Renewable Energy 34 (2009) 640–645

Contents lists available at ScienceDirect

Renewable Energy
journal homepage: www.elsevier.com/locate/renene

Evaluation of thermal efficiency of double-pass solar collector with

porous–nonporous media
K. Sopian a, *, M.A. Alghoul a, Ebrahim M. Alfegi b, M.Y. Sulaiman a, E.A. Musa b
a
Solar Energy Research Institute, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
b
Mechanical and Materials Engineering Department, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

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

Article history: The double-pass solar collector with porous media in the lower channel provides a higher outlet
Received 17 September 2007 temperature compared to the conventional single-pass collector. Therefore, the thermal efficiency of the
Accepted 12 May 2008 solar collector is higher. A theoretical model has been developed for the double-pass solar collector. An
Available online 30 June 2008
experimental setup has been designed and constructed. The porous media has been arranged in different
porosities to increase heat transfer, area density and the total heat transfer rate. Comparisons of the
Keywords: theoretical and the experimental results have been conducted. Such comparisons include the outlet
Solar
temperatures and thermal efficiencies of the solar collector for various design and operating conditions.
Collector
Double-pass
The relationships include the effect of changes in upper and lower channel depth on the thermal effi-
Porous–nonporous media ciency with and without porous media. Moreover, the effects of mass flow rate, solar radiation, and
Thermal efficiency temperature rises on the thermal efficiency of the double-pass solar collector have been studied. In
addition, heat transfer and pressure drop relationships have been developed for airflow through the
porous media. Close agreement has been obtained between the theoretical and experimental results. The
study concluded that the presence of porous media in the second channel increases the outlet tem-
perature, therefore increases the thermal efficiency of the systems.
Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction A simulation study of a double-pass solar collector with porous

media has been analyzed by Mohamad [13]. The main idea is to
Several configurations of solar air heaters (SAHs) have been minimize heat losses from the front cover of the collector and to
developed in literature in searching of a suitable design for different maximize heat extraction from the absorber. Forcing air to flow
types of applications, various designs of solar collectors have been over the front glass cover (preheat the air) before passing through
the subject of many theoretical and experimental investigations the absorber can achieve this objective. Hence, this design needs an
[1–6]. There are many alternative designs to the conventional sin- extra cover to form a counter-flow heat exchanger. Porous media
gle-pass collector. These designs must be able to reduce the heat forms an extensive area for heat transfer, where the volumetric
losses from the collector to increase in the operating temperature heat transfer coefficient is very high; it will enhance heat transfer
and collector efficiencies of the system. Therefore, single-pass solar from the absorber to the airstream. In the design of this type of
collector with porous media has been introduced. Inexpensive collector, which combines double air passage and porous media,
porous materials such as stones [7], crushed glass [8], wool [9], and pressure drop should be minimized. However, the thermal effi-
metal wool [10] have been used for application in developing ciency of this type of collector is significantly higher than the
countries. The double-flow types of SAHs have been introduced for thermal efficiency of conventional air heaters, exceeding 75% under
increasing the heat transfer area, leading to improve thermal per- normal operating conditions. The pressure drop is not so significant
formance. This increases the thermal energy between the absorber if high porous medium is used and careful design of U-return
plate and the air, which clearly improves the thermal performances section is considered.
of the solar collectors with obstacles arranged into the air channel Sopian et al. [14] conducted experimental studies on the double-
duct. These obstacles allow a good distribution of the fluid flow pass solar collector with and without porous media in the second
[11,12]. channel. The collector has only one glass cover and a blackened
metal absorber and the material used as the porous media is steel
wool. To ensure good flow distribution across the bed it is necessary
that the pressure drop across the packed bed is large. However, it is
* Corresponding author. Tel.: þ60 3 8921 4592. also necessary to keep the pressure drop low so that the energy
E-mail address: ksopian@vlsi.eng.ukm.my (K. Sopian). spent in pumping the air through the bed is low to make the system

0960-1481/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.renene.2008.05.027
 K. Sopian et al. / Renewable Energy 34 (2009) 640–645 641

Nomenclature ag glass absorptivity

d thickness
A area of solar air heater (m2) s glass transmittance
B width of the collector (m) s Stefan’s Boltzmann constant (W/m2 K4)
C specific heat (J/kg K) ap plate absorptivity
G rate of airflow (kg/s) 3 emissivity
Gr Grashof number h efficiency
d1 first channel depth (m) m kinematic viscosity of air (kg/m s)
d2 second channel depth (m) Ø porosity
h heat transfer coefficient (W/m2 K)
I solar radiation (W/m2) Subscripts
k thermal conductivity (W/m K) 1&2 referred to first and second stream
L length of the collector (m) a ambient
M mass per unit area (kg/m2) b back plate
m number of harmonics c convective
Nu Nusselt number f fluid
Pr Prandtl number g glass
Re Reynolds number i inlet
T temperature (K) o outlet
t time (s) p plate
UR real loss factor (W/m2 K) pm porous media
V velocity (m/s) r radiative
x coordinate s sky

cost effective. The use of a double-pass resulted in increasing the from experimental studies used for generating the required ex-
pressure drop across the collector. However, the increase in the perimental data for validating the model are presented. It is shown
operating cost due to the increased pressure drop in the collector is that the model can predict the performance of the MNCSCD fairly
considered small. This is due to the fact that the pressure drop accurately and therefore can be used as a design tool for prototype
across the collector is small compared to the total pressure drop development.
across the system. Six different types of natural circulation air-heating solar col-
Mohamad [15], who referred the conventional double-pass lectors were designed, constructed and analysed by Koyuncu [18]
collector as a counter-current solar collector, showed that the for their performance. Each collector mainly consisted of a frame
thermal efficiency can be improved by 18% compared to the con- constructed from hardboard, vent holes, hardboard insulation,
ventional solar heater. The study also suggested an extra fan power absorbing surface made of black coated aluminium sheet and clear
of 2–3 W, which is not high. Also noted that the cost of construction plastic glazing. All solar air heaters were tested simultaneously
of the double glazing collector is comparable to the cost of the under the same environmental conditions. The experimental setup
double-pass collector. However, necessary trade-off between the was instrumented for the measurement of solar radiation, tem-
fan power and the efficiency of packed bed solar collector must be perature and relative humidity of the atmosphere air, outlet air
analyzed to obtain a cost-effective design configuration. temperature, surface temperature of the back and edge insulator
The thermal performance of a double-glass double-pass solar air and absorber plate, air speed and wind velocity. It is understood
heater with a packed bed (DPSAHPB) above the heater absorber from the results of the investigation that the performances of
plate was investigated experimentally and theoretically by Rama- Model-1, Model-2, Model-3, Model-4, Model-5 and Model-6 are
dan et al. [16]. Limestone and gravel were used as packed bed 42.11%, 45.88%, 44.23%, 39.76%, 39.05% and 36.94%, respectively,
materials. Numerical calculations were carried out, on typical and the performance of the most efficient collector (Model-2) is
summer days of 2003, to study the effect of different operational approximately 9% more than the least efficient one (Model-6). In
and configurational parameters on the heater performance. Effects addition, it is seen that unlike number of glazing sheet and air pass
of the mass flow rate of air and the mass and porosity of the packed method, the effect of the shape of the absorbing surface on the
bed material were also studied. It was inferred that for increasing performance is considerably less.
the outlet temperature Tfo of the flowing air after sunset, it is ad- In this paper, a theoretical model of a double-pass solar collector
visable to use the packed bed materials with higher masses and with porous media in the second channel has been commenced and
therefore with low porosities. It is recommended to operate the compared with indoor testing facility results. The testing facility
system with packed bed with values of equal 0.05 kg/s or lower to consists of a solar collector and a solar simulator.
have a lower pressure drop across the system.
A mathematical model for drying agricultural products in 2. Mathematical model
a mixed-mode natural convection solar crop dryer (MNCSCD) using
a single-pass double-duct solar air heater (SPDDSAH) is discussed The unsteady-state mathematical model has been developed.
by Forson et al. [17]. The model comprises the air-heating process This involves unsteady-state energy balance equations linking the
model, the drying model and the technical performance criteria outer glass cover heat transfer coefficient, and the heat transfer
model. The governing equations of the drying air temperature coefficients between the moving airstreams and surfaces forming
and humidity ratio; the material temperature and its moisture the upper and lower channels as shown in Fig. 1(a) and (b). To
content; and performance criteria indicators are derived. The simplify the analysis, the energy balance equations are written
model requires the solution of a number of interrelated non-linear under the following assumptions: (a) the temperatures of the cover
equations and a set of simultaneous differential equations. Results and plates vary only in the direction of fluid flow (x-direction);
642 K. Sopian et al. / Renewable Energy 34 (2009) 640–645

The airflow in the lower channel can be described by

 
vTf2 G C vT v2 Tf2
d2 rf2 Cf2 ¼  f2 f2  f2 þ kpm dpm
vt B vx vx2
   
þ hcpf2 Tp  Tf 2 þ hcbf2 Tb  Tf2 (4)

Heat balance at the bottom is written as

vTb    
Mb Cb ¼ hrpb Tp  Tb  hcbf2 Tb  Tf2  UR ðTb  Ta Þ
vTt
v2 T
þ kb db 2b (5)
vx
The boundary conditions are obtained from the conditions that
there is no heat loss from the side of the metallic plates. One of the
boundary conditions state that at entry point, air temperature
equals ambient temperature such as

vTf1 
Tf1 ð0; tÞ ¼ Ta ðtÞ; ¼ 0
vx x¼ðL;tÞ

Eqs. (1)–(5) are subjected to the following boundary conditions:

vTg vTp vT
For x ¼ 0 and x ¼ L; ¼ ¼ b ¼ 0
vx vx vx

Tf2 ðL; tÞ ¼ Tf1 ðL; tÞ

Radiative and convective heat transfer coefficients should be
known in order to solve above equations. Radiative heat transfer
Fig. 1. (a) Schematic of the double-pass solar collector with porous media. (b) Sche- coefficient is a function of the surfaces temperature of both sides,
matic of heat transfer coefficients in the double-pass solar collector.
while convective heat transfer coefficient is a function of the
dimensionless parameter known as Nusselt number (Nu).
 
s T12 þ T22 ðT1 þ T2 Þ
hr ¼  (6)
1 1
(b) the side losses are negligible and leakage of air to/or from ð þ 1
the collectors is negligible and (c) ideal gas with constant specific
31 32
heat.
Heat balance through glass cover can be described by
Nuk
  hc ¼ (7)
vTg   Dh
Mg Cg ¼ ag I þ hrpg Tp  Tg þ hcgf 1 Tf1  Tg
vt
    where Dh is the equivalent (hydraulic) diameter of the duct. In the
 hrgs Tg  Ts  hcga Tg  Ta (1) case of noncircular cross-sections without porous media, Dh is
Airflow between the glass cover and the plate can be written as given by

vTf 1 G C vT   4A 4ðBdÞ 2ðBdÞ

d1 rf1 Cf1 ¼  f1 f1 f1 þ hcpf1 Tp  Tf 1 Dh ¼ ¼ ¼ (8)
vt B vx p 2ðB þ dÞ ðB þ dÞ
 
þ hcgf 1 Tg  Tf 1 (2) In the case with porous media, it can be written as

Heat balance through the absorber plate can be written as 4A 2ðBdÞ

Dh ¼ f ¼ f (9)
p ðB þ dÞ
vTp v Tp 2    
Mp Cp ¼ I ap sg þ kp dp 2  hrpg Tp  Tg  hcpf 2 Tp  Tf2 Nu which is the Nusselt number is a function of Reynolds
vt vx
  number of the flow which is given by
 hrpb ðTP  Tb Þ  hcpf1 Tp  Tf1
rf Vf Dh
(3) Re ¼ (10)
m
Eq. (3) assumes that the air and solid matrix are in thermal
The flow can be divided into three regimes as
equilibrium, i.e. the temperature of the solid is equal to the tem-
perature of the air locally. The value of the effective thermal con-
(a) Laminar flow regime (Re < 2300):
ductivity (kpm) is a function of porosity, the thermal conductivity of
the solid material and the thermal conductivity of air and its value h im
is of the order of 10 times the thermal conductivity of fluid [19]. The a RePrðDLh Þ
Nu ¼ NuN þ h in (11)
value of thermal conductivity is set to 300 W/m K which is about
1 þ b RePrðDLh Þ
10 times the thermal conductivity of the air.
 K. Sopian et al. / Renewable Energy 34 (2009) 640–645 643

where the constants are a ¼ 0.00190, b ¼ 0.00563, m ¼ 1.71, n ¼ 1.17,

Pr ¼ 0.7, and NuN ¼ 5.4.
(b) Transition flow regime (2300 < Re < 6000):

   2=3 ! 0:14
2=3 1=3 Dh m Halogen lamps
Nu ¼ 0:116 Re  125 Pr 1þ
L mw
Heater
(12)
where m is evaluated at film temperature and mw is evaluated at wall Inlet
Collector
temperature.
(c) Turbulent flow regime (Re > 6000):

Nu ¼ 0:018Re0:8 Pr 0:4 (13)

where Prandtl number Pr is given as Fan
Outlet

mf Cf
Pr ¼ (14)
kf
Fig. 2. Schematic of the experimental setup with the solar simulator.
The determination of the average heat transfer coefficient, h,
between the porous media and air as follow:
3. Experimental setup
 
 T o  T i
h ¼ Gp Cp   (15) Fig. 2 shows the solar simulator and the collector undergoing
A  T m  T a
testing. The simulator uses 45 halogen lamps, each with a rated
Pressure drop or lost head is directly proportional to the length power of 300 W. The maximum average radiation of 642 W/m2 can
of the duct, proportional to the square of the flow rate, and pro- be reached. Dimmers are used to control the amount of radiation
portional to the fifth power of the duct size. Therefore, the duct- that the test collector received. The dimmers are divided into six
work designer can be relatively unconcerned about the length of scales for producing different amount of radiation values. These
the run, only moderately concerned with the circulation rate, but values have been previously measured using the pyranometer. The
must be extremely sensitive that the size of the duct is appropriate measurement errors are about 3.16% for radiation value of 277.8 W/
for the flow rate. Consequently, the pressure drop through the m2 and 4.05% for radiation value of 642 W/m2 [20]. A heater is
collectors is of highest interest since that is where the minimum placed at the inlet of the collected undergoing test to vary the inlet
dimensions are most likely to be found. We now discuss the char- temperature.
acteristics of friction factor in fluid in duct runs in the collector. An The collector consists of the glass cover, the insulated container
important fundamental relationship is the Fanning equation, given and the black painted aluminum absorber. The size of the collector
here in a modified form as is 120 cm in width and 240 cm in length. The first and second
channels can be adjusted for optimal operations. The inlet tem-
4fG2f L perature to the collector can be adjusted by heating the inlet air to
DP ¼ (16)
2gc A2x rDh the collector. Thermocouples are located strategically at the inlet,
end-of-the first pass, outlet, absorber plate and glass cover. The
where DP is the frictional loss or pressure drop, Gf is the fluid mass temperature measurements are recorded using data acquisition
flow rate, L is the length of the duct, Ax is cross-sectional area, gc is system. The flow rates are measured using the vane type
a constant (1 kg m/N s2 or 32.17 ft/s2), r is the fluid density, and f is anemometer.
a friction factor. The friction factor, f, is as empirical function of the
relative roughness of the duct.
For smooth duct, when the flow is laminar the friction factor is
given by 100 100

16 90 =70% 90
f ¼ (17)
THERMAL EFFICIENCY (%)

Re 80 Theoretical 80

And when it is turbulent is given by 70 70

60 60
0:125
f ¼ 0:00140 þ (18) 50 50
Re0:32 Experiment
40 40
The thermal performance of solar air heater can be expressed
as 30 30
20 20
GCf ðTo  Ti Þ
h¼ (19) 10 10
IA
The following values of physical parameters have been used: 0 0
546 555 565 583 614
B ¼ 1.2 m, L ¼ 2.2 m, d1 ¼ 0.07 m, d2 ¼ 0.07 m, mg ¼ 5.5 kg/m2,
SOLAR RADIATION (W/m2)
mp ¼ 6.55 kg/m2, Cf ¼ 1012 J/kg K, Cg ¼ 840 J/kg K, Cp ¼ 500 J/kg K,
kg ¼ 0.0263 W/m K, kp ¼ 237 W/m K, kb ¼ 116 W/m K, ag ¼ 0.06, Fig. 3. Variations of the experimental and theoretical efficiencies of the double-pass
ap ¼ 0.95, dg ¼ 0.004 m, 3g ¼ 0.92, and sg ¼ 0.92. solar collector with porous media (f ¼ 70%, Ta ¼ 33.5  C).
644 K. Sopian et al. / Renewable Energy 34 (2009) 640–645

100 100 100

90 =90% 90 Theoretica 90
=90
THERMAL EFFICIENCY (%)

THERMAL EFFICIENCY (%)

Theoretical
80 80 80
70 70 70
60 60 60
Experimental
50 50 Experimental 50
40 40 40
30 30 30
20
20 20
10
10 10
0
540 550 560 570 580 590 600 610 620 0 0
7.14 13.8 17.74 17.9 18.24
SOLAR RADIATION (W/m2)
TEMPERATURE RISE(oC)
Fig. 4. Variations of the experimental and theoretical efficiencies of the double-pass
Fig. 6. Effect of temperature rise on the thermal efficiency on the double-pass solar
solar collector with porous media (f ¼ 90%, Ta ¼ 33.5  C).
collector with porous media (Ta ¼ 33.5  C).

4. Experimental procedures

The lighting control of the simulator is adjusted to obtain the

required radiation levels. The solar collector is operated at varying
inlet temperature, airflow rate, channel depth, and radiation con-
ditions. Air is circulated for 30 min prior to the period in which data 100 25
are taken. The depths for the upper (d1) and lower (d2) channels are
90
THERMAL EFFICIENCY (%)

T: With porous media

TEMPERATURE RISE (OC)

varied. The upper channel is varied from 3.5 cm to 10.5 cm and the
80 : With porous media 20
lower channel is varied from 7 cm to 14 cm. The mass flow rate, G, is
varied from 0.03 kg/s to 0.07 kg/s. The porosity of the porous media 70
has been changed for each set of experiments. 60 15
50
5. Error analysis 40 10
30
The error during the experiment as follows: the mass flow rate is 20 T: Without porous media 5
about 3.2%, temperature rise is about 2.8%, area of the collector : Without porous media
10
according to the measurements is about 1.8%, and the pressure drop
0 0
through the collector was measure by a micro-manometer has an 480 500 520 580 600
error of about 0.5%. Therefore, the error on calculating the thermal
SOLAR RADIATION (W/m2)
efficiency of the system is about 8%.
Fig. 7. The effect of solar radiation on temperature rise and thermal efficiencies.

6. Results and observations

Figs. 3 and 4 give a comparison between the theoretical and

experimental efficiency for the double-pass solar collector with
saturated porous media, which varies from 70% to 90% under solar
radiation from 546 W/m2 to 614 W/m2. The thermal efficiency is 0.45

25 100 0.4 I = 550W/m2

T: With porous media 90 0.35
THERMAL EFFICIENCY (%)
TEMPERATURE RISE (OC)

: With porous media

20 80
0.3 Theoretical
70
Nu x 10-2

0.25 450W/m
15 60
50 0.2 Experimental

10 40 0.15
30
0.1
5 T: Without porous media
20 Nuap Nubp Nucp Nut,
0.05
10
: Without porous media
0 0 0
0.037 0.04 0.053 0.059 0.079 5.2 6.2 7.2 8.2 9.2 10.2 11.2
MASS FLOW RATE (kg/sec) REYNOLDS NUMBER Rex10-3

Fig. 5. Effect of the solar radiation on the thermal efficiency on the double-pass solar Fig. 8. Comparison between the experimental and theoretical Nusselt number of the
collector with porous media (f ¼ 80%, Ta ¼ 33.5  C). double-pass solar collector with porous media.
 K. Sopian et al. / Renewable Energy 34 (2009) 640–645 645

0.2 Fig. 9 shows the effect of the Reynolds number on the friction
factor. Porous media in the lower channel can be used to increase
the heat transfer coefficient since the friction factor depends on the
0.16
Without porous media
losses and velocity of the airflow rate.
FRICTION FACTOR (f)

0.12
7. Conclusion

The addition of the porous media in the second channel of the

0.08
double-pass solar collector increases the performance of the col-
With porous media lector. The theoretical model has been developed and the experi-
mental validation has been carried out. It was shown that the
0.04
theoretical simulation and experimental data were in close agree-
ment with each other. Introducing porous media in the second
0 channel increases the heat transfer area. This type of collector has
5.2 6.2 7.2 8.2 9.2 10.2 11.2 a higher thermal performance compared to the conventional sin-
REYNOLDS NUMBER, Rex10-3 gle-pass solar collector. Typical thermal efficiency of the double-
pass solar collector with porous media is about 60–70%.
Fig. 9. Effect of the Reynolds number on the friction factor on the double-pass solar
collector with porous media.

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