is much closer to the real f ; a are the thermal diffusion coefficient and the liquid volume
state. In the Neumann method, the material is presumed to be solid fraction in the control volume. The liquid phase temperature (Tl)
with the initial temperature very different from the melting tem- and solid (Ts) are obtained using the following equations:
perature, at first. Assuming constant the thermophysical properties, . pffiffiffiffiffi
the Neumann problem is formulated as follows [256,257]. erf x 2 al t
Tðx; tÞ ¼ Tl þ ðTl Tm Þ (6)
erfcðlÞ
vT v2 T
r cp ¼ k 2 (2)
vt vx . pffiffiffiffiffi
erf x 2 as t
This relationship, actually, represents the energy equation Tðx; tÞ ¼ Ts þ ðTm Ts Þ pffiffiffiffiffiffiffiffiffiffiffi (7)
assuming one-dimensional conductivity. To find the melting line, erfc l al =as
the heat flux between liquid and the interface must be calculated.
Simultaneously, the latent heat is absorbed by the PCM and the l is obtained as follows:
position of the liquid-solid boundary is determined using the en- pffiffiffiffiffi
ergy conservation equation: Stel Stes as pffiffiffi
2 qffiffiffiffiffiffiffiffiffiffiffi
ffi pffiffiffiffiffiffiffiffiffiffiffi ¼ l p (8)
erfc l erf ðlÞ a l2 as erfc l a =as
vxt vT vTs l l
r hm ¼ kl l þ ks (3)
vt vx vx
where Ste is the Stefan number. Despite the accuracy of this solu-
where hl and r are the latent heat of the substance phase change tion, this problem is applicable to model the moving boundary
Fig. 21. Thermal storage for home heating [146].
Fig. 22. Schematic of the overall preparation of a) MS, b) PCM & MS stabilized composite [149].
conditions in the Cartesian coordinate framework and assuming calculate the temperature by using FDM for derivatives. At each
only conductive heat transfer [258]. time step, as shown in Fig. 34, the moving boundary is set between
two neighboring points of the grid, for example between mDx and
(mþ1)Dx (at position fDx, 0 > f > 1.0).
10.4. Fixed grid method The numerical solution of melting ice is a simple example of
fixed grid method. The temperature at the upper point is obtained
This technique is capable to use the standard solution process using the temperature of neighbors as follows:
for energy equations and is suitable for multi-dimensional prob-
lems. In this method, the heat transfer equation is solved to
Fig. 23. General selection characteristics of PCMs for the purpose of storing energy [157].
Fig. 26. A thermal storage system with partial capacity: variable load [170,171].
Fig. 24. Full capacity energy storage system [170,171].

Dt
Ti;jþ1 ¼ Ti;j þ Ti1;j 2Ti;j þ Tiþ1;j ; i ¼ 0; 1; …m 1
Dx2
(9)
Hence, the temperature at the points x ¼ mDx is calculated as
follows:

2Dt 1 1
Tm;nþ1 ¼ Tm;n þ T Tm;n (10)
Dx2 fnþ1 m1;n fn
The position of interface between two phases is computed as
follows:

Dt εn 1
εnþ1 ¼ εn T Tm;n (11)
Dx2 fnþ1 m1;n fn
The enthalpy and the effective heat capacity methods are two
approaches based on the fixed grid method. Nevertheless, fixed
grid method sometimes does not work optimally, especially when
the interface at a time step leaps over more than one grids.
Fig. 25. A thermal storage system with partial capacity: constant load [170,171].
10.5. The enthalpy method
In this method, enthalpy is considered as the temperature-

Fig. 27. Schematic of the geometry considered by Haq et al. [194].
does not need to explicitly examine the phase change boundary

[260].
The basic enthalpy approach can be explained as a conduction-
controlled transition in one-dimensional. The conservation energy
is stated using enthalpy and total volume temperature in the phase-
change procedure, through which a continuous function is ob-
tained. Fig. 35 shows the temperatureeenthalpy diagram for the
isothermal and non-isothermal phase change.
The energy conservation equation using temperature and
enthalpy is as follows:
vh
r ¼ VðkVTÞ (12)
vt
Fig. 28. Application percentage of PCMs.
where h is the specific enthalpy expressed by the sensible and
latent enthalpies:
dependent factor. Using the enthalpy method, a two-phase region

called mushy region is considered, which avoids the severe hðTÞ ¼ DhðTÞ þ hm f (13)
discontinuity due to numerical instability. This method was re- According to the above relation, it constituents of sensible and
ported that is consistent with the practical problems because it latent heat of the substance in terms of the melt fraction f. The
Fig. 29. An example of the preparation of PCMs and the rate of increase in thermal conductivity coefficient [248].
Fig. 30. Thermal performance enhancement of PCMs employing carbon nanotubes and graphene as additives of lithium-ion batteries [249].
referred to as the porous enthalpy method because it assumes that

each grid is a solid and liquid porous medium. Due to the use of the
enthalpy method in this research, more details are presented in the
next sections.
10.6. Effective heat capacity method (energy-based method)
The latent heat is obtained by the difference between the

melting and freezing temperatures. A direct relation between the
heat capacity and the energy augmentation/rejection of PCMs ex-
Fig. 31. Application of PCM in PVT cooling [250]. ists, while an inverse relationship exists with the temperature
difference. This proportion is given by the following relation:
sensible heat is obtained from relation (14): hl

ceff ¼ þ cs (17)
T2 T1
ðT
Dh ¼ cdT (14) where T1 and T2 are respectively the melting or freezing tempera-
ture and the temperature at which the material is completely
Tm
frozen or melted.
The melt fraction is: This method in simulating phase change problems cannot
8 accurately predict conditions when the temperature difference is
< 0 T < Ts solid low or the temperature is constant. Bonacina et al. [261] presented
f¼ ð0; 1Þ Ts < T < Tm mushy (15) a one-dimensional model to increase the precision of the heat ca-
:
1 T > Tm liquid pacity method. Using heat capacity method, a multi-dimensional
numerical solution was proposed by Rabin and Korin [262]. As
On the other hand, by integrating the energy equation and total
can be seen from Fig. 36, there are considerable numerical simu-
enthalpy, the following alternative relation is obtained for the one-
lations of phase change materials. By examining the above
dimensional heat transfer during phase-change process [58,222]:
methods, it was concluded that the enthalpy method has been of
much interest to researchers [263] (Fig. 37).
vDh v vDh vf
¼ a rl f (16)
vt vx vx vt
11. Melting and freezing of PCMs and nano PCMs
The last right-hand side term of equation (16) shows the change
in volume fraction versus the time. By placing the enthalpy value of The first studies on rectangular geometry were performed in
relation (13) in equation (16), the melting line location is obtained 1975 and 1976 by Shamsundar and Sparrow [264e266] through the
so that wherever there is a volume fraction between zero and one, use of FDM. Hamdan and Elwerr [267] proposed a model for
the melt line is located. The enthalpy method is also sometimes studying the melting process in a cavity. The melting rate was
Fig. 32. Different methods for investigating PCMs [253].
Fig. 34. Phase change line position concerning fixed grid [259].
contact melting of PCMs in a square cavity containing free con-

vection. The results of this numerical study showed that the melt
volume at the bottom of the cavity is greater than that of the case in
which pure conduction is dominant. Free convection effect has
Fig. 33. Stefan problem for two-phase state [256].
been studied by Lamberg and Siren [269] to analytically discover
how the melting front behaves in a semi-infinite PCM cavity with
the presence of fins. This analytical model involves the solution of
largely dependent on thermal diffusion, adhesion, thermal con- the Neumann equation, in a pure conduction problem. They also
ductivity, specific heat, and latent heat. Using the energy balance, estimated the location of the melting zone using the exact solution
Lacroix [268] provided a mathematical model to investigate the of the Newman equation. A similar study was performed by
engulfed by hot water was studied by Regin et al. [272] to capture

the melting front of paraffin capsules. The melting process was
higher in the upper part of the cylinder than in the lower part of the
cylinder. Also, free convection has a deep influence on the coinci-
dence of the numerical and experimental results. The PCM-filled
cylinder with heated-sidewall, shown in Fig. 38, was studied by
Jones et al. [273]experimentally and numerically. Their results
indicated that the melting layer along the vertical direction uni-
formly varies in the early stages. The thickness of the melting layer
changes with time similar to the rectangular enclosure. This in-
dicates the dominance of natural convection.
Melting of paraffin in a cylinder was studied by Akgün et al.
[274]. They observed that the melted PCM expanded radially out-
ward and forms a conical shape. Bahrami [275] performed exper-
imental studies on PCM melting in a sphere. The dome shape of the
solid-liquid intermediate plate with higher at the top persists
during melting process. Also, the solid PCM moves downward due
to its higher density than liquid PCM and settled down to the
bottom of the spherical cavity. Akhilesh et al. [276] numerically
Fig. 35. Relationship between enthalpy and temperature during the phase change
studied melting in a rectangular enclosure with a heated upper wall
[260].
(Fig. 39). This analysis involved examining the number of fins per
unit length, leading to a rise in heat transfer and energy storage.
They found that attaching more fins could not increase thermal
efficiency significantly.
Gharebaghi and Sezai [277] investigated the efficiency of rect-
angular cavities with the presence of horizontal and vertical fins. In
both cases, the heated wall was kept at a fixed temperature above
the PCM melting temperature. The heat transfer rate is raised by
attaching fins horizontally for the differentially heated sidewalls.
Moreover, raising the distance between fins rises the heat transfer
rate. It was also found that increasing the number of fins more than
a certain amount results in a slight increase in the heat transfer.
Declining the buoyancy effect, leading to the dominance of the
conduction heat transfer mechanism. The phase change of a fin-
attached enclosure shown in Fig. 40 has been studied by Lacroix
and Benmadda [278]. This study investigated the effect of the
Fig. 36. Percentage of studies in terms of experimental and numerical performed for
the modeling of phase change.
number and length of fins on PCM melting rate. For short fins, the
melting rate depended on the number of fins. They found that the
melt front passing through the fins is almost similar to the case
without fins. On the flip side, melting rate constantly increased
with the fins number. The results also showed that at high
Fig. 37. Percentage of numerical studies implementing various modeling of phase

change.
Lamberg et al. [270] in the presence and absence of free convection

and a comparison was made against experiments. The results
showed that ignoring the natural convection effect doubled the
time of the maximum temperature. The spatio-temporal variation
of the interface during the melting process in a rectangular cavity
has been obtained by Stritih [271] experimentally and compared
against analytical results. The results showed that analytical results
accurate just in the acute response. But, the difference between the
results increases considerably with the melting time. A cylinder
Fig. 38. Cylindrical enclosure dimensions and boundary conditions [273].
Fig. 39. (a) Schematic of the CHS design and (b) computational domain for numerical analysis [276].
melting process.
Latent Heat Thermal Energy Storage (LHTES) was proposed by
Deng et al. [282] with new positioning and shape of fins. These fins
were tested in the lower half of the cavity and mirror positions
relative to the centerline of the tube. An unsteady 2D numerical test
was performed on the Luric acid melting process as PCM. The pair
fins were used in the experimental test at the angles of 0 , 30 , 60 ,
90 , 120 , 150 , and 180 . The results showed that at angles of
30 e120 are optimal to achieve complete melting time. Increasing
the inclination angle, up to 120 , increases the heat transfer rate. In
addition, it was found that by increasing the fin length, the LHTES
role could be significantly improved rather than the base state. As
the melting process continues, natural heat transfer dominates.
This factor is such that a hole is created in the shell of the cavity.
Two fins in the down hemisphere with an angle of 120 led to
maximum natural heat transfer. It increases by increasing the fin
length.
Blade embedding is an effective method to enhance heat
transfer between PCM and heat transfer fluid (HTF). A proper
Fig. 40. Rectangular cavity with horizontal fins embedded on the heated vertical walls arrangement of blades can play an important role in LHTES. Deng
[278]. et al. [283] defined a two-dimensional model based on finite vol-
ume method (FVM) concerning natural heat transfer and found the
effective order in the arrangement of the fins used in the design for
temperature difference, raising the fins number raises the heat
charge rate in LHTES. They compared the results with experimental
transfer rate. They revealed that the optimal number of fins is also
data (Fig. 41). First, the heat transfer characteristics of the LHTES
affected by the temperature of the hot wall. The research has been
unit were investigated by arranging different fins. These models
developed by Lamberg et al. [270] and Lamberg [279] to compare
include non-fin pair of tubes, pair of tubes with straight fins, pair of
three configurations of no fin, single fin, and twin fin. These studies
tubes with angular fins, pair of tubes with fins in lower hemisphere,
revealed that the heat transfer rate of the twin fin configuration is
and pair of tubes with fins in upper hemisphere. Then, the effect of
higher than a single fin, followed by the no fin system.
the number of blades (N), dimensionless fin length (L), heat transfer
Fin thickness was studied by Shatikian et al. [280,281]. For the
fluid temperature (Tw) and outer tube materials on the melting and
same sizes of rectangular cavities, the melting rate of the thicker
fusion were studied for four models. Then, the best type of fin
case is slower than the thinner ones. Also, in thicker cavities, the
arrangement was proposed to increase thermal efficiency.
fluid movement becomes more with the melting process time. On
Increasing the capability of the LHTES unit by applying the position
the other hand, in thin cavities, the fluid moves slowly in the
Fig. 41. Physical configurations of all cases: (a) no fins, (b) straight fins, (c) angled fins, (d) lower fins, and (e) upper fins [244].
of the fins quantitatively based on the full melting time and heat metal foams combined with paraffin and other materials to make
storage capacity was described and the following results were ob- composite materials to determine effective heat transfer and
tained: The number of optimal fins is N 6. When angular fins are thermophysical properties. A WeP model was used for the simu-
used N > 6. For N ¼ 6 only the length of the fins (L) can change the lation of melting foam at a constant temperature using a combi-
optimal value. In the case of angular fins, the optimal value of L is nation of 6 types of tetradecahedron and two types of irregular
0.5 and 0.95. At L ¼ 0.75, the optimal value is minimum. In the first dodecahedron. It was reported that the thermophysical properties
40 s of the melting process, it was observed that the melting pro- of the metal foam and the PCM have a profound effect on the heat
cess is due to the natural heat transfer. Finally, Deng et al. [283] transfer of PCM composites when the porosity size has no consid-
studies the role of natural convective heat transfer in PCM melting erable effect. The effective heat transfer of the PCM composite in-
by defining different models of the fins’ arrangement immersed in creases with the increase in heat transfer of the metal foam, which
lauric acid. Based on the experimental data and simulation results, becomes more and more in its lower porosity. The effective thermal
it is concluded that the area with the least volume fraction of melt conductivity of PCM composites depends on the ratio of the metal
can be moved and the melting time of PCM can be changed conductivity to the conductivity of PCM. The melting front is highly
depending on the position of the fins in the enclosure. However, affected by the metal foam microstructure and most of the heat
comparing the finned and unfinned models, it is concluded that the transfer occurs in the liquid phase. While the porous structure is
charge rate in the unfinned model is higher than that of the finned influenced by conduction rather than convection such that the
ones due to the maximum melting time of PCM and thus trapping thermal conductivity and the temperature are the most effective
more heat energy due to natural convection heat transfer. factors. The growth of the fluid phase varies non-linearly over time.
Poran and Ahmed [284]performed a two-dimensional model of The melting rate is very high in later stages but gradually decreases
PCM melting in the enclosure using ANSYS software. Seven with time. In other words, the natural heat transfer is suppressed
different shapes of cavity and heat source were tested and a well and conductive heat transfer is raised by increasing the percentage
agreement was reported against experiments. The results showed of porous materials in the composite.
that heat source shape has a deep effect on the PCM melting pro- Bondareva and Sheremet [288] simulated this process numeri-
cess than the enclosure shape. It was then observed that the cir- cally. In this study, the two opposite walls had low heat transfer and
cular heat source improves the PCM melting process under the other walls were insulated with the bottom-attached heater.
adiabatic boundary condition. The melting efficiency of the circular The governing equations were formulated non-dimensionally. The
source in the circular enclosure increases from 60% to 97%. So, if the finite difference method was used. The distribution of velocity and
heat source is covered by the PCM with the desired melting point temperature for different values of Ra and dimensionless time led
may be useful in the process of heat rejection in electronic ma- to the understanding of flow patterns and heat transfer within the
chines or other devices. enclosure. It was observed that for the average values of the Ray-
Bouhal et al. [285] investigated two-dimensional numerical leigh number, single thermal plume can be considered. For high
analysis of solid gallium melts on porosity-enthalpy formulation to values of Rayleigh number, double thermal plume is observed. The
optimize the mold geometry (Fig. 42). The effects of geometry on evolution of the phase-change process is a function of the mode of
PCM melting were investigated. Two designs were proposed, sim- thermal plume and heating not only vertically but also horizontally.
ple design and the one with 4 fins, which reduced the melting time At high values of the Rayleigh number, rapid asymmetric devel-
from 18.35 to 13.35 min. In other words, the fins improve heat opment was observed. In the two-dimensional enclosure model,
transfer and melting time. the process of melting was carried out rapidly, while the cooling of
Pourakabar and Darzi [286] studied the melting of PCMs in the material is a characteristic of the cubic cavities.
enclosures with different inner tube arrangements. Nine different The natural heat transfer of paraffin melt in a cubic and rect-
cavities were examined. Their temperature was assumed to be angular cavity with a local heat source located on its bottom was
constant and their walls were adiabatic. It was found that in early studied by Bondareva and Sheremet [289] numerically. The gov-
times, conduction heat transfer is the dominant mechanism. Then, erning equations were formulated in non-dimensional form. The
the natural convection increases the melting process, especially the potential-vortex equations and the flow-vortex equation have been
upper part is more affected. The lowest and the highest melting solved through the use of the FDM for three- and two-dimensional
rates are associated with the dual tube and the single tube con- simulations, respectively. Comparison between two- and three-
figurations. Also, the fastest and the slowest freezing times are dimensional cases showed that the occurrence of melting is diffi-
allocated with the diamond arrangement and the dual-tube cult in the early stages in the two-dimensional model. However, it
configuration. Injecting copper foam into the PCM acts as a cata- changes with time. The melting process is more concentrated in the
lyzer. It was reported that the temperature of the PCM varies slower 3D model but in weaker heat transfer compared to the 2D model.
than the metal foam. In addition, injecting metal foams almost Different boundary conditions of the heat source have been
doubled the melting and freezing rates. studied by Kant et al. [290] numerically. Firstly, a constant heat flux
Wang et al. [287] used a square cube cavity and studied various between 500 and 500 W/m2 is considered, and secondly, a
Fig. 42. Physical modeling of cylindrical heat sources and the ones with fins [285].
sinusoidal function, similar to the previous one, were used for mechanism. As displayed, the natural convention at the top of the
cooling and heating the PCM wall of the cavity. The results showed cavity is greater than that at the bottom of the enclosure. It was also
that the sinusoidal function performs better than the constant observed that f and m of NEPCM are in a direct relationship, which
function in PCM melting and the melting time is less than the is one of the negative effects of natural heat transfer. It was also
freezing time. found from diagram I that the PCM full melting time decreases by
Further types of boundary conditions in the square TES cavity, 29% and 34% by reducing the porosity from 1 to 0.95 and 0.9,
shown in Fig. 43, has been studied by Satbhai et al. [291]. The respectively. However, from diagram II it can be seen that the
simulations performed by solving governing equations using PISO complete melting time of the PCM with the porosity of 0.95 is
algorithm over unstructured computational cells. This was done delayed in comparison to the pure PCM, which is originated from
using the porous enthalpy model. In the bottom-heated cavity, the weakness of vortices in the porous PCM.
maximum Nusselt number and little change in total entropy gen- Zhao et al. [292] carried out a three-dimensional numerical
eration were reported compared to the other two models (left- and study of PCM melting in a cubic enclosure. An enthalpy-based
top-heated models). The top-heated model had the highest melting incompressible Thermal Lattice Boltzmann method (iTLBM) was
time compared to the other two models and the bottom-heated applied for different heater positions. The results showed that the
model had the highest Nusselt number (3.14). It was 13.47% and melting rate is profoundly affected by the heater size and its heat
36.14% for left- and upper heated surface, respectively. It was found flux strength. Moving the heat flux from the two sides toward the
that the melting time in the upper heated wall model is about twice center increases the heat flux rate and thus the melting rate. The
(FO ¼ 35.25) compared to other two models. A comparison of the change of the location of the heat source from the top to the bottom
three models in the mean entropy value showed that the bottom- of the enclosure was found that has an increasing impact on ther-
heated model has the highest mean entropy value. This value was mal performance.
16.291 J/m3K. For up- and left-heated walls, a decrease of 0.6% and Their low heat transfer rates lead many efforts to increase the
0.08% was reported, respectively. The fastest melting with the capability of PCM melting processes. Meanwhile, the design of a
highest Nu number is associated with the bottom-heated model PCM cavity has also been employed to enhance natural heat
and this was the best case for energy storage considering the transfer. Li et al. [293] explained the two-dimensional PCM melting
Nusselt, Prandtl, Rayleigh numbers and entropy generation. Natural process in the walls of a semi-enclosure. They found that vertical
heat transfer was identified as a dominant heat transfer adiabatic walls facing the heated wall inversely affected the heat
Fig. 43. The geometry considered in Ref. [291].

transfer phenomenon. The walls are optimum as the melting flow is Using the enthalpy-based LBM, which provides the simplified
in front of them. The effect of other enclosure constraints including style of the algebraic velocity distribution function, phase change
the upper and lower walls was also studied. They found that the procedure was simulated by Jourabian et al. [299] with emphasis on
inclination of the top wall outward generally leads to the acceler- the free convection. Boltzmann’s function, f (x,c,t), denotes the
ation in the heat transfer and heat energy storage during the probability of a random particle being positioned at x at time t,
melting the PCM. But, bottom wall inclination has a little effect. In moving at the velocity c. This theory may be derived from older
this study, the Prandtl of 40, Stefan number of 0.33 and Rayleigh theories, including the theory of marker-and-cell and particle
number of zero (pure conductivity), 105 and 107 were used. The tracking. This study was carried out at Stefan number of 10, Ray-
bottom wall did not affect the upper region due to the buoyancy leigh number of 106, and at different inclination angles relative to
flow where the melting zone has a large effect. Therefore, it has the horizon (30 to þ30 ). Raising in the Rayleigh number results
little effect on PCM melting. Here, it is emphasized that the design in a rise in the melting rate for all inclination angles. In addition,
of the enclosure should be in a manner that is more in line with when the enclosure rotates counterclockwise, the convection effect
natural heat transfer, not vice versa. is higher and when it rotates clockwise, the effect of thermal con-
Cao et al. [294] investigated the temperature conditions of the ductivity on melting is higher.
enclosure by the deviation of the heat source relative to the center Zennouhi et al. [300] investigated the influence of the enclosure
of the horizontal enclosure experimentally and numerically. In this angle on melting (Fig. 44). They investigated the melting of gallium
study, the temperature variations in different locations of heat at different angles of the enclosure in two-dimensional simula-
source were measured and numerical model was investigated. By tions. They solved the natural convection while phase changing
increasing the amount of source deviation from the center, the occurs using the FVM and the porous enthalpy technique. Valida-
thermal performance and the melting rate increased. The ideal tion of the numerical model was performed by previous numerical
sample with the best thermal performance (e ¼ 30 mm) was found results. The results indicated that the melting rate increases by
to have a reduction of 57% in the PCM melting time. As the Reynolds declining the inclination angle from 90 to 0 .
number increases, natural heat transfer enhances, so the liquid Karami and Kamkari [301] investigated the effect of PCM
phase front moves faster. The Reynolds number and the ratio of buoyancy force due to the slope deflection on charge and discharge
out-of-center heat source have a direct effect on the melting rate. rates of heat source (Fig. 45). One and three fins in the rectangular
Vogel and Thess [295] investigated the melting process of enclosure from one side began to heat within the PCM material
octadecane attached symmetrically on both sides in TES systems under 0 to 180 . Luric acid was used as PCM material. Numerical
experimentally and numerically. The aim of this paper was to simulations under control volume operation were also investigated
evaluate the accuracy of the numerical melting model by experi- on properties such as phase field, flow field, temperature distri-
mental data. The numerical method that was used to calculate the bution, heat transfer rate, and TES for different configurations. The
fluid flow, temperature and phase area included two approaches: results showed that the melting time is declined with the natural
the first one uses variable thermophysical properties together with convection by increasing the deviation of the rectangular source.
the VOF method that is allowed to have air distance over the PCM to The maximum melting time decreases by 72% in the three-fin
consider its expansion. The second one uses Boussinesq approxi- enclosure and 0 compared to the no-fin enclosure. The results
mation and constant thermophysical properties, which are solved showed that the enclosure with one fin is less time consuming than
in two or three dimensions. Comparison of these two methods the one with three fins. Finally, the inclination angle was found that
showed about 4% downward deviation in the simulation results has a raising effect on Nu number.
compared to the experimental results in thermal flow rate, liquid Souayfane et al. [302] used the enthalpy method and studied the
phase fraction and the temperature, i.e. the value of the simulation phase changes to reveal the favorable impact of natural heat
results was lower than that of experimental ones. transfer on the thermal performance of PCM melting. In addition,
Attaching fins is another approach to increase the heat transfer short-wave radiation is also used as a heat source to solve the
and rate of phase change in the enclosures. The number and length defined algorithm in the two-dimensional FVM fashion. A numer-
of fins were studied by Lacroix and Benmadda [296]. It was showed ical platform has been developed for the melting simulation and
that a few long fins result in a higher melting rate than many short compared against the available experiments and numerical studies.
ones. Gharebaghi and Sezai [277] showed that vertical protrusions Then a simplified model was used to melt a type of fatty acid by a
increase the melting rate. Woon-Shing [297] investigated the combination of natural heat transfer and radiation. This hybrid
melting of paraffin and gallium PCMs in enclosures with different model was applied by the lattice Boltzmann-discrete ordinate
boundary conditions to provide a deep understanding of the phase method (LBM-DOM). The simplified suggested model is handy with
change and natural convection at large Rayleigh numbers were a higher simulation speed than the CFD and LBM-DOM models.
studied using the porous enthalpy method. The authors proposed Also, again approved that during the PCM melting process, natural
relationships for the Nusselt number and the melting volume heat transfer acts as a key parameter in raising the average liquid
fraction in terms of the dimensionless governing numbers such as fraction and progressive melting position. Finally, shortwave radi-
the Fourier and Stefan numbers. ation increases the average liquid fraction.
Using FVM and porous enthalpy approach, melting of gallium The effect of inclination angle on melting performance was
around a circular cylinder was numerically investigated by Mah- checked studied by Kamkari and Groulx [303]. The lauric acid
daoui et al. [298]. The results of flow and temperature fields during melting was investigated at 90 , 45 and 0 in various fins number.
melting time were presented along with the Nu number. Also, the Interface movement varies noticeably with the angle and defined
volume fraction of the liquid and rate of melting were measured the vortex strength such that it was made clear that raising the
with the time in various surface temperature and heat flux. The inclination angle improves either configuration with and without
results of this study highlighted the role of conductive and con- fins. The heat transfer enhancement in the horizontal enclosure
vection heat transfer in the melting process. Conduction mode was and the vertically-finned enclosure with 3 fins was compared with
found that plays a central role in heat transfer near the cylinder the no-fin vertical enclosure, i.e. this value was 115% and 56%,
wall and as the time increases, the convection heat transfer be- respectively. This behavior showed that an increase of inclination
comes stronger. In addition, the conduction mechanism is domi- angle can be used instead of using more fins in the PCM melting
nant under the cylinder. process in horizontal enclosures. The horizontal enclosure with
Fig. 44. Schematic of the problem studied by Zenouhi et al. [300].
Fig. 46. The geometry studied in Ref. [304].
highest porosity samples can be used to achieve the highest heat

transfer efficiency in this thermal storage unit. The point to note is
Fig. 45. Schematic of the problem used by Karami and Kamkari [301]. that as porosity increases, thermal storage capacity increases but
natural heat transfer decreases.
During PCM heat transfer in closed enclosures, natural heat
three fins was revealed that has the highest thermal conductivity
transfer and contact melting act as key factors in heat transfer
and thus the lowest melting time.
improvement. An improved Nusselt model for melting PCM melts
The instantaneous ice melting within a porous horizontal
in rectangular enclosures with different inclination angles was
enclosure made by nickel steel alloy with two vertical cylinders was
proposed by Zhao et al. [305]. This study was conducted for a 2D
studied by Jourabian et al. [304] (Fig. 46). In this paper, the
experimental model. The melting process of n-octadecane was
enthalpy-based LBM with dual distribution function on represen-
recorded for square enclosures at different angles (0, 15, 30, 45, 60,
tative elementary volume scale was used. Using porous materials in
75, and 90) by a digital camera. In this method, the non-
the base PCM makes the role of conduction dominant and sup-
dimensional height, liquid fraction, and complete melting time
pressing the vortex strength. The porous model was compared with
were determined. The dimensional height was consistent with the
pure or non-porous PCM model. It was found that reducing porosity
theoretical results and the fastest operation corresponded to 60 -
leads to a decline in the complete melting time and thermal storage
cavity. Natural heat transfer played an essential role in enhancing
capacity of the system. The rate of thermal conductivity was
heat transfer. The fastest melting is for the inclined models than
developed in the samples with the highest porosity. It was
that for horizontal and vertical ones.
demonstrated that the pure PCM slowly melted from its top with
A model was developed by Ji et al. [306] to reveal the impact of
increasing thermal resistance of the melted layer, leading to a delay
fin inclination angles of 0 , þ15 , þ30 , 15 and 30 . It was found
in the complete melting of the PCM. By using nickel steel alloy
that the angle of 15 is the most suitable configuration for
porous matrix in the ice, the conduction heat transfer was domi-
increasing natural heat transfer compared to the other 3 angles. In
nant and the natural heat transfer flow was stopped. Reducing
this model, there was a 23.8% increase in PCM melting time
porosity resulted in a reduction in thermal storage capacity. The
compared to straight fins. However, this time for the models with
the angles of þ15 and þ30 resulted in a reduction of 45.2% and phases of the PCM particles within the solid phase, two-phase, and
71.4%, respectively. In other words, the fin with the angle of 15 liquid phase. The influence of rectangular enclosure size ratio and
was found as an optimum value for PCM melting rate and saving of PCM concentration on natural heat transfer was examined. They
62.7% in melting time. revealed that the Nu value increases partially in the concentration
Using longitudinal arrangement of two fins, Ji et al. [307] of PCM in the solid phase. The Nusselt number was increased by
numerically studied the improvement of a PCM-made TES unit. increasing the concentration of PCM volume at low Ra. No signifi-
RT42 was used as PCM in a rectangular enclosure heated at a cant difference was observed in PCM free convection in its low
constant temperature of 70 C to absorb thermal energy. A transient concentrations (<10 mass%), while it became larger with raising the
numerical model was developed and the results were validated by concentration. Even for low concentrations of PCM, the maximum
natural heat transfer. It was concluded that the short fin embedded Nusselt number was reported that has a direct relation with Ra
on the upper wall and the long fin on the lower wall melts PCM within the phase change region. Scattering of fatty particles had an
faster. The fin lengths ratio of 0.25 resulted in an enhancement of effect on enhancing natural heat transfer. The modified Stefan
25% in the PCM melting time. The optimum arrangement of fins number introduced in this study leads to a rise in the dominancy of
was found for the storage improvement such that, the longer length convection. The Nusselt number in the PCM phase change pro-
of the upper fin and the shorter length of the lower one had an cedure has an inverse relation with the Stefan number. The Nusselt
unfavorable effect. To study the underlying physics of how the number increased with the concentration of PCM. It was found that
system performance improves by in a special configuration of the although PCM viscosity may increase with increasing PCM con-
fin pairs, the liquid fraction contours showed good behavior of the centration, it has a favorable effect on the thermal performance.
liquid PCM flow. It was observed that for the length ratio of lower The sidewalls effect on natural heat transfer and an increase in
than 1, the free heat transfer flow through the chaotic flow temperature on viscosity reduction were evident. Concerning the
appeared to be quite effective. However, the flow motions guided Nusselt number, it was found that the PCM in the liquid phase and
by natural heat transfer due to the longitudinal ratios more than 1 phase change process was more deviated than the solid phase PCM.
become weaker. The length ratio of 0.25 showed the highest length Considering the increasing use of PCMs as TES sources, re-
of solid-melt interface among other ratios. The average Nusselt searchers are looking for methods to increase the amount of heat
number in three stages were compared to show which mechanism storage in these materials. With the development of human
is dominant. Further optimization studies showed that when the knowledge and the introduction of high-conductive nanomaterials,
ratio of length decreases, the full melting time decreases. The solid many researches were done on the phase change of these materials,
phase melts by 40.5% faster than the case in which the fins are the which may be discussed in a few instances.
same. The time ratio was also decreased by 45% by decreasing the Using LBM, the melting process of ice inside the bottom-heated
inlet temperature from 70 C to 50 C. enclosure in presence of copper nanoparticles was studied by Feng
Hong et al. [308] simulated the liquid-solid phase change of the et al. [311] (Fig. 48b). The results of this study were presented for
PCM in a square enclosure with isothermal walls. The idea of flow and temperature fields for the three cases of base fluid and
rotating the enclosure during the melting process was suggested as nanofluid combinations with volume fractions of 0.5 and 1% and
a feasible way to increase the performance of the energy storage Grashof numbers of 5 104 104 and 2.5 105. The composition of
system. The porous enthalpy model was used for this purpose and nanoparticles and PCM has higher heat transfer efficiency than
the numerical model validated with the published papers. The pure material. As the concentration of nanoparticles increases, the
maximum raise in the liquid fraction occurs mostly between 24.3% melting line progresses faster. In addition, the energy stored also
and 40% standard time units, compared to when the enclosure increases. On the other hand, it was seen that for high concentra-
inversion operation was not performed. The rotated enclosure is tions of nanoparticles for the Grashof number 2.5 105, an
the simplest way of increasing the phase change compared to the asymmetric melting front is created.
available methods. In addition, for cases where it is not possible to Melting of the hybrid of paraffin-alumina nanoparticles in a
fully invert, it is recommended to incline the enclosure as far as square enclosure shown in Fig. 48 under cross-sectional heating
possible. Good performance by inversion is generally because of the and cooling was examined by Arici et al. [312]. This study was
dominancy of the convection mode. performed for different volume fractions of 1, 2 and 3%. The highest
Li et al. [309] compared the natural heat transfer of three models melting rate was found that happens for the volume fraction of 1%
of different materials including MPCM slurry, MPCM particle and and bottom-heated enclosure. Addition of alumina nanoparticles to
ordinary PCM (Fig. 47). This test was evaluated by three lower, paraffin resulted in an increase by 6.7% and 10.6% in the thermal
upper and lateral walls of the enclosure. MPCM slurry exhibited the storage and melting rate, respectively, for the concentration of 1%.
best thermal control among the three materials. Excluding the ef- According to the investigations on nanofluids and the effect of
fect of natural heat transfer, MPCM slurry had the lowest surface adding nanoparticles to the base fluid, it was observed that the
heat when having the highest heat transfer. On the contrary, thermal conductivity and viscosity increase and the heat capacity
without fluid convection, the lowest heat transfer and the worst decreases by increasing the volume percentage of nanoparticles
interfacial heat resistance were observed for MPCM particles. The [313e316]. Therefore, the results of Arici et al. [312] demonstrated
highest increase in temperature gradient was observed for MPCM that the buoyancy force cannot overcome the force due to the
slurry, especially in the vicinity of the heat source. The highest viscosity by increasing the volume percentage of nanoparticles and
internal heat distribution was seen from lower heating. MPCM enhancing the viscosity. On the other hand, the heat capacity of
slurry with the lowest MPCM distribution showed the lowest time PCMs is decreased. Hence, the melting rate and thermal energy
to reach the melting temperature. The results showed that MPCM storage decrease with the volume fraction of nanoparticles.
slurry exhibits the best thermal control among the two models Similar work on paraffin-copper nanoparticles was conducted
because of the rise in natural convection. Pure PCM and MPCM by Sebti et al. [317] through the use of enthalpy method. This study
particles were placed in second and third place, respectively. showed that the volume fraction of nanoparticles in the base fluid is
Inaba et al. [310] used a blend of fatty microparticles for their effective on the melting rate by affecting the rate of conductive heat
experiments: water, surfactants, and fine particles PCM. The PCM transfer. This effect results in a raise in the melting rate as the
volume concentration ranges from a maximum 30% to the mini- concentration rises. Phase change of water-Cu nanomaterial in an
mum 5% and the experiments were in three separate temperature insulated enclosure was examined by Darzy et al. [318] to reveal the
Fig. 47. Experimental setup used by Lee et al. [309].
importance of convection effects using LBM (Fig. 48C). In this study, rate rises by 0.02 in the base fluid by increasing the concentration.
the effect of the heater location inside the enclosure was also It was demonstrated that as the concentration increases, the
investigated. An increase in the concentration from zero to 4% re- melting rate begins to decrease until the melting rate less than that
sults in a rise in the melting rate by 52.7%, 41.2%, and 30%, for pure paraffin for the volume fraction of 5%. The amount of heat
respectively, for the location of heat source in top, center, and absorbed by the nanofluid is declined with the percentage of
bottom of the enclosure. Solidification of the same mixture was alumina nanoparticles. Thus, lower volume fractions of alumina
further analyzed by Kashani et al. [319] with corrugated vertical nanoparticles in paraffin not only create a better melting process
walls. The effect of wall wave, concentration of nanomaterials, and but also increase energy storage capacity for constant dimensions
Grashof number, in wide ranges, on freezing time and natural of the enclosure.
convection were investigated. In this study, the supercooling phe- Fan and Khodadadi [324] experimentally investigated nonlinear
nomenon and the effect of nanoparticle diffusion at the freezing fast freezing in cyclohexane fluid. This compound was prepared
point were ignored. However, it is found that the supercooling using copper oxide nanoparticles of different mass concentrations.
occurs in reality because pure water cools to 5 C to 7 C and The problem was considered one-dimensional for a wall of limited
then begins to freeze. The porosity-enthalpy method was used for thickness and high depth. Initially, the liquid PCM was assumed at a
numerical study of solidification phenomenon. This method has temperature above freezing temperature. The sidewall temperature
been used for years as one of the methods of modeling the melting drops suddenly to a temperature lower than the melting point. By
and freezing processes. The energy equation has been derived in neglecting the effects of supercooling, freezing begins rapidly in the
terms of enthalpy. The results of this study showed that by adjacent left wall and moves to the right wall. The Fourier equation
increasing the concentration and the Gr value, the Nu value in- was used to mathematically describe the conduction and convec-
crease. Overall, this study showed that the shape of the enclosure, tion in the solid and liquid phases. Khodadadi and Fan [325]
along with other influencing factors such as nanoparticle volume described this method in another study to show that the highest
fraction and free convection rate has a positive impact on the phase freezing rate occurs at volumetric concentration of 0.02, while the
change procedure. freezing rate decreases as the concentration rises by 0.04 probably
Melting of paraffin-aluminum oxide nanofluid was examined by due to a cross-sectional increase in thermal conductivity of the
Arasu et al. [323] for the 25 mm 25 mm enclosure. The enclosure solid phase. Melting process of nanoparticle-reinforced PCM in the
was heated from its sidewalls. In this study, the effect of orientation two-dimensional enclosure shown in Fig. 49 was numerically
of heat source and volume fraction of aluminum oxide particles on studied by Sebti et al. [326] using FVM over a non-uniform grid. In
the melting process was investigated. Fig. 49 shows an overview of this study, paraffin-copper nanofluid with different volume frac-
the enclosure. Navier-Stokes equations and the enthalpy method tions was used. The enthalpy-porosity method was used to track
were solved as the governing equations. The equations were the melting line. In this study, the effect of nanoparticle diffusion in
analyzed in FLUENT software. The results showed that the melting the base fluid and some of the governing parameters such as hot
Fig. 48. The geometries and boundary conditions discussed in previous researches, a) (Bondareva and Sheremet [320], b) Feng et al. [321], c) Arici et al. [312], d) Sebti et al. [317], e)
Dhaidan et al. [322], f) Darzi et al. [318].
wall temperature and enclosure volume on the flow field, heat declines the latent heat of melting lead to hastening the melting.
transfer rate and melting line motion were investigated. The Khodadadi and Hosseinizadeh [328] simulated the freezing
incompressible steady nanofluid flow was presumed Newtonian procedure of water using CuO nanoparticles in a rectangular
with uniform properties, and all thermodynamic properties except enclosure. Horizontal surfaces were assumed to be insulated and
the density modeled with Boussinesq approximation were sidewalls were at 283.15 K and 273.15 K. At the freezing point, the
assumed to be constant. The left wall temperature was higher than temperature on both sides was reduced to 10 K. In this way, the
the melting temperature with a difference of 10 C. They reported freezing process begins. The simulation was performed using
the following results: i) at the beginning of the melting, the con- FLUENT software. The results were analyzed for different Grashof
duction mechanism plays a key role in thermal performance and and Stefan numbers. In general, using nanoparticles can signifi-
the melt line moves parallel to the heated surface, ii) solid fraction cantly increase thermal performance.
decreases linearly with the time, but the freezing rate is initially fast The annulus filled with nanoparticle-reinforced PCMs was
and becomes slow at the end, iii) distribution of nanoparticles numerically and experimentally studied by Dhaidan et al. [322].
within the PCM hasten the melting time due to a rise in the thermal The inner cylinder was kept at a constant heat flux, while the outer
conductivity and Nu, iv) the effect of dispersing nanopowder to the surface of the outer cylinder was well insulated. N-octadecane was
base fluid on heat transfer is greater for larger enclosures, v) the selected as the PCM with copper oxide nanoparticles as the thermal
higher the temperature difference, the faster the melting proced- conductivity enhancer. The process of melting and changing tem-
ure, vi) fluid flow and melting line shape depend on the melt layer perature was observed at many points during the experiment. In
thickness and the concentration during phase-change, and vii) the this study, the FEM was used for numerical simulations of the
amount of energy stored can be increased by proper nanoparticle process and the effect of volume percentages of nanoparticles and
dispersion within the PCM. Rayleigh number on melting process was investigated. The results
Hosseinizadeh et al. [327] investigated the melting of a of this study showed that in acute response of melting, the domi-
nanoparticle-reinforced material in a cylindrical enclosure experi- nant phenomenon of heat transfer is the conduction mechanism,
mentally. The base fluid of paraffin and copper nanoparticles were which is characterized by concentric isothermal lines. Subse-
used (Fig. 49). The fluid was precooled with the initial temperature quently, free convection and the melting rate rises in the upper half
of 23 C. The results of this study showed that adding nanoparticles of the enclosure. In other words, melting in the lower half is
to the base PCM either increases the thermal conductivity and controlled by thermal diffusion and becomes more powerful as the
Fig. 49. The geometries considered in previous researches: a) Kashani et al. [279], b) Arasu et al. [280], c) Sebtei et al. [283], d) Hosseinizadeh et al. [284], e) Jourabian et al. [260],
and f) Dhaidan et al. [288].
Ra rises. variables such as heat transfer and melting rates as well as charge
Altohamy et al. [329] investigated heat transfer in a spherical time was investigated. They approved that increasing the heat flux
capsule containing water and alumina nanoparticles experimen- and concentration raises the melting rate and declines the charge
tally. The results were extracted and compared for distilled water time. Either the conduction and convection mechanics play
and nanofluid concentrations of 0.5, 1 and 1.5%. A Freon 404 important roles in promoting phase change. At the early stages of
refrigerant with temperatures of 6, 8, 10 and 12 C and melting, which most of the cavity is still solid, the conduction
different flow rates was used to cool and freeze the PCM. The results phenomenon is dominant. The liquid fraction inside the enclosure
showed that as the volume fraction of nanoparticles increases, the increases over time and convection becomes dominant. The inter-
percentage of energy storage increases. esting point in this study is that the positive effects of nanoparticles
Melting of n-octadecane copper oxide nanomaterial in the occur at low weight fractions. However, at higher weight fractions,
horizontal cylinder shown in Fig. 49C under a fixed heat flux on the the effect of solid nanoparticles was negligible compared to the
outer wall was examined experimentally and numerically by Dai- influence of the viscosity and consequently natural convection heat
dan et al. [330]. The experimental apparatus was equipped with transfer.
several temperature sensors located at different angles of the cyl- Using the porosity-enthalpy method, Kashani et al. [331]
inder. So that it was possible to track the melting line in different simulated the solidification process of n-hexadecane with copper
test modes. The numerical approach was performed using the FEM. nanoparticles. The results of this study revealed that the thermal
The effect of different volume fractions and Rayleigh numbers on properties inside the base material increase with the addition of
nanoparticles. The researchers believed that using appropriate concentrations, Ra and Ste numbers. The rapid propagation of
nanoparticles can improve the properties of the PCM as a storage melting front and heat transfer rate were reported as the concen-
material. tration increased. A scale analysis was first introduced to describe
Zarma et al. [332] investigated photovoltaic focusing on CPV- different melting regimes. The results presented were consistent
nanoparticles-PCM numerically (Fig. 50). The effect of different with previous results.
nanoparticles of Al2O3, CuO, SiO2 with a mass fraction of 1%e5% on Ren et al. [334] proposed adding nanoparticles and metal foam
the photovoltaic concentration was investigated. In this research, to the PCM for the purpose of thermal performance improvement.
2D simulations of models including photovoltaic nanoparticle Their study was based on enthalpy and buoyant boundary in the
layers in PCM were validated with experimental data. It was LBM. The average PCM liquid fraction, energy stored per unit width
observed that by an increase in the PCM temperature and the Q, and mean temperature at LHTES were systematically studied in
melting rate, a reduction in the solar cell temperature and the use of various porosities and sizes of metal foam, nanoparticle volume
nanoparticles in the PCM lead to that the temperature becomes fraction, and heat pipe radius. The results were as follows: i) the
more uniform and electrical efficiency in the CPV system increases. melting rate of PCM with nanoparticles in LHTES can be increased
It was also found that using Al2O3 nanoparticles with a mass frac- by decreasing the porous metal foam or by increasing the nano-
tion of 5% in PCM leads to an electrical efficiency of 8% and a uni- particle volume fraction. In this paper, an optimum amount of
form temperature of 12 C, whereas pure PCM results in maximum porous metal foam mixture and nanoparticles were obtained to
electrical efficiency of 6.36% and uniform temperature of 20 C. In achieve maximum energy storage capacity f ¼ 0.01 and εave ¼ 0.95,
this study, n-octadecane, paraffin, and graphene were used as PCM. ii) it was observed that by declining the metal foam porosity at a
Melting of three types of CuO nano-PCM including, paraffin wax, constant volume, the melting rate of PCM increases. Both the
coconut oil, and Rubitherm, in a cubic enclosure were compared by conduction and convection heat transfer was found that have ef-
Al-Jethelah et al. [333] (Fig. 51). Their melting point respectively fects in the same order on the thermal performance. For high
were 54 C, 24 C, and 18 C with the ambient temperature of 24 C. porous metal foams, the average temperature increases with the
The left surface was kept at constant temperature and the hori- porosity size during conduction heat transfer. Reduction of porosity
zontal and right surfaces were isolated. The continuum and mo- of metal foam can decrease the heat transfer of the LHTES due to
mentum equations were solved for liquid and the energy equation the use of metal foam with small porosity size, iii) the heat pipe
was solved in solid and liquid regions using FEM. The spatio- radius of the LHTES unit has a significant impact. As the diameter
temporal variation of the melting front was captured as well as increases, the melting rate increases, and iv) the effect of porous
the temperature and flow pattern for various nano-PCM metal foam on energy storage in LHTES is greater than that of
Fig. 50. Schematic of the problem examined by Zarma et al. [332].

Fig. 51. Schematic of the problem considered by Jetla et al. [333].
nanoparticles. simulations. According to the results of previous studies about the

Ebadi et al. [335] studied melting, heat transfer, and TES prop- use of PCM for heat energy storage, it can be stated that in all cases
erties of a CuO nano-PCM in a Cylindrical TES System (C-TES) in the reduction of energy consumption, in some cases up to 20% is
various concentrations and Ra values, then they validated the nu- one of their advantages (especially during peak power hours). The
merical results with experimental ones. The mathematical model benefits of using these materials in buildings can be attributed to
based on nonlinear differential equations was used to study mass, the increased thermal comfort of residents due to the reduction of
momentum, and transport properties within C-TES. The bottom temperature fluctuations. Also, the reduction of temperature fluc-
was insulated and it was heated from sides and up surfaces. The tuations in sensitive cases such as greenhouse, solar heaters, and
numerical results obtained from the solid-melt interface and the dryers can affect the desired quality of the finished product. Despite
liquid fraction for PCM and nano-PCM were compared with the the advantages of using PCMs and their potential for high tem-
experiments and good agreements were shown. The flow pattern perature latent heat storage, there are some technical challenges
was shown that is not sensitive to the concentration. The results that need to be addressed in future works, such as supercooling,
showed that the stored energy did not significantly vary with Ra which is a major problem for PCMs that affects the storage per-
values in early stages, while its sensitivity becomes more and more formance and material stability. Therefore, further studies are
over time. Hence, a large difference is observed when the melting suggested. The presence of salts and hydrated salts in PCMs causes
increases at high Rayleigh numbers. corrosion and damage to warehouses and building materials,
Finally, according to recent studies and articles, using latent heat requiring further investigation to determine the compatibility be-
storage units that use PCMs is an effective method to save energy tween PCMs and various building materials, which will affect the
that has received much attention in recent years. PCMs are used to life and stability of heat storage units. Since PCM micro-capsulation
store thermal energy and their importance has environmental and is a potential solution to the corrosion problem, a standard test
economic aspects. Due to the fact that materials release energy method must be established for leakage tests, as most enclosed
phase change during phase change, their use reduces energy con- PCMs are not currently tested. In addition, the micro-encapsulation
sumption [41,122,336,337]. can be used to increase heat transfer and prevent phase separation
According to studies, the use of nanoparticles in phase change during the melting process, so the stability test is crucial for the
materials improves the thermal conductivity of phase change ma- final evaluation of the effects of the encapsulation process.
terials. In fact, the use of nanoparticles in phase change materials Although the melting points of most PCMs and nano-PCMs are
improves the performance of energy storage systems. On the other known, thermal conductivities, densities, specific heat capacities,
hand, the use of phase change materials reduces energy con- and volume expansions of liquids and solids are not fully consistent
sumption and causes temperature uniformity in different temper- across studies. Therefore, these features are sometimes unavailable
ature fluctuations [41,121,338e341]. for PCMs and nano-PCMs. Thus, to provide reliable results and data,
Recent studies also demonstrate that when the melting and a standard test method and a database should be provided.
freezing behavior of PCMs and nano-PCMs are evaluated, their Increasing heat transfer is another subject that needs further
thermophysical properties, especially the viscosity, must also be studies, especially with the focus on their thermal conductivities.
carefully measured. Previous studies show that the wrong value of As one can see from previous researches, one of the potential ad-
viscosity leads to the incorrect output of numerical simulation re- vances is dispersing highly conductive nanoparticles in PCMs.
sults from experimental data significantly [342e345]. However, there are a few studies to strengthen PCMs using
nanoparticles.
12. Conclusions, challenges, and suggestions Price of PCMs has been high due to demand and supply.
Currently, due to limited demand, they are mainly produced with
In this study, a detailed review of recent researches and de- relatively high prices. However, there is a huge market potential for
velopments in PCM technology and their natural convection were PCMs in a variety of applications, including building energy man-
presented, focusing on the models used for the numerical agement. Since producers set their prices based on future market
expectations, prices decrease in the future. Current studies are of solar energy systems using artificial neural network: a comprehensive
review. Sol Energy 2019;180:622e39.
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A Review of Melting and Freezing Processes of PCMnano-PCM and

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Energy 211 (2020) 118698

Contents lists available at ScienceDirect

A review of melting and freezing processes of PCM/nano-PCM and

Fig. 2. Melting temperature and enthalpy for some PCMs [39,40].

Fig. 3. Schematic of heat transfer in buildings [44,45].

Fig. 4. Energy storage methods in buildings.

Fig. 5. Applications of PCMs in refrigerated vehicle [57,58].

Fig. 6. Heat capacity of different materials compared to PCMs [64].

Fig. 7. Temperature changes during the freezing and melting [69,70].

Fig. 8. PCMs classiﬁcation, stability and cost [82].

Fig. 9. Temperature range of PCMs and their thermal conductivity [106,107].

It is easily understood that the liquid-solid phase change

Fig. 10. The performance of PCMs [108].

Fig. 12. Chemical, kinetic and thermophysical properties of PCMs [92e96].

boundary conditions and the presence of SWCNT in the enclosure.

Fig. 14. Types of stabilizing materials in PCMs applications [127].

Fig. 15. PCMs application methods [28].

Fig. 17. Schematic summary of future trends in PCMs [135].

and the liquid density, respectively. It should be noted that the

Fig. 21. Thermal storage for home heating [146].

Fig. 24. Full capacity energy storage system [170,171].

In this method, enthalpy is considered as the temperature-

Fig. 27. Schematic of the geometry considered by Haq et al. [194].

does not need to explicitly examine the phase change boundary

dependent factor. Using the enthalpy method, a two-phase region

referred to as the porous enthalpy method because it assumes that

10.6. Effective heat capacity method (energy-based method)

The latent heat is obtained by the difference between the

sensible heat is obtained from relation (14): hl

Fig. 32. Different methods for investigating PCMs [253].

contact melting of PCMs in a square cavity containing free con-

engulfed by hot water was studied by Regin et al. [272] to capture

Fig. 37. Percentage of numerical studies implementing various modeling of phase

Lamberg et al. [270] in the presence and absence of free convection

Fig. 43. The geometry considered in Ref. [291].

Fig. 44. Schematic of the problem studied by Zenouhi et al. [300].

Fig. 46. The geometry studied in Ref. [304].

highest porosity samples can be used to achieve the highest heat

Fig. 47. Experimental setup used by Lee et al. [309].

Fig. 50. Schematic of the problem examined by Zarma et al. [332].

Fig. 51. Schematic of the problem considered by Jetla et al. [333].

nanoparticles. simulations. According to the results of previous studies about the

2018;119:841e59. review. Sol Energy 2020;197:163e98.

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