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7/28/2019 Performance evaluation of solar air heater for various artificial roughness geometries based on energy, effective
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Review
Performance evaluation of solar air heater for various artificial roughness
geometries based on energy, effective and exergy efficiencies
M.K. Gupta*, S.C. Kaushik
Centre for Energy Studies, Indian Institute of Technology, Delhi 110016, India
a r t i c l e i n f o
Article history:
Received 21 March 2008
Accepted 5 June 2008
Available online 24 July 2008
Keywords:
Solar air heater
Artificial roughness geometries
Energy efficiency
Effective efficiency
Exergy efficiency
Reynolds number
a b s t r a c t
A comparative study of various types of artificial roughness geometries in the absorber plate of solar air
heater duct and their characteristics, investigated for the heat transfer and friction characteristics, has
been presented. The performance evaluation in terms of hI, hef and hII has been carried out, for various
values of Re, for some selected artificial roughness geometries in the absorber plate of solar air heater
duct. The six roughness geometries as per the order of ability to create turbulence and a smooth surface
have been selected. The correlations for heat transfer and coefficient of friction developed by respective
investigators have been used to calculate efficiencies. It is found that artificial roughness on absorber
surface effectively increases the efficiencies in comparison to smooth surface. The hI in general increases
in the following sequence: smooth surface, circular ribs, V shaped ribs, wedge shaped rib, expanded
metal mesh, rib-grooved, and chamfered ribgroove. The hef based criteria also follows same trend of
variation among various considered geometries, and trend is reversed at very high Re. The hII based
criteria also follows the same pattern; but the trend is reversed at relatively lower value of Re and for
higher range ofRe the hII approaches zero or may be negative. It is found that for the higher range of Re
circular ribs and V shaped ribs give appreciable hII up to high Re; while for low Re chamfered ribgroove
gives more hII.
2008 Elsevier Ltd. All rights reserved.
1. Introduction
The heat transfer between the absorber surface (heat transfer
surface) of solar air heater and flowing air can be improved by
either increasing the heat transfer surface area using extended
and corrugated surfaces without enhancing heat transfer
coefficient or by increasing heat transfer coefficient using the
turbulence promoters in the form of artificial roughness on
absorber surface. The artificial roughness on absorber surface may
be created, either by roughening the surface randomly with
a sand grain/sand blasting or by use of regular geometric rough-
ness. It is well known that in a turbulent flow a laminar/viscoussub-layer exists in addition to the turbulent core. The artificial
roughness on heat transfer surface breaks up the laminar
boundary layer of turbulent flow and makes the flow turbulent
adjacent to the wall. The artificial roughness that results in the
desirable increase in the heat transfer also results in an undesir-
able increase in the pressure drop due to the increased friction;
thus the design of the flow duct and absorber surface of solar air
heaters should, therefore, be executed with the objectives of high
heat transfer rates and low friction losses. To balance useful
energy and friction losses, second law considerations are suitable,
and exergy is a suitable quantity for the optimization of solar air
heaters having different design and roughness elements.
Exergy is maximum work potential which can be obtained from
a form of energy [1,2]. Exergy analysis is a useful method, to com-
plement not to replace the energy analysis. Exergy analysis yields
useful results because it deals with irreversibility minimization or
maximum exergy delivery. Exergy analysis can indicate the possi-
bilities of thermodynamic improvement of the process under
consideration. The exergy analysis has proven to be a powerful tool
in the thermodynamic analyses of energy systems. Recently, theconcept of exergy has received great attention from scientists,
researchers and engineers, and exergy concept has been applied to
various utility sectors and thermal processes. In general, more
meaningful efficiency is evaluated with exergy analysis rather than
energy analysis, since exergy efficiency is always a measure of the
approach to the ideal. Ozturk and Demirel [3] experimentally
evaluated the energy and exergy efficiencies of the thermal per-
formance of a solar air heater having its flow channel packed with
Raschig rings. Kurtbas and Durmus [4] experimentally evaluated
the energy efficiency, friction factor and dimensionless exergy loss,
of a solar air heater having five solar sub-collectors of same length
and width arranged in series in a common case, for various values
* Corresponding author. Tel.: 91 11 26591253; fax: 91 11 26862037.
E-mail addresses: mkgupta1969@indiatimes.com , mk_gupta70@rediffmail.com
(M.K. Gupta), kaushik@ces.iitd.ac.in (S.C. Kaushik).
Contents lists available at ScienceDirect
Renewable Energy
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / r e n e n e
0960-1481/$ see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.renene.2008.06.001
Renewable Energy 34 (2009) 465476
mailto:mkgupta1969@indiatimes.commailto:mk_gupta70@rediffmail.commailto:kaushik@ces.iitd.ac.inhttp://www.sciencedirect.com/science/journal/09601481http://www.elsevier.com/locate/renenehttp://www.elsevier.com/locate/renenehttp://www.sciencedirect.com/science/journal/09601481mailto:kaushik@ces.iitd.ac.inmailto:mk_gupta70@rediffmail.commailto:mkgupta1969@indiatimes.com7/28/2019 Performance evaluation of solar air heater for various artificial roughness geometries based on energy, effective
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of Reynolds number. The popularity of exergy analysis method has
grown consequently and is still growing [1,57].
2. Fluid flow and heat transfer characteristic of
various type of artificial roughness geometry
The geometry of the artificial roughness has, therefore, to be
such that it should break the laminar sub-layer only without
disturbing the core to keep the pressure drop within range. The
regular geometric roughness may be classified on the basis of shape
of rib (rectangular, circular, wedge, chamfered), orientation
(transverse, inclined, V shape), arrangement on surface (continu-
ous, discrete, staggered), cavity (groove, pits/dimples) and imper-meable or porous rib. The porous rib offers lower drag force in
comparison to solid rib. Many investigators analysed various
roughness geometry [813] and attempted to develop accurate
predictions of the heat transfer coefficient and friction factor of
a given roughness geometry, and to define a roughness geometry
which gives the best heat transfer performance for a given flow
friction. Webb et al. [9] developed friction and heat transfer
correlations, for turbulent flow in tubes having repeated rib-
roughness, based on law of the wall similarity and application of
the heatmomentum transfer analogy to flow over a rough surface,
respectively. They verified the correlations with experimental data,
and argued against a single correlation for all roughness geome-
tries. Han et al. [10] investigated the rib-roughened surface for
effects of rib shape, angle of attack, spacing and pitch to heightratio. They developed the correlation for friction factor and heat
Nomenclature
Ac Collector area (m2)
Cf Conversion factor
Cp Specific heat (J/kg K)
de Equivalent hydraulic diameter of collector duct (m)
e Rib height
e Roughness Reynolds number
Ex Exergy (W)
Exc,S Exergy of solar radiation incident on glass cover (W)
Exu Exergy output rate ignoring pressure drop (W)
Exu,p Exergy output rate considering pressure drop (W)
Exd,p Exergy destruction due to pressure drop (W)
F0 Collector efficiency factor
Fr Collector heat removal factor
f Coefficient of friction
g Groove position (m)
h Enthalpy (J/kg)
hc,fb Convective heat transfer coefficient between air and
bottom plate (W/m2 K)
hc,fp Convective heat transfer coefficient between air and
absorber plate (W/m2 K)he Equivalent heat transfer coefficient (W/m
2 K)
hr,pb Radiative heat transfer coefficient between absorber
and bottom plate (W/m2 K)
hw Wind heat transfer coefficient (W/m2 K)
H Solar air heater duct depth (m)
I Radiation intensity (W/m2)
IT,c Radiation incident on glass cover (W/m2)
IR Irreversibility (W)
ki Thermal conductivity of insulation (W/m K)
ka Thermal conductivity of air (W/m K)
l Long way of mesh
L Spacing between covers (m)
L1 Collector length (m)
L2 Collector width (m)L3 Collector depth (m)
m Mass flow rate (kg/s)
M Number of glass cover
p Pressure (N/m2)
P Roughness pitch
Pr Prandtals number
Q Heat (J)
q Heat per unit area (J/m2)
Re Reynolds number
s Short way of mesh
S Absorbed flux (W/m2)
Sgen Entropy generation (J/K)
St Stanton number
T Temperature (K)
Tbm Mean bottom plate temperature (K)
Tfm Mean fluid temperature (K)
Tpm Mean absorber plate temperature (K)
Ub Bottom heat loss coefficient (W/m2 K)
Ul Overall heat loss coefficient (W/m2 K)
Us Side heat loss coefficient (W/m2 K)
Ut Top heat loss coefficient (W/m2 K)
V Velocity of air through collector duct (m/s)
VN
Wind velocity (m/s)
WP Pump work (W)
Greek symbols
aA Angle of attack for V shaped rib
aC Chamfer angle of rib
aR Rib wedge angle
b Tilt angle of collector surface
db Bottom insulation thickness (m)
ds Side insulation thickness (m)
Dp Pressure drop (N/m2)
hI Energy efficiency
hII Exergy efficiencyhef Effective energy efficiency
hpm Pumpmotor efficiency
m Viscosity of air (Ns/m2)
r Density of air (kg/m3)
s Transmissivity
sa Transmissivityabsorptivity product
j Exergy efficiency of radiation
s Stefans constant
3c Emmisivity of cover
3p Emmisivity of absorber plate
Subscripts
a Ambient
f Fluid (air)fb Fluid (air) to bottom plate
fp Fluid (air) to absorber plate
g glass
i Inlet
l Lost
o outlet/exit
p Plate
r Rough
s Smooth
S Sun
T Tilted surface
u Useful
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transfer, in order to define a roughness geometry which gives the
best heat transfer performance for a given flow friction. The use of
artificial roughness in solar air heaters owes its origin to several
investigations carried out in connection with the enhancement of
heat transfer in nuclear reactors [10], cooling of turbine blades and
electronic components. As in solar air heater the solar radiation is
absorbed by absorber plate,which is the main heat transfer surface;
therefore, the solar air heaters are modeled as a rectangular
channel having one rough wall and three smooth walls.
Prasad and Mullick [14] recommended protruding wires on the
underside of the absorber plate of an unglazed solar air heater used
for cereal grains drying to improve the heat transfer characteristics
and hence the plate efficiency factor.
Prasad and Saini [15] developed the relations to calculate the
average friction factor and Stanton number for artificial roughness
of absorber plate by small diameter protrusion wire. They used
these relations to compare the effect of height and pitch of
roughness element on heat transfer and friction factor with already
available experimental data. The friction factor for one side rough
duct is determined byassuming that the total shear force in the one
side rough duct is approximately equal to the combined shear force
from three smooth walls in a four-sided smooth duct and the shear
force from one rough wall in a four-sided rough duct. They used thefriction similarity law and heatmomentum transfer analogy.
Saini and Saini [16] carried out experimental investigation for
fully developed turbulent flow in a rectangular duct having
expanded metal mesh as artificial roughness, and developed
correlations for Nusselt number and friction factor in terms of
geometry of expanded metal mesh.
Karwa et al. [17] carried out experimental investigation, to
develop the correlation of heat transfer and friction, for flow of air
in rectangular ducts with integral and repeated chamfered rib-
roughness on one broad uniformly heated wall, and remaining
walls insulated. They observed that the Stanton number and
friction factor take their maximum values at the chamfer angle
of 15.
Verma and Prasad [18] developed the heat transfer and frictionfactor correlation for roughness elements consisting of small
diameter wires, and evaluated the thermo-hydraulic performance
using the efficiency index suggested by Webb and Eckert [20]. The
criterion for efficiency index, which is Str=Sts=fr=fs1=3, is heat
transfer of roughened duct to smooth wall duct for same pumping
power.
Jaurker et al. [19] developed the correlations for Nusselt number
and friction factor, for rib-grooved artificial roughness on one broad
heated wall. They carried out the thermo-hydraulic performance
analysis of air duct (solar air heater), based on efficiency index [20],
andconcluded that rib-grooved arrangement is better than rib only.
Similar investigations for heat transfer and fluid flow charac-
teristics have been carried out by Gupta et al. [21] for transverse
wire roughness; Momin et al. [22] for V shaped ribs; Bhagoria et al.[23] for wedge shaped rib; Sahu and Bhagoria [24] for broken
transverse ribs; and Layek et al. [25] for chamfered ribgroove
roughness.
Gupta et al. [26] investigated the thermo-hydraulic performance
in terms of effective efficiency [27] of solar air heater with rib-
roughened surface by using the heat transfer and friction factor
correlation developed by them. The effective efficiency is ratio of
net thermal energy gain to the incident radiation. The effective
efficiency takes in account the pump work by subtracting the
equivalent thermal energy from useful heat gain by air heater to get
net thermal energy gain. The equivalent thermal energy is the
amount of thermal energy that will be required to produce the
friction power/ pump work after considering the various efficien-
cies (thermal power plant efficiency; transmission efficiency; mo-tor efficiency; efficiency of the pump) of conversion from a typical
thermal power plant to the site of collector installation. Though the
effective efficiency takes in account the pump work/equivalent
thermal energy, but it does not distinguish the quality of thermal
energy. The quality of thermal energy required in thermal power
plant is superior than obtained by air heater. For a given duct
roughness geometry they computed the effective efficiency by
varying relative roughness height and mass flow rate for different
insolation, an angle of attack 60, ambient temperature equals to
300 K and wind velocity 1 m/s. They concluded that effective
efficiency attains a maximum as flow rate is varied and effective
efficiency is found to decrease with roughness height.
Karwa et al. [28] carried out the experimental investigation for
the performance of solar air heaters with chamfered repeated rib-
roughness on the airflow side of the absorber plates, and reported
substantial enhancement in thermal efficiency over solar air
heaters with smooth absorber plates. They theoretically evaluated
the thermal efficiency using correlations [17] and concluded that
these correlations can be utilized with confidence for prediction of
the performance of solar air heaters with absorber plates having
integral chamfered rib-roughness. Based on effective efficiency,
they reported that at lower Reynolds numbers relative roughness
height should be high while at higher Reynolds numbers (>14,000)
either smooth duct or roughened duct with less relative roughnessheight performs better.
Mittal et al. [29] evaluated and compared the effective
efficiency, of solar air heaters having different roughness geometry
on absorber plate, for a set of fixed system and operating param-
eters. They determined the effective efficiency by using the corre-
lations for heat transfer and friction factor developed by various
investigators. They plotted the variation of the effective efficiency
with Reynolds number for smooth absorber plate, as well as
roughened absorber plate solar air heaters for different relative
roughness height. They reported that at higher Reynolds numbers
either smooth duct or roughened duct with less relative roughness
height performs better, and reverse for lower Reynolds number.
The Reynolds number for maximum effective efficiency was in the
range 10,00014,000 for the set of parameters investigated.Layek et al. [30] numerically calculated the augmentation
entropy generation number [31] in the duct of solar air heater
having repeated transverse chamfered ribgroove roughness on
one broad wall [25]. They evaluated the entropy generation during
heat exchange between flowing air and absorber plate.
It is evident that various investigators have developed correla-
tions for heat transfer and friction factor for solar air heater ducts
having artificial roughness of different geometries. Several
researchers carried out the thermo-hydraulic performance evalu-
ation on the basis of efficiency index or effective efficiency; but the
exergy based performance evaluation of solar air heater duct
having artificial roughness on absorber plate has not been reported
so far. Thus the aim of present investigation is to carry out the
performance evaluation of the some selected artificial roughnessgeometry (Fig. 1) on the basis of exergy analysis.
2.1. Effect of Reynolds number and roughness geometry
on heat transfer and friction characteristics
There are several parameters that characterize the roughness
elements, but for heat-exchanger and solar air heater the most
preferred roughness geometry is repeated rib type, which is
described by the dimensionless parameters viz. relative roughness
height e/de and relative roughness pitch P/e. The friction factor and
Stanton/Nusselt number are function of these dimensionless
parameters, assuming that the rib thickness is small relative to rib
spacing or pitch. Although the repeated rib surface is considered as
roughness geometry, it may also be viewed as a problem inboundary layer separation and reattachment [9]. The rib creates
M.K. Gupta, S.C. Kaushik / Renewable Energy 34 (2009) 465476 467
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turbulence, by generating the flow separation regions (vortices)
one on each side of the rib, which results in enhancement in heat
transfer as well as friction. Fig. 2 shows the various possible flow
patterns downstream from a rib, as a function of the relative
roughness pitch P/e [9]. Flow separates at the rib, forms a widening
free shear layer, and reattaches at a distance of 68 times rib-
roughness height downstream from the rib. Reattachment does not
occur for P/e less than about eight except for chamfered rib or rib
groove roughness. The local heat transfer coefficients in the sepa-
rated flow region are larger than those of an undisturbed boundary
layer and wall shear stress is zero at the reattachment point; themaximum heat transfer occurs in the vicinity of the reattachment
point. A reverse flow boundary layer originates at the reattachment
point and tends toward redevelopment downstream from the
reattachment point. The effect of various parameters of artificial
roughness geometry on heat transfer and friction characteristics
based on the literature is given below:
1. Effect of Reynolds number: as the Reynolds number increases,
the friction factor decreases due to the suppression of viscous
sub-layer and approaches a constant value; whereas the
Nusselt number increases monotonously with Reynolds
number.
2. Effect of relative roughness height e/de: the enhancement of
heat transfer coefficient depends on the flow rate and therelative roughness height. As e/de increases, both the friction
factor and Nusselt number increase. The rate of increase of
average friction factor increases whereas the rate of increase of
average Nusselt number decreases, with the increase of relative
roughness height. At very low Reynolds number the effect ofe/
de is insignificant on enhancement of Nusselt number. If the
roughness height is less than thickness of laminar sub-layer
then there will not be any enhancement in heat transfer, hence
the minimum roughness height should be of same order as
thickness of laminar sub-layer at the lowest flow Reynolds
number. The maximum rib height should be such that the fin
and flow passage blockage effects are negligible.3. Rib cross-section: it is reported that by changing the rib cross-
section from rectangular to trapezoidal the friction factor is
reduced; while there is minor effect on reduction of Nusselt
number and this effect disappears at higher values of Reynolds
number.
4. Effect of relative roughness pitch P/e: the behavior has been
explained on the basis of flow separation. Forsmall P/e the flow
which separates after each rib does not reattach before it
reaches the succeeding rib. For larger relative roughness pitch
at a P/e value of about 10 the reattachment point is reached and
a boundary layer begins to grow before the succeeding rib is
encountered. However, enhancement decreases with an
increase in P/e beyond about 10.
5. Effect of angle of attack: the induced form drag is reduced dueto change in angle of attack for ribs from 90 (transverse), and
a better thermal to hydraulic performance is obtained by hav-
ing optimum angle of attack. As the angle of attack decreases,
the friction factor reduces rapidly; however, there is marginal
decrease in Nusselt number with change in angle of attack from
90 to 45. Both the heat transfer and the friction approach the
smooth wall case as the angle of attackis decreased further. The
two fluid vortices immediately upstream and downstream of
a transverse rib are essentially stagnant relative to the
mainstream flow. The span wise secondary flow created by
inclination of the rib, and movement along the rib to
subsequently join the mainstream, is responsible for the
significant span wise variation of heat transfer coefficient.
The same concept also applies in V shape arrangement of theribs and it has been reported that such arrangement enhances
Fig. 1. Roughness geometry investigated by: [a] Saini and Saini [16], [b] Verma and
Prasad [18], [c] Momin et al. [22], [d] Bhagoria et al. [23], [e] Jaurker et al. [19], [f] Layek
et al. [30].
Fig. 2. Flow pattern as a function of relative roughness pitch.
M.K. Gupta, S.C. Kaushik / Renewable Energy 34 (2009) 465476468
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the heat transfer more. The apex of such rib may be up or
downstream to flow. It can be said, on the basis of flow be-
havior, that both Stanton number and friction factor are higher
for apex down. It may be pointed out that the expanded metal
mesh is a combination of apex up and down V shape ar-
rangement of the ribs.
6. Chamfering of the rib: chamfering of the rib decreases the
reattachment length by deflecting the flow and to reattach it
nearer to the rib. The decrease in reattachment length permits
to organize the ribs more closely. Chamfering of the rib also
increases the shedding of vortices generated at the rib top that
results in increase turbulence. The optimum chamfering angle
on the basis of thermodynamically performance has been
reported equal to 1518. For higher chamfer angle flow
separates from the rib top surface and generates boundary
layer, which decreases the heat transfer. The friction factor
increases monotonously due to the creation of vortices.
7. Combined turbulence promoter: the groove in inter rib space
and nearer the reattachment point of heat transfer surface
induces vortices in and around the groove. These vortices
increase the intensity of turbulence. The optimum relative
roughness pitch is less in comparison to simple ribbed
surface; the reported optimum relative groove position g/P isabout 0.4.
3. Thermodynamic modeling
3.1. Analysis of solar air heater
The collector under consideration consists of a flat glass cover
and a flat absorber plate with a well insulated parallel bottom plate
forming a passage of high duct aspect ratio through which the air to
be heated flows as shown in Fig. 3. The heat gain by air may be
calculated by following equations
Qu Ac
S Ul
Tpm Ta
AcsgapIT;c Ul
Tpm Ta
(1)
Qu mcpTo Ti (2)
Qu AcFrS UlTi Ta (3)
where Fr is collector heat removal factor and is given by
Fr mcpUlAc
"1 e
UlAc F0
mcp
#(4)
The collector efficiency factor F0 is
F0
1
Ulhe
1(5)
and the equivalent heat transfer coefficient he is
he hc;fp hr;pbhc;fb
hr;pb hc;fb
(6)The hc,fp and hc,fb are heat transfer coefficient due to convec-
tion from absorber plate to flowing air, and from bottom plate to
flowing air, respectively. The hr,pb is heat transfer coefficient due to
radiation from absorber plate to bottom plate.
The mean absorber plate temperature from Eqs. (1) and (3) isgiven by
Tpm Ta Ql
UlAc Ti
QuAcFrUl
1 Fr (7)
where Ql SAc Qu is heat loss from the air heater.
The mean fluid temperature is given by
Tfm 1
L1
ZL10
Tf dx Ti Qu
AcFrUl
1
FrF0
(8)
Considering solar air heater (Fig. 3) as a control volume (CV), the
law of exergy balance [2] for this CV can be written as
Exi Exc;S ExW Exo IR (9)where Exi and Exo are the exergy associated with mass flow of
collector fluid entering and leaving the CV; Exc;S IT;cAcjS [32] is
exergy of solar radiation falling on glass cover; ExW is exergy of
work input required to pump the fluid through FPSC, and IR is ir-
reversibility or exergy loss of the process. The exergy balance (Eq.
(9)) can be written as
IR Exc;S Exo Exi ExW (10)
The term in the bracket (Eq. (10)) represents the useful
exergy or exergy output rate delivered by the solar collector. As
the Exc,S, exergy of solar radiation falling on glass cover, is
fixed for a particular instant; thus minimization of entropy
generation or irreversibility is equivalent to maximization of
exergy output rate delivery of collector. Thus our aim in FPSC
must be to increase the exergy output rate delivered to
collector fluid out of the solar radiation/heat absorbed by the
absorber. The useful exergy or exergy output rate Exu
delivered by a solar collector using exergy balance equation for
collector fluid, ignoring pressure drop/pumping work Wp or
ExW, is given by
Exu mho Taso hi Tasi mho hi Taso si
(11)
For an incompressible fluid or perfect gas it can be written as
Exu mcpTo Ti Ta lnTo=Ti Qu mcpTa lnTo=Ti
(12)
The Exu,p, actual exergy rate delivered considering pressure drop
of collector fluid, is
Exu;p Exu Exd;p (13)
where the exergy destruction due to pressure drop Exd,p is
Exd;p TaTi
Wp (14)
The Wp, pump work, is
Wp mDp=hpmr
(15)
where hpm, the pumpmotor efficiency, is taken equal to 0.85.Fig. 3. Flat plate solar air heater.
M.K. Gupta, S.C. Kaushik / Renewable Energy 34 (2009) 465476 469
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Table 1
Correlations for heat transfer and coefficient of friction
Authors Types of
roughness
Correlations
Nusselt number Coefficient of friction
Saini and
Saini [16]
Expanded
metal meshNu 4:0 104Re1:22
e
de
0:625 s10e
2:22 l10e
2:66
exp
1:25
ln
s
10e
2!exp
" 0:824
ln
l
10e
2#f 0:815Re0:361
10e
de
0:591 le
0:266 s10e
0:19
Verma and
Prasad
[18]
Circular
ribsNu 0:08596Re0:723
e
de
0:072Pe
0:054for e 24
Nu 0:02954Re0:802
e
de
0:021Pe
0:016for e > 24
9=;
where e e
de
ffiffiffif
2
rRe
f 0:245Re1:25
e
de
0:243Pe
0:206
Momin
et al. [22]
V shaped
ribsNu 0:067Re0:888
e
de
0:424aA60
0:077exp
0:782
ln
aA60
2!f 6:266Re0:425
e
de
0:565aA60
0:093
exp 0:719lnaA60
2
!
Bhagoria
et al. [23]
Wedge
shaped ribNu 1:89 104Re1:21
e
de
0:426Pe
2:94aR10
0:018
exp
" 0:71
ln
P
e
2#exp
1:5
ln
aR10
2!f 12:44Re0:18
e
de
0:99Pe
0:52aR10
0:49
Jaurker et al.
[19]
Rib-
groovedNu 0:002062Re0:936
e
de
0:349Pe
3:318exp
"
0:868
ln
P
e
2#exp
2:486
ln
g
P
21:406
ln
g
P
3!gP
1:108f 0:001227Re0:199
e
de
0:585
P
e
7:19g
P
0:645
exp
"1:854
ln
P
e
2#exp
1:513
ln
g
P
2
0:862
lng
P
3!
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3.2. Heat transfer and pressure drop
The overall heat loss coefficient Ul is sum of Ub, Us and Ut of
which Ub and Us for a particular collector can be regarded as con-
stant while Ut varies with temperature of absorber plate, number of
glass covers and other parameters. The top heat loss coefficient Ut is
evaluated empirically [33] by
Ut
264
MC
Tpm
Tpm Ta
M f0
0:252 1hw375
1
s
T2pm T2a
Tpm Ta
1
3p 0:0425M
1 3p 2M f0 1
3c M
26664
37775 16
In which f0 9=hw 9=h2wTa=316:91 0:091M,
C 204:429cos b0:252=L0:24 and the heat transfer coefficient
due to convection at the top of cover due to wind is
hc;ca
hw
5:7
3:8VN (17)
The overall loss coefficient is given by
Ul Ub Us Ut In which Ub kidb
and
Us L1 L2L3ki
L1L2ds18
The radiation heat transfer coefficient hr,pb between absorber
plate and bottom plate is given by
hr;pb
Tpm Tbm
s
T4pm T4bm
1
3p
1
3b 1
(19)
For small temperature difference between Tpm and Tbm on ab-
solute scale the above equation can be written as
hr;pby4sT3av=1=3p 1=3b 1, where Tav Tpm Tbm=2
and Tav is taken equal toTfm in iterativecalculation using thesame logic.
For smooth duct the convection heat transfer coefficients be-
tween flowing air and absorber plate hc,fp, and flowing air and
bottom plate hc,fb are assumed equal. The following correlation for
air, for fully developed turbulent flow (if length to equivalent di-
ameter ratio exceeds 30) with one side heated and the other side
insulated [34] is appropriate:
Nu hc;fpde
ka 0:0158Re0:8 (20a)
If the flow is laminar then following correlation by Mercer fromDuffie and Beckman [35] for the case of parallel smooth plates with
constant temperature on one plate and other plate insulated is
appropriate:
Nu hc;fpde
ka 4:9
0:0606
Re Pr
deL1
0:5
1 0:0909
Re Pr
deL1
0:7Pr0:17
(20b)
The characteristic dimension or equivalent diameter of duct is
given by
de
2L2H
L2 H (21)Layeketal.
[30]
Chamfered
ribgroove
Nu
0:
00225Re0
:92
ede
0
:52P e1
:72g P
1:
21
a1
:24
C
exp
"
0:
46
ln
P e2#e
xph
0:
22lnaC2i
exp
0:
74
lng P2!
f
0:
00245Re
0:
124
ede
0
:365P e4
:32g P
1:
24
exp0
:005aC
exp1
:09lnP e
2
exp0
:68lng P2
i
i
e=de:
0:
022
0:
04f0
:04g
P=e:4
:5
10f6g
g=P:0
:3
0:
6f0
:4g
aC:
5
30f18g
Re:
30
00
21
;000
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For a particular Reynolds number Re, the velocity of flow is
calculated by
V mRe
rde(22)
While the mass flow rate is calculated by
m L2HVr mL2 HRe2 (23)
The pressure loss Dp through air heater duct is
Dp 4fL1V
2r
2de(24)
If Re rVde=m 2300, i.e. laminar flow, then coefficient of
friction for smooth duct is calculated by
f 16
Re(25)
otherwise the coefficient of friction f for the turbulent flow in
smooth air duct is calculated from Blasius equation, which is
f 0:0791Re0:25 (25b)
The correlations developed for heat transfer and friction
factor, for artificially roughened solar air heater of some selected
roughness geometries by their investigators are given in Table 1.
The equivalent heat transfer coefficient for roughened solar air
heater is calculated from he kaNu=de, using the Nusselt
number relation of that particular roughness geometry; similarly
the coefficient of friction f is calculated using the relation of that
particular roughness geometry. Table 1 also shows the range of
parameters investigated by the respective investigators. For Re
less than the lowest value of investigation, the correlations for
smooth duct are used even though the duct is roughened. As at
lower Re the variation in Nu with roughness parameters i.e. P/e, e/
de is insignificant, hence, for Re less than the lowest value ofinvestigation, the heat transfer and coefficient of friction corre-
lation for smooth duct are used. Also for laminar flow and
turbulent flow at low Re, as fdoes not depend on roughness, thus
as per Nuners law the correlation for smooth duct can be used
even though the duct is roughened.
3.3. Energy efficiency, effective efficiency and exergy efficiency
The energy efficiency of solar air heater based on first law of
thermodynamics is calculated by
hI Qu
IT;cAc(26)
The effective efficiency [27] of solar air heater is calculated by
hef Qu
Wp=Cf
IT;cAc
(27)
The conversion factor Cf takes in account various efficiencies
(thermal to mechanical) and is taken 0.2.
The exergy collection efficiency based on second law of
thermodynamics, by taking exergy of sun radiation [32], can be
written as
hII Exu;p
AcIT;cjS
Exu;p
Ac
IT;c1
4
3Ta
TS
1
3Ta
TS4
(28)
4. Numerical calculations
Numerical calculations have been carried out to evaluate the
energy efficiency, effective efficiency and exergy efficiency, for
a collector configuration, system properties and operating condi-
tions.The thermal behavior of artificially roughened solar air heater
is similar to that of usual flat plate conventional air heater; there-
fore, the usual procedures of calculating the absorbed irradiation
and the heat losses are used. The set of system roughness param-
eter (shown in bracket of Table 1, column-5) for particular rough-
ness geometry, at which thermo-hydraulic behavior has been
reported best, is selected for the analysis.
In order to evaluate the efficiencies for a particular Re first
initial values of Tpm and Tfm are assumed according to inlet
temperature of air and various heat transfer coefficients are
calculated; and new values of Tpm and Tfm are calculated using Eqs.
(16)(23) and (3)(8). If the calculated new values of Tpm and Tfmare different than the previously assumed values then the iteration
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
10
20
30
40
50
60
70
80
Reynolds number
Efficiency(%)
IIx10
ef
I
Bhagoria et al. (2002)
Fig. 4. Variation of energy, effective and exergy efficiencies with Reynolds number for
wedge shaped roughness geometry.
0 2000 4000 6000 8000 10000 12000 14000 16000 180000
10
20
30
40
50
60
70
80
Reynolds number
Efficiency(%)
IIx10
ef
IMomin et al. (2002)
Fig. 5. Variation of energy, effective and exergy efficiencies with Reynolds number forV shaped roughness geometry.
M.K. Gupta, S.C. Kaushik / Renewable Energy 34 (2009) 465476472
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is repeated with these new values till the absolute differences of
new value and previous value of mean plate as well as mean fluid
temperature are less than or equal to 0.05. Air properties are
determined at Tfm by interpolation from air properties [36]. The
heat gain and outlet temperature of air are calculated from Eqs. (2)
and(3). Theexergy output rate is calculated using the Eqs. (24), (25)
and (12)(15). The various efficiencies are evaluated from the Eqs.
(26)(28).
In order to obtain the results numerically, codes are developed
in Matlab-7 using the following fixed parameters:
L1 2 m, L2 1 m, Ac 2 m2, H 3.0 cm, Ki 0.04 W/m K,
L 4 cm, db
6 cm, ds
4 cm, 3p
0.95, 3c
0.88, 3b
0.95,
ap 0.95, sg 0.88, sa 0.9, b 30, Tfi 30
C, Ta 30C,
VN 1.5 m/s, TS 5600 K and IT 1000 W/m2.
The performance evaluation has also been carried out for
various values of duct width (L2) and duct depth (H).
5. Results and discussion
Figs. 46 show the variation of efficiencies (hI, hef and hII) with
Reynolds number to show the difference in these efficiencies. The
variation ofhI with Re, for various considered geometries (rough or
smooth), is shown in Fig. 7. It is evident from Figs. 47 that the hIincreases with Re forall type of geometries, andhI of any considered
rough surface is always higher than smooth surface. It is also clear
that hI of roughened surface, at a Re, depends on ability to create
turbulence. The hI, among the considered geometries, in general
increasesin the following sequence: smooth surface, circular ribs, V
shaped ribs, wedge shaped rib, expanded metal mesh, rib-grooved,and chamfered ribgroove. The hI of expanded metal mesh geom-
etry becomes greater than hI of rib-grooved and chamfered rib
groove geometry for higher values of Re; while at low Re the hI of V
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
40
45
50
55
60
65
70
75
80
Reynolds number
I(%)
Saini and Saini (1997)
Verma and Prasad (2000)
Momin et al. (2002)
Bhagoria et al. (2002)
Jaurker et al. (2006)
Layek et al. (2007)
smooth duct
Fig. 7. Variation of energy efficiency with Reynolds number for various roughnessgeometries.
0 0.5 1 1.5 2 2.5
x 104
0
10
20
30
40
50
60
70
Reynolds number
Efficiency(%)
IIx10
ef
ISmooth duct
Fig. 6. Variation of energy, effective and exergy efficiencies with Reynolds number for
smooth solar air heater duct.
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
40
45
50
55
60
65
70
75
Reynolds number
ef(%)
Saini and Saini (1997)
Verma and Prasad (2000)
Momin et al. (2002)
Bhagoria et al. (2002)
Jaurker et al. (2006)
Layek et al. (2007)
smooth duct
Fig. 8. Variation of effective efficiency with Reynolds number for various roughness
geometries.
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
40
45
50
55
60
65
70
75
Reynolds number
ef(%)
L2=0.5m, H=0.03m
Saini and Saini (1997)
Verma and Prasad (2000)
Momin et al. (2002)
Bhagoria et al. (2002)
Jaurker et al. (2006)
Layek et al. (2007)
smooth duct
Fig. 9. Variation of effective efficiency with Reynolds number for various roughnessgeometries at duct width0.5 m.
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shaped ribs geometry is more than hI of wedge shaped rib
geometry.
It is evident from Figs. 46 that initially the hI is nearly equal to
hef, and their difference increases with Re; though (hI hef) is not
appreciable up to very high Re.
The variation ofhef with Re, for various considered geometries
(rough or smooth), is shown in Fig. 8. It is evident that hef follows
the trend, of variation among various considered geometries,
indicated by variation ofhI with Re (Fig. 7), up to very high value
(>20,000) of Re. The hef attains maximum, and then decreases
with Re; though this is not clear from Fig. 8 with the taken value
of duct width (L2) and duct depth (H). As the frictional pressure
drop/pump work through a duct strongly depends on flow cross-sectional area, thus the simulation has been done for various
reduced values of L2 and H; and the variation of hef with Re for
various reduced values of L2 and H is shown in Figs. 911. It can
be concluded from Figs. 911 that effect, on hef, of reduction in H
is more dominant than reduction in L2. The hef, for lower duct
depth, reaches maximum value at reduced value of Re; for values
of Re greater than 12,00014,000 the roughness geometry which
creates less turbulence gives more hef. The trend, of variation
among various considered geometries, for lower value of L2 and H
is reversed even at low Re as pump work becomes significant. It is
also evident that at higher Re only circular ribs and V shaped ribs
become effective, as there is no appreciable gain in effective
efficiency (for Re 12,00018,000) from other geometries. The
maximum hef of roughened geometries, which creates greater
turbulence, decreases with decrease in duct depth. The hef of
roughened geometries creating greater turbulence becomes less
than that of smooth surface duct at higher Re.The hII (Figs. 46) first increases, reaches maximum value
corresponding to Re in laminar flow regime (for low inlet tem-
perature of air) and then decreases with Re. The useful heat gain
will be less corresponding to Re in laminar flow regime, thus the
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
0
5
10
15
20
25
Reynolds number
L2=0.5m, H=0.03m
Saini and Saini (1997)
Verma and Prasad (2000)
Momin et al. (2002)
Bhagoria et al. (2002)
Jaurker et al. (2006)
Layek et al. (2007)smooth duct
Fig. 13. Variation of exergy efficiency with Reynolds number for various roughnessgeometries at duct width0.5 m.
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
0
5
10
15
20
25
Reynolds number
IIx10(%)
Saini and Saini (1997)
Verma and Prasad (2000)
Momin et al. (2002)
Bhagoria et al. (2002)
Jaurker et al. (2006)
Layek et al. (2007)
smooth duct
Fig. 12. Variation of exergy efficiency with Reynolds number for various roughness
geometries.
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
45
50
55
60
65
70
75
Reynolds number
ef(%)
L2=0.5m, H=0.02m
Saini and Saini (1997)
Verma and Prasad (2000)
Momin et al. (2002)
Bhagoria et al. (2002)
Jaurker et al. (2006)
Layek et al. (2007)
smooth duct
Fig. 10. Variation of effective efficiency with Reynolds number for various roughness
geometries at duct width0.5 m and duct depth0.02 m.
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 104
45
50
55
60
65
70
75
Reynolds number
ef(%)
L2=0.3m, H=0.02m
Saini and Saini (1997)
Verma and Prasad (2000)
Momin et al. (2002)
Bhagoria et al. (2002)
Jaurker et al. (2006)
Layek et al. (2007)
smooth duct
Fig. 11. Variation of effective efficiency with Reynolds number for various roughnessgeometries at duct width0.3 m and duct depth0.02 m.
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flow may be made turbulent at the cost of decrease in hII. The hIIdecreases with Re in turbulent flow regime for low inlet tem-
perature of air, as quality of collected heat decreases and pump
work increases.
The variation ofhII with Re, for various considered geometries
(rough or smooth), is shown in Fig. 12. It is evident that initially hIIalso follows the trend, of variation among various considered
geometries, indicated by variation ofhI with Re (Fig. 7), but only up
to value ofRe around 14,000. The trend, of variation among various
considered geometries, is reversed for value of Re higher than
around 14,000. For higher Re around 20,000 the hII of considered
geometries, except smooth duct, circular ribs and V shaped ribs,
approaches zero. The reason for this is that at higher Re the Exd,papproaches Exu due to increase in pumping power requirement.
Figs. 1315 show the variation of hII with Re for various reduced
values ofL2 and H. It is also evident from Figs. 1315 that thehII may
be negative at even lower value of Re. The hII, for lesser duct depth,
decreases rapidly with Re for wedge shaped rib, expanded metal
mesh, rib-grooved, and chamfered ribgroove i.e. in the order of
ability to create turbulence. The hII also follows the trend, of
variation among various considered geometries, as indicated by
Figs. 911; but the trend is reversed at further low value of Re in
comparison to hef trend. The maximum hII of roughened geome-
tries, which occurs at low Re, increases with decrease in duct depth.
The hII of roughened geometries, creating greater turbulence, at
higher Re becomes less than that of smooth surface duct.
6. Conclusion
The efficiencies are improved by using roughened geometries in
the duct of solar air heater. The hef based criterion suggests to use
the roughened geometries for very large value of Re. The hII based
criterion shows that at very large value ofRe the hII may be negative
or exergy of pump work required exceeds the exergy of heat energy
collected by solar air heater. Thus hII provides the meaningful cri-
terion for performance evaluation. There is not a single roughened
geometry which gives best exergetic performance for whole range
ofRe. For largerflow cross-section area of solar air heaterduct along
with low Re the roughened geometry should create more turbu-
lence; while smooth surface, circular ribs and V shaped ribs are
suitable for smaller flow cross-section area of solar air heater duct
and high Re.
Acknowledgement
The first author gratefully acknowledges Ujjain Engineering
College, Ujjain, M.P. (India) and IIT Delhi (India), for sponsorship
under quality improvement program of government of India.
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