Materials Today: Proceedings xxx (xxxx) xxx

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Optimal hydraulic and thermal constrain for plate heat exchanger using
multi objective wale optimization
S. Dinesh Kumar a,⇑, D. Chandramohan a, K. Purushothaman a, T. Sathish b
a
Department of Mechanical Engineering, St. Peter’s Institute of Higher Education and Research, Avadi, Chennai 600 054, Tamil Nadu, India
b
Department of Mechanical Engineering, SMR East Coast College of Engineering and Technology, Thanjavur 614 612, Tamil Nadu, India

a r t i c l e i n f o a b s t r a c t

Article history: In this paper the hydraulic and thermal constrain of the plate heat exchanger is optimized to enhance the
Received 14 July 2019 sensitivity of the heat exchanger. In the proposed method the multi objective wale optimization (MOWO)
Accepted 24 July 2019 is used for optimizing the parameter of the plate heat exchanger. In MOWO the parameters of the plate
Available online xxxx
heat exchangers such as, horizontal port centre distance, vertical port centre distance, enlargement fac-
tor, port diameter, plate thickness, number of thermal plates and plate spacing are optimized to achieve
Keywords: better sensitivity. The thermal and hydraulic drop are consider as the objective function, in which the
Heat exchanger
heat transfer is enhanced and the pressure drop is minimized by using MOWO. Then the proposed system
Wale Optimisation
Hydraulic and thermal constrain
is implemented using matlab and its performance are analysed. The obtained performance proves the
Plate heat exchanger effectiveness of the proposed system.
Simulation analysis Ó 2019 Elsevier Ltd. All rights reserved.
Peer-review under responsibility of the scientific committee of the International Conference on Recent
Trends in Nanomaterials for Energy, Environmental and Engineering Applications.

1. Introduction new heat transfer correlation also agrees with the experimental
data of Al2O3/water Nano-fluids flowing inside the plate heat
Now a day the heat exchangers are used in the process, power, exchanger very well. Fully developed turbulent forced convective
transportation, air-conditioning and refrigeration, cryogenic, heat flow and heat transfer behaviour of the Nano-fluid containing
recovery, alternate fuels, and manufacturing industries [1]. It’s water, ethylene glycol, mercury and propane based Al2O3 nanopar-
being key components of many industrial products available in ticles in a two-dimensional corrugated trapezoidal plate heat
the marketplace [2]. The importance of heat exchangers has exchanger. According to the results obtained; adding nanoparticles
increased immensely from the viewpoint of energy conservation, to base fluids increases heat transfer [10]. It is also seen that the
conversion, recovery, and successful implementation of new heat transfer is increased by increasing the volume fraction of
energy sources [3]. Its importance is also increasing from the posi- the Nano-fluid. The effect of using different nano-fluid as a coolant
tion of environmental concerns such as thermal pollution, air pol- fluid on the thermal performance of Pillow plate heat exchanger
lution, water pollution, and waste disposal [4]. An industrial heat (PPHE). A new heat transfer enhancement method in PPHE by uti-
exchanger design problem consists of coupling component and lizing nano-fluid instead of pure fluid as a heat transfer [11].
system design considerations to ensure proper functioning [5]. Ceramics as functional materials durable at high temperatures
Based on industrial experience in designing compact heat exchang- are suitable candidates for manufacturing heat exchangers. A ser-
ers for automobiles and other industrial applications [6]. It ies of numerical simulations was carried out to the heat transfer
included more material than is necessary for the placing equal in micro heat exchanger made by TiB2–SiC and TiB2–SiC doped
emphasis on four basic heat exchanger types: shell-and tube, plate, with 2 wt% carbon fibre [12]. Experimental thermal diffusivity data
extended surface, and regenerator. of materials were obtained by laser flash method and used for
Accordingly, heat transfer and pressure drop of three water- numerical simulations. This article demonstrates the feasibility of
based nano-fluids including Al2O3, CuO and TiO2 medium [9]. The better heat transfer and performance for ceramic heat exchangers.
Conduction heat transfer equation in solid walls of heat exchanger
⇑ Corresponding author. along with fluid flow governing equation was used for solid and
E-mail address: dinesh.15mech@gmail.com (S. Dinesh Kumar). fluid domains [13]. The obtained results presented that the thermal

https://doi.org/10.1016/j.matpr.2019.07.710
2214-7853/Ó 2019 Elsevier Ltd. All rights reserved.
Peer-review under responsibility of the scientific committee of the International Conference on Recent Trends in Nanomaterials for Energy, Environmental and Engineering
Applications.

Please cite this article as: S. Dinesh Kumar, D. Chandramohan, K. Purushothaman et al., Optimal hydraulic and thermal constrain for plate heat exchanger
using multi objective wale optimization, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.710
2 S. Dinesh Kumar et al. / Materials Today: Proceedings xxx (xxxx) xxx

conductivity of both TiB2-based composites are approximately the where the ‘Nc’ is the number of channels and the ‘m’ is the viscosity
same and small amount of carbon fibre had no considerable effect of the fluid. The heat transfer correlation of plate heat exchanger is
on the thermal properties of the composites [14]. For the ceramic given in Eq. (3).
heat exchanger, a higher heat transfer with 15.5% enhancement
occurs using TiB2 composites compared to utilization of Al2O3. NU ¼ 0:2267  R0:631
e  P0:33
r ð3Þ
Plate heat exchangers having high efficiency and small size are whereas k is thermal conductivity of the fluid. The overall heat
one of the mostly used heat exchangers. They are used in many transfer coefficient and number of transfer units are given in Eq.
applications ranging from cooling to heating. Heat transfer (4) and Eq. (5) respectively.
improvement of plate heat exchangers can be performed using
nanoparticle-including using fluids, i.e. nano-fluids. Influences of 1 1 1 1
¼ þ þ ð4Þ
kaolin-including nano-fluid utilization as working fluid on heat U hc kp hh
transfer performance of the plate heat exchanger. In various work-
ing conditions with changes in mass flow rate and temperature. UA
NTU ¼ ð5Þ
The obtained results showed that nano-fluid usage as the working C min
fluid enhanced the heat transfer rate in plate heat exchanger in
For the heat exchanger the heat transfer is given in Eq. (6).
comparison to the results acquired from the tests conducted by


deionized water. The improvement rate in mean heat transfer coef- Q ¼ e  C min  T h;i  T c;i ð6Þ
ficient was achieved as 9.3% when kaolin–deionized water nano-
fluid was used as the working fluid in plate heat exchanger [15]. The pressure drop across the plate heat exchanger consists of
A recent fabrication method for chevron-type plate HEXs, as a four components; pressure drop due to acceleration of the fluid,
proof of-concept demonstration, using flat embossing process. To due to change in elevation, due to inlet/exit manifolds, and due
measure the performance of the proposed graphite plate heat to friction inside the corrugated plate heat exchanger. Total pres-
exchanger, a custom-designed water-water experimental testbed sure loss is given in Eq. (7).
is designed based on ANSI/AHRI Standard 400 [16]. The heat trans- DP ¼ ðDPÞf þ ðDPÞp ð7Þ
fer rate and the pressure drop of the fabricated graphite plate heat
exchanger is compared to a conventional stainless-steel chevron where
HEX with similar plate dimensions and number of plates. Com-
pared with the commercially available unit, the proposed graphite 4  f  Le  G2
ðDPÞf ¼
plate heat exchanger shows identical thermal performance and a 2  q  Dh
26% higher pressure drop, due to its narrower channel design [17].
Indirect evaporation between the exhaust gas and the organic 1:5  ðV Þ2
ðDPÞp ¼
fluid in the parallel plate heat exchanger (ITC2) implied irreversible 2q
heat transfer and high investment costs, which were considered as
objective functions to be minimized [18]. Energy and exergy bal- The Eq. (6) and Eq. (7) are consider as the objective function, for
ances were applied to the system components, in addition to the the optimization of plate heat exchanger.
phenomenological equations in the ITC2, to calculate global energy
indicators, such as the thermal efficiency of the configuration, the 3. Multi objective whale optimization algorithm (MOWOA)
heat recovery efficiency, the overall energy conversion efficiency,
the absolute increase of engine thermal efficiency, and the reduc- The WOA is a newly developed meta-heuristic algorithm, it is
tion of the break-specific fuel consumption of the system, of the inspired from the behaviour of humpback whales such as bubble
system integrated with the gas engine [19]. calculation of the plate net hunting method. The whales are creating a shape of circle
spacing, plate height, plate width, and chevron angle that mini- through bubble creation in the surface of the water for encircle
mized the investment cost and entropy generation of the equip- the fish and catch the prey. The attacking of the prey by whales
ment, reaching 22.04 m2 in the heat transfer area, 693.87 kW in through bubble net attacking are main concern to develop the
the energy transfer by heat recovery from the exhaust gas, and WOA algorithm. The bubble net hunting technique can be defined
41.6% in the overall thermal efficiency of the ORC as a bottoming as humpback whales dive near to 12 m down and start to create
cycle for the engine [20,21]. This type of result contributes to the bubbles in the shape of spiral around the prey and swim to the sur-
inclusion of this technology in the industrial sector as a conse- face. The concepts of multi-objective optimization and the related
quence of the improvement in thermal efficiency and economic description of the MOWOA are all described in this section. The
viability [22,23]. inspiration of the MOWOA and mathematical model is presented
below.
2. Problem formation
3.1. Inspiration of MOWOA
The objective of the proposed work is to maximize the heat
transfer rate and minimize that pressure drop of plate heat exchan- The whales are considered as the bulk mammals in the world.
ger. The heat transfer rate of the heat exchanger is depends on is The adult whale can be heighten up to 30 m long and increase
geometry and operating conditions. The mass velocity and Rey- weight to 180 ft. From the whales, seven different types of the
nolds number can be calculated using Eq. (1) and Eq. (2) mammals presented in the world such as blue, finback, right,
respectively. humpback, Sei, Minke and killer. The whales are taken as a preda-
tors it does not sleep ever as have to breathe from the ocean sur-
m_
G¼ ð1Þ face areas so only half of brain sleeps. The social behaviour of the
ðNc  b  WeÞ whale, it is live in groups or alone. Their mostly live in their groups.
From the various whales, the baleen whale is considered as a big-
G  Dh
Re ¼ ð2Þ gest whale and it is called as a humpback whales. Their favourite
l prey are small fish herds and krill. The whales are catching prey

Please cite this article as: S. Dinesh Kumar, D. Chandramohan, K. Purushothaman et al., Optimal hydraulic and thermal constrain for plate heat exchanger
using multi objective wale optimization, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.710
 S. Dinesh Kumar et al. / Materials Today: Proceedings xxx (xxxx) xxx 3

by the bubble net attacking technique. The bubble net attacking !

where A is referred as linearly decreased from 2 to 0 finished the
technique is illustrated in the Fig. 1. sequence of iterations it is combination of exploitation and explo-
The humpback whales are hunting the prey of krill and small !
ration phases. The R is described as the random vector in [0, 1].
fishes near to the surface area. The prey has been catches that for-
After the encircling phase, the bubble net strategy to get their food.
aging behaviour is completed through generating distinctive bub-
The mathematical model of the bubble net strategy is mentioned
bles with the shape of circles or 9 shaped path which is
below.
illustrated in the Fig. 1. The humpback whales are only attacking
prey by using bubble net attacking techniques and it is a unique
3.2.2. Bubble-net attacking method (exploitation phase)
technique. In the optimization process is concentrated by the bub-
The development the mathematical model of bubble net attack-
ble net attacking technique. To attain the multi-objective opti-
ing method, two techniques are need to be designed. The
mization process, the mathematical model of the bubble net
approaches are mentioned below,
attacking technique, spiral bubble net attacking is described in
the below section.
Shrinking encircling mechanism: the mechanism is achieved by
!
3.2. Mathematical model of MOWOA decreasing the value of A . The variation (fluctuation) range of
! ! !
a also decreased by the A . a is the random value at the inter-
In this section provides the mathematical model of bubble net val of ½A; A. Here, the A is decreased from 2 to 0 in the itera-
attacking technique, encircling prey, search of the prey. tions. Assuming random value of a in [1, 1], based on this
the new position of a search agent can be determined in among
3.2.1. Encircling prey the position of the current best and original position of the
The identification of prey and encircle of the prey is processed agent.
by the humpback whales for catch their food. The optimal location Spiral updating position: The spiral updating is computed the
of the prey does not known before. Initially, the whales are distance among the prey located at ðx ; y Þ and whale located
assumed that the current best candidate solution is the goal prey at ðx; yÞ. The spiral updating equation is generated among prey
or is near to the optimum. Based on the assumption, the best to mimic the helix shaped movement and position of the
search agent is identified. Depends on the best search agents, the whales. The spiral updating equation is mentioned below,
others agents also try to update the positions near to the best
search agent. The characteristics of the whales are presented by ! !0 !
x ðt þ 1Þ ¼ d :EBL :Cosð2pLÞ þ x ðt Þ ð12Þ
the Eqs. (8) and (9),
! ! ! !  !0 ! !
d ¼ c : x  ðt Þ  x ðtÞ ð8Þ d ¼  x ð t Þ  xð t Þ  ð13Þ

! ! !! !0
x ðt þ 1Þ ¼ x  ðt Þ  a : d ð9Þ where d is referred as the distance of the ith whale to prey, l is a
! random number in [1, 1], b is defined as the constant for shape
where t can be taken as the current iteration, x  is defined as the of the logarithmic shape and : is an element by element
! !
position vector of the best solution achieved so far, a and c are multiplication.
!
the coefficient vectors, k is referred as the absolute value, d can The humpback whales are swim near to the prey and produce
be a position vector, can be an element by element multiplication. the bubbles to attack the prey. For the assumption, the whale
! use to attack the prey, fifty percentage of shrinking encircling
Based on the equations, the x  must be updated in each and every
iteration if it is a better solution. The coefficient vectors are calcu- mechanism and fifty percentage of spiral updating mechanism.
lated based on the below equations, Based on the probability function, the mathematical model for
optimization is presented below,
! !! ! 8
a ¼ 2A:R  A ð10Þ !!
<! 
x ðt Þ  a : d if P < 0:5
!
x ð t þ 1Þ ¼ ð14Þ
! ! : !0 BL !
c ¼ 2: R ð11Þ d :E :Cosð2pLÞ þ x ðt Þ if P < 0:5
where p is represented as the random number. After the bubble
attacking method, the whales need to search the prey. The mathe-
matical model of the prey is mentioned below.

3.2.3. Search of the prey

The search the prey (exploration) is attained by the variation of
!
the a vector. The humpback whales search randomly based on the
position with each other. For assumption, taking the random val-
ues greater than 1 or less than 1 to trigger search agent move
away from the whale of reference. At same, the exploitation phase,
the updating position of a search agent in the exploration phase
allowing to a randomly select search agent as the substitute of
the best search agent compute so far. The performance of global
search in the whale is based on the exploitation in addition
jaj > 1 highlight exploration. The mathematical model for search
of the prey is mentioned below,
! ! ! !
d ¼  c :xran  x  ð15Þ

Fig. 1. Bubble net attacking technique.

Please cite this article as: S. Dinesh Kumar, D. Chandramohan, K. Purushothaman et al., Optimal hydraulic and thermal constrain for plate heat exchanger
using multi objective wale optimization, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.710
4 S. Dinesh Kumar et al. / Materials Today: Proceedings xxx (xxxx) xxx

Fig. 2. Flow chart to the MOWOA algorithm.

Fig. 3. Heat transfer and pressure drop with respect to horizontal port centre distance.

! ! ! ! Based on the above process, the MOWOA is used for multi-
x ðt þ 1Þ ¼ xran  a : d ð16Þ
objective functions. The MOWOA optimization algorithm, initially
! generated some random solutions. After that each iteration, the
where xran is a defined as the random position vector (a random
whale) chosen from the current population. search agents update their positions based on the randomly

Please cite this article as: S. Dinesh Kumar, D. Chandramohan, K. Purushothaman et al., Optimal hydraulic and thermal constrain for plate heat exchanger
using multi objective wale optimization, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.710
 S. Dinesh Kumar et al. / Materials Today: Proceedings xxx (xxxx) xxx 5

Fig. 4. Heat transfer and pressure drop with respect to vertical port centre distance.

Fig. 5. Heat transfer and pressure drop with respect to plate facing.

selected search agent and best solution achieved so far. The Step 3: Initial population randomly generated and search agent.
achievement of the exploration and exploitation based on the Based on this, computation of the fitness function
decreased the parameter A from 2 to o. The random selected search Step 4: selected the best search agent
agent is depend on the condition of |a| > 1. The best solution is Step 5: The following process are repeated until reach the termi-
obtained in the condition of |a| < 1, based on this, the search agents nation condition
update their positions. The spiral or circular movement of the The parameters of a; A; c; l and p are updated
whale is computed depends on the value of p. At last, the MOWOA According to value p, the exploration and exploitations
algorithm is terminated by the termination condition. Based on the are attained
process, the multi-objective functions are achieved. The overall Step 6: Based on the exploration and exploitations process, best
flow chart of the MOWOA algorithm is presented in the Fig. 2. search agent identified
Step 7: The overall process is repeated until termination condi-
3.3. Process of the MOWOA tion satisfied
Step 8: Store the result
The MOWOA is used to optimize the multi objective function.
The process of the MOWOA is described below,
4. Results and discussion
Step 1: Initialize the no of population size, parameters A, coeffi-
The performance of the proposed technique is analysed based
cients of a and c, maximum no of iteration
on the sensitivity. The sensitivity of the system is analysed by vary-
Step 2: Initialize the iteration count
ing the horizontal and vertical port centre distance, plate facing

Please cite this article as: S. Dinesh Kumar, D. Chandramohan, K. Purushothaman et al., Optimal hydraulic and thermal constrain for plate heat exchanger
using multi objective wale optimization, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.710
6 S. Dinesh Kumar et al. / Materials Today: Proceedings xxx (xxxx) xxx

Fig. 6. Heat transfer and pressure drop with respect to plate thickness.

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Please cite this article as: S. Dinesh Kumar, D. Chandramohan, K. Purushothaman et al., Optimal hydraulic and thermal constrain for plate heat exchanger
using multi objective wale optimization, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.07.710