 Open Access
 Total Downloads : 293
 Authors : Ankit Kumar, Vijay Singh Bisht
 Paper ID : IJERTV6IS080050
 Volume & Issue : Volume 06, Issue 08 (August 2017)
 DOI : http://dx.doi.org/10.17577/IJERTV6IS080050
 Published (First Online): 04082017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Exergetic Performance Evaluation and Comparative Study of A Roughened Solar Air Heater using MATLAB
Ankit Kumar 1,
1 CSIRIndian Institute of Petroleum, Dehradun, Uttarakhand, 248005, India
Vijay Singh Bisht 2
2Department Of Thermal Engineering,
Faculty of Technology, Uttarakhand Technical University, Dehradun 248007, Uttarakhand, India
Abstract A comparative study based on exergetic performance of two different types of artificial roughness geometries on the absorber plate of solar air heater has been presented. The performance evaluation in terms of thermal efficiency (th), effective efficiency (eff), exergetic efficiency (II) and different exergy loss parameters has been carried out analytically, for various values of temperature rise parameter (T/I) and relative roughness height (e/D). The second law based exergy analysis is suitable for design of rib roughened solar air heaters as it incorporates quality of useful energy output and pumping power. The two roughness geometries are discrete Wshape rib roughness and Wshape rib roughness have been selected. The correlations for heat transfer and coefficient of friction developed by respective investigators have been used to calculate efficiencies. It was investigated that discrete Wshape rib roughness has better thermal efficiency (th), effective efficiency (eff) and exergetic efficiency (II) as compared to the Wshape rib roughness. The optimum parameters are relative roughness height (e/D) of 0.3375 at an angle of attack of 60Âº and isolation value of 1000 w/m2. It was investigated that discrete Wshaped rib roughness has 33% more exergetic efficiency then Wshaped rib roughness under similar performance parameters such as aspect ratio (8), relative roughness height (e/D) of 0.03375, angle of attack () of 60Âº, relative roughness pitch (P/e) of 10 and isolation value of 1000 w/m2 with Reynolds number ranges from 4000 to 14000. Curves of thermal efficiency (th), effective efficiency (eff), exergetic efficiency (II) and different exergy loss parameters with respect to temperature rise parameter (T/I) and relative roughness height (e/D) are also plotted.
Keywords Exergetic efficiency, MATLAB, Artificial roughness, Solar air heater, W and discrete W shape roughness.

INTRODUCTION
Energy is defined as the universal measure of work for human, nature and machine. It is basically an input to everything to perform work however it also refers to a condition or state of matter. Energy is a basic ingredient to the recipe of day to day life. Solar energy, one of the sources of renewable energy, is the only energy whose small amount supplies a lot of energy. It is clean and most plentiful energy resource among renewable energy resources. Solar energy is universally available source of
inexhaustible energy but the major drawbacks of this energy are that it is a dilute form of energy, which is available sporadically and uncertainly. Solar air heaters are mostly acceptable because of their simplicity in structure, functioning and most widely used solar energy collector device (i.e., [1]). These are the device which converts solar energy into thermal energy which is used for various purposes. They are less efficient because of low convective heat transfer coefficient value between absorber plate and flowing air. Their efficiency can be increased with the provision of roughness that can break laminar sub layer. Due to this artificial roughness local turbulence is created which helps in increasing the amount of heat transfer. Numerous study of artificial roughness attributed largely in the field of solar air heater to enhance their performance. Important phenomena responsible for heat transfer enhancement in solar air heater are enhanced turbulence, generation of secondary flows, flow separations and reattachments and mixing. Initial investigated roughness are transverse wires (i.e., [2,3]) Vup (i.e., [4]), (transverse,
inclined, Vup and Vdown) (i.e., [5]), arc shaped (i.e., [6]) and multiple Vrib (i.e., [7]). They contributed
Nomenclature
Ap
Surface area of absorber
T
Temperature rise across duct
D
plate/collector, m2
Equivalent hydraulic diameter
T/I
Temperature rise parameter,
of duct, m
Km2/W
e
Rib height, m
Ub
Bottom loss coefficient,
W/m2K
e/D
Relative roughness height
Us, Ue
Side/Edge loss coefficient,
f
Friction factor
Ul
W/m2K
Overall heat loss coefficient,
h
Convective heat transfer
Ut
W/m2K
Top loss coefficient, W/m2K
I
coefficient, W/m2K
Insolation, W/m2
W
Width of absorber plate, m
Isc
Solar constant, W/m2
W/w
Relative roughness width
Nu
Nusselt number
V
Velocity of air in duct, m/s2
Nus
Nusselt number for smooth duct
VR
Volume of ribs per meter square of collector plate,m3
P/e
Relative roughness pitch
Vw
Wind velocity, m/s2
(P)d
Pressure drop across duct
ELT
Exergy losses by working
fluid
Pr
Prandtl number
ELP
Exergy losses by friction
Qu
Useful heat gain, KW
ELA
Exergy losses by Absorber
plate
Re
Reynolds number
ELE
Exergy losses by convective
and radiative
Ta
Ambient temperature, K
th
Thermal efficiency
Tfm
Mean bulk air temperature, K
eff
Effective efficiency
Ti
Inlet air temperature, K
Greek symbols
To
Outlet air temperature, K
Angle of attack(Â°)
Tpm
Mean plate temperature, K
c
Carnot efficiency
tg
Thickness of glass cover, m
II
Exergetic efficiency
tp
Thickness of absorber plate, m
th
Thermal efficiency
Transmissivityabsorptivity
product of glass cover
Well in thermal performance but do not affect value of convective heat transfer coefficient. It was obtained that inclination of rib results generation of vortices and secondary flow which affect value of heat transfer as compared to the continuous ribs. With the continuous research over solar air heater roughness further enhancement in effectiveness of solar air heaters, studis were performed by applying discrete rib roughness in various configurations such as Vshaped discrete (i.e., [8]), Vup and Vdown discrete rib arrangements (i.e., [9]) and staggered discrete Vshaped ribs (i.e., [10]) In all these arrangements Vdown discrete arrangement gives the best heat transfer performance but at the expanse of large friction losses. To reduce frictional losses investigator, introduce gaps with in the roughness geometries; viz. inclined rib with gap [(i.e., [11]) Vrib with gap [(i.e., [12]) and multi Vrib with gap [(i.e., [13]) With the help of gap added advantage of secondary flow through the gaps while moving along inclined ribs and through gaps fluid accelerated which erupting the growth of boundary layer
and on the other hand friction factor encountered less then continuous ribs. Other than inclined and transverse ribs roughness arc shape roughness are also investigated to enhance the heat transfer and efficiency of solar air heater. Saini and Saini (i.e., [14]) investigated Arc shaped ribs in which enhancement obtained in order of 3.6 and 1.75 for Nusselt number (Nu) and Friction factor (f). Singh et al (i.e., [15]) investigate multi arc shaped rib roughness on the underside of absorber plate to produce an effective and economical method to improve thermal performance of solar air heater where maximum enhancement in Nusselt number (Nu) and friction factor (f) is 5.07 and 3.71 respectively for multiple arcshaped roughness geometry as compared to smooth one. Pandey et al (i.e., [16]) experimental studied the effect of multiple arc with gap on absorber plate. The air passing through gap creates turbulence at the downstream side. Larger the value of gap width, smaller is air velocity through gap and higher the downstream disturbance area. Further increase in relative roughness pitch (p/e) number of reattachment point
diminishes hence less amount of heat transfer takes place. Various CFD investigation have reported enhancement in the thermal performance of solar air heaters by testing roughness geometries similar to those being employed for the experimental investigations by many researchers in the past. Bhagoria et al. (i.e., [17]) studied thermo hydraulic investigation of Equilateral triangular sectioned rib roughness on the absorber plate. Bhagoria et al. (i.e., [18]) studied a CFD based heat transfer and fluid flow characteristic investigation of repeated transverse square sectioned rib roughness on the absorber plate. The maximum enhancement in the Nusselt number (Nu) and friction factor (f) was found to be 2.86 & 3.14 times over the smooth duct. The exergy is given for any system at particular state is maximum extraction of work up to its thermodynamic equilibrium state with the surrounding. Exergetic concept is very important for all energy producing, energy consuming and energy conveying system. First law of thermodynamics clarifies energy analysis of thermodynamic system without any comment on its quality. Second law of thermodynamics clarify that different form of energy has different quality and energy always degrade by its quality. it is analyzed from first and second law of thermodynamics that energy and exergy based analyses has to be carried out for every energy producing, energy consuming and energy conveying system to make them more exergy efficient, which leads us to energy saving for given system. So it is the second law of thermodynamics which provide information about quality of energy. It provides the concept of available
roughness geometries and operating parameters, as given in Table (1) for the collector under consideration, have been selected. The procedure adopted for the estimation of exergetic efficiency is same as it was given by Chamoli et al. (i.e., [19]) & Sahu et al. (i.e., [20]) and the computation procedure was carried out in MATLAB. For this purpose a step by step procedure has to be followed. The procedure for the estimation of exergetic efficiency is discussed below.
Table 1: Typical values of system and operating parameters used in analytical calculations
Parameters
Range / Base Values
System parameters
Collector length (L)
1.5 m
Collector width (W)
0.02 m
Collector height (H)
0.025 m
Transmittance absorptance ()
0.8
Emittance of glass (g)
0.88
Emittance of plate (p)
0.9
Thickness of glass cover (tg)
0.004
Number of glass covers (N)
1
Thickness of insulation (ti)
0.05 m
Thermal conductivity of insulation (K)
0.037 W m1 K1
Relative roughness pitch (P/e)
10
Aspect ratio (W/H)
8
Angle of attack ()
60Âº
Operating parameters
Relative roughness height (e/D)
0.0180.03375
Ambient temperature (Ta)
300 K
Wind velocity (Vw)
1 m s1
Insulation (I)
1000,500 W m2
Temperature rise parameter (T/I) Âºc
m2/W
0.0050.035
Step 1: Area of plate is calculated as,
energy or exergy. With the concept it is possible to analyze means of minimizing the consumption of exergy to
perform given process, thereby ensuring the most efficient
Ap W H
(1)
possible conversion of energy for the required task. In this paper exergetic investigation has carried out on roughened
Step 2: Hydraulic diameter of duct is calculated as
D 2(W H )
solar air heater having discrete Wshape and Wshaped rib
roughness on absorber plate. As well as comparative study
W H
(2)
of their performance on different flow parameters and optimum results are obtained. On the basis of design plots were also prepared in order to facilitate the designer for designing roughened solar air heater within the investigated operating and roughness parameters.

MATHEMATICAL MODEL AND MATLAB CODE FORMATION
Step 3: A set of system parameters namely relative roughness pitch (P/e) and relative roughness height ratio (e/D) is selected.
Step 4: A set of values of design parameters namely isolation and temperature rise parameter is selected.
Step 5: The outlet temperature To is calculated as.
T T T I
(3)
In order to evaluate the exergetic efficiency (eff) of solar air heater as per Eq. (21), the calculation starts and proceeds by taking values (base and range) of systems and operating parameters as applicable for solar air heaters. The stepwise calculation procedure is given below. The range/base values of system parameters including
o i I
Step 6: Inlet air temperature equals to ambient temperature. The outlet air temperature is calculated from desired temperature rise of air across the duct (T) and the inlet air temperature.
Step 7: Mean film temperature is calculating as.
Tfm Ti To
2
(4)
Qu 2 Fo[I () UL(To Ti)]Ap
(12)
Step 8: Approximate initial mean plate temperature is assumed.
Tpm 300;
Step 9: Using the value of the plate temperature Tp, value of top loss coefficient, Ut is computed by using equation proposed by Klein (1975) given as, (i.e., [21])
Step 17: At this stage, the difference between the two values of useful heat gain Qu1 and Qu2 is checked. Ideally the two values should be same. However, if the difference in two values is more than 0.1% of Qu1, then the plate temperature is modified as,
Ut [( (Tp2 Tg 2 )Tp Tg) / A) (kaNu / Lg)]1 B (5) Where,
Tpm Ta [(I () (Qu 2 / Ap) / UL]
(13)
A (1/ p) (1/ g ) 1
B [ g (Tp 2 Tg 2 )(Tp Tg ) hw]1 (tg / kg )]
Tg [F1Tp CTa / 1 F1]
F1 [12108 (Ta 0.2Tp) hw]1 0.3tg] / D
D [6108 ( 0.028)(Tp 0.5Ta)3 0.6Lg 0.2{(Tp Ta) cos }0.25 ]1
Step 18: Friction factor, f is calculated using the correlation
developed in a previously, this is mentioned above in equation;
Step19: Using the value of friction factor, the pressure drop (P), across the duct is calculated as follow:
C [((T / T ) (h / 3.5)) / (1 (h / 3.5))]
P 4 fLv2 / 2D
(14)
s a w w
T 0.0522(Ta)1.5
Back loss coefficient Ub is expressed as
Ub (ki / ti)
The edge loss coefficient, based on the collector area is
Step 20: Thermal efficiency is calculated
th Fo[ UL((Tfm Ta) / I )]
(15)
given as; Ue (Dteki / ti)
Step 21: The effective efficiency, eff is calculated as;
Finally,
[(Q (P / c)) / IA ]
(16)
UL Ub Ue Ut
eff u m p
Step 10: Useful energy gain is calculated by Hottel WhillierBliss equation,
Step 22: Logarithmic mean fluid temperature (T
fm) is
Qu1 [I () UL(Tp Ta)]Ap
(6)
calculated as follow,
Step 11: Mass flow rate is determined from the expression given as;
Tfm [(To Ta) / (ln(To / Ta)]
(17)
m [Qu1 / CpT ]
(7)
Step 23: Carnot efficiency based on logarithmic mean fluid
Step 12: Reynolds number of flow of air in the duct is computed as;
temperature as source and ambient temperature as sink can be calculated as follows,
Re (GD / )
(8)
Where, G is the mass velocity of air through the collector;
c[1 (Ta / Tfm)]
(18)
G (m / W H )
Step13: The Nusselt number (Nu) is calculated using the correlation mention in equation convective heat transfer coefficient is calculated as follows,
The maximum exergy efficiency can be obtained by minimizing exergy losses and maximizing the net exergy flow. The components of exergy losses are (i.e., [22])
Step 24: Net exergy flow is calculated as
h (Nu k / D)
(9)
En IApthc Pm(1c)
(19)
Step 14: The plate efficiency factor is then determined as,
Step 25: Exergy input is calculated as;
F ' h / (h UL)
(10)
Es IAp(1 (Ta / Tsun))
(20)
Step 15: The heat removal factor is calculated as,
Step 26: Exergetic efficiency is calculated as;
Fo [(mCp / ULAp) exp{J}1 ]
Where,
J (F 'ULAp / mCp)
(11)
exe (En / Es)
Step 27: Optical losses are calculated as:
(21)
Step16: The useful heat gain, Qu2 is computed as,
ELO IApexe(1)
(22)
Step 28: Exergy losses by absorption of irradiation by the absorber are calculated as:
temperature rise parameter and then start decreasing. It happens because of lower convective heat transfer coefficient (h) value of air. For different values of relative
ELA IApexe (1 (Ta / Tpm))
(23)
roughness height (e/D) shown in Figure (4.14) the lower exergetic efficiency found for relative roughness height
Step 29: Exergy losses by both radiative and convective
heat transfer from the absorber to the atmosphere are calculated by:
(e/D) value of 0.018 and high exergetic efficiency found for relative roughness height (e/D) value of 0.03375 at angle of attack () value of 60Â° as shown in (Fig. 1).
ELE ULAp(Tpm Ta)(1 (Ta / Tpm))
(24)

Exergy losses by absorber (ELA)
Step 30: Exergy losses by the heat transfer to the working fluid are calculated by:
Exergetic losses by absorber are due to insufficient temperature rise of mean plate temperature. At angle of
attack () of 60Â° maximum decrement gap of exergetic
ELT Apth{(Ta / Tfm) (Ta / Tpm)}
(25)
losses by absorber are obtained at relative roughness height
Step 31: Exergy losses by friction are determined by:
of 0.018 for Wshape while minimum decrement gap obtained for discrete Wshape roughness at relative
ELP [(m / )P(Ta / Tfm)]
(26)
roughness height of 0.0375 in (Fig. 2). This is due to the fact that at relatively higher values of relative roughness
The experimental investigation had been carried out by
investigator and on that Nusselt number and friction factor correlations were obtained, which were used in this paper for further calculation purpose of exergetic efficiency. Correlations for Nusselt number (Nu) and Friction factor (f) for discrete Wshaped rib roughness and Wshaped rib roughness; Re = 400014,000 and relative roughness height (e/D) is as follows:
Correlation for Wshaped rib roughness (i.e., [23])
Nu 0.0613 Re0.9079 (e / D)0.4487 (alp / 60)0.1331
height, the reattachment of free shear layer might not occur. As lower relative roughness height value does not create as much disturbance within the fluid flow which results less heat gain by flowing fluid and maximum losses on absorber.

Exergy losses by friction (ELP)
A higher exergy loss due to friction is because of higher mass flow rate associated with lower temperature rise parameter at higher Reynolds number in the beginning of fluid flow in the duct. The maximum amount of frictional exergetic losses are obtained at angle of attack () of 60Â°.
exp((0.5307 (log(alp / 60)2 )))
(27)
At this angle of attack flow separation in secondary flow as result of discrete Wshaped rib roughness and movement of
f 0.6182 Re0.2254 (e / D)0.04622 (alp / 60)0.0817
resulting vortices combine to yield an optimum value as
exp((0.28 (log(alp / 60)2 )))
(28)
shown in (Fig. 3). A higher relative roughness height pertain higher friction factor because of higher level of
Correlation for discrete Wshaped rib roughness: (i.e.,[24])
Nu 0.105 Re0.873 (e / D)0.453 (alp / 60) 0.081
turbulence in the flow.

Exergy losses by working fluid (ELT)
exp((0.059 (log(alp / 60)2 )))
(29)
Increase in temperature rise parameter (T/I) leads to higher amount of irreversibility and hence higher exergy
f 0.568 Re0.40 (e / D)0.49 (alp / 60)0.081
losses. Absorber plate temperature increases with an
exp((0.579 (log(alp / 60)2 )))


MATLAB SIMULATION RESULTS

Exergetic efficiency (II)
(30)
increase of temperature rise parameter (T/I). Thus maximum exergetic losses result from higher value of temperature rise parameter (T/I). Value of exergy losses by working fluid (ELT) with temperature rise parameter increase for relative roughness height (e/D) 0.018 but after
The exergy of a system is the maximum useful work possible during a process up to the equilibrium process, but we always deal with exergetic efficiency. At lower temperature rise parameters the negative value of exergetic efficiency occurred because of higher mass flow rate and insufficient temperature rise but after this exergetic efficiency reaches maximum at certain value of
a certain point it decreases and found maximum for relative
roughness height (e/D) 0.03375 as shown in (Fig. 4) for angle of attack () of 60Â°.

Exergy losses by convective and radiative (ELE)
The losses are occurred because of the higher temperature difference between absorber plate and the environment. As the absorber plate temperature
continuously increasing, the losses due to the radiation become more dominant then conductive losses. Thus minimum exergy losses as a result of heat transfer to environment occur for minimum temperature rise parameter. From Figure (4.11) the higher value of ELE found at relative roughness height (e/D) value of 0.018and minimum for relative roughness height (e/D) value of 0.0375 at angle of attack () of 60Â° as shown in (Fig. 5).

Thermal efficiency (th)
Thermal efficiency is defined as the ratio of useful heat gain to the intensity of radiation incident on the heat transfer surface. So it is clear that the roughened surface responsible to maximize the useful heat gain will have maximum thermal efficiency. Thermal efficiency decreases with increase in temperature rise parameter (T/I). The minimum decrement in thermal efficiency obtained by discrete Wshaped rib roughness at relative roughness height (e/D) of 0.03375 as shown in (Fig. 6).

Effective efficiency (eff)
Effective efficiency defines as difference between useful heat gain and heat losses to the product of total isolation incident on solar absorber. Initially losses are minimum so the effective efficiency achieved maximum and after that it keep on decreasing because of losses as shown in (Fig. 7).
It can be analysed from the (Fig. 8) that the value of exergetic efficiency varies with Reynolds number (Re) up to <6000 and relative roughness height (e/D) = 0.03375 have highest exergetic efficiency for Reynolds no. (Re) < 6000. Exergetic efficiency (exe) started decreasing after > 6000 because of thermal energy thermal energy transfer domination over the pumping power consumption. The smooth plate solar air heater is having a low value of exergetic efficiency (exe) for all values of Reynolds number (Re) as compared to the roughened solar air heater duct.
Fig.1 – Variation of (exe) with temperature rise parameter for angle of attack () of 60Â°
Fig.2 – Variation of (ELA) with temperature rise parameter for angle of attack () of 60Â°
Fig.3 – Variation of (ELP) with temperature rise parameter for angle of attack () of 60Â°
Fig.4 – Variation of (ELt) with temperature rise parameter for angle of attack () of 60Â°
Fig.5 – Variation of (ELE) with temperature rise parameter for angle of attack () of 60Â°
Fig.6 – Variation of effective efficiency (eff) with temperature rise parameter (T/I) for angle of attack () 60Â°
Fig.7 – Effect of temperature rise parameter (T/I) on thermal efficiency (eff)
Fig.8 – Effect of temperature rise parameter (T/I) on Reynolds number (Re)



OPTMZATON OF ROUGHNESS PARAMETERS
Fig.9 – Variation of angle of attack () with temperature rise parameter for different intensity of radiation for discrete Wshaped rib roughness
The optimum values plots of relative roughness height (e/D), and relative angle of attack () that correspond to maximum exergetic efficiency (exe) for a given value of temperature rise parameter (T/I) are shown in (Fig. 9), (Fig. 10), (Fig. 11) and (Fig. 12) respectively. From the plots it is concluded that the optimum value of relative roughness height (e/D) is 0.03375 for Wshape rib and discrete Wshape rib roughness for different value of insolation (I) and optimum value of angle of attack () is 60Â° for Wshape rib and discrete Wshape rib roughness for different value of insolation (I).
Fig.10 Variation of relative roughness height (e/D) with temperature rise parameter for different intensity of radiation for discrete Wshaped rib roughness
Fig.11 – Variation of relative roughness height (e/D) with temperature rise parameter for different intensity of Radiation for Wshaped rib roughness
Fig.12 – Variation of angle of attack () with temperature rise parameter (T/I) for different intensity of radiation for Wshaped rib roughness

CONCLUSON
This study was taken up with purpose of heat transfer in Wshaped and discrete Wshaped rib as roughness element of the duct of solar air heater. This is considered as an important objective throughout the study of solar air heater. An analytical model based upon MATLAB programming has been developed based upon which the exergetic efficiency criteria has been used for optimization of roughness parameters for specified operating condition of solar air heater.
There is significant increase in exergetic efficiency (exe) of solar air heater with arc shaped wire rib roughened absorber plate. The exergetic efficiency enhances up to 63% over the smooth plate solar air heater. The maximum exergetic efficiency for the relative roughness pitch (p/e) is found at relative roughness height (e/D) of 0.03375, and angle of attack () value of 60Â° for discrete Wshaped rib roughness respectively with variation of temperature rise parameter (T/I) as compared to the Wshaped rib roughness. Exergetic efficiency obtained maximum at angle of attack () of 60Â° followed by angle of attack () of 45Â° and then angle of attack () of 75Â° for both Wshaped rib roughness and discrete Wshaped rib roughness. At higher Reynolds number (Re) above 20,000, exergetic efficiency of roughened solar air heater becomes negative and thus it is not desirable to run the system beyond this Reynolds number. Different exergetic components of artificially roughened solar air heater with Wshaped and discrete Wshaped rib for different values of system and operating parameters have been concluded. Different exergetic factors determination of the set of optimum values of the roughness parameters (Relative roughness height (e/D), and flow angle of attack ()) to result in best exergetic performance of solar air heater has been carried out during the study. The study will help the designer in future to select optimum roughness geometry that bears best performance from the design plots and tables.

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FLOWCHART
START
Read L,W,H,N,Ki,Ti,,p,g,tg,,t,I,D,N, T/I,e/D,
Calculate Tfm and To
Calculate properties of air at Tfm
Initialize TP = Tfm
Calculate Ub, Ue Ut, UL
Calculate QU1
Calculate, Re, G, Nu, h
Calcula te TP using Qu2
Calculate Fp, Fo, Qu2
ABS (Qu1Qu2)
0.1% Qu1
Calculate, Re, G, Nu, h
Calculate QU1
STOP