Exergy loss-based efficiency optimization of a double ...

Energy 94 (2016) 799e810

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Exergy loss-based efficiency optimization of a double-pass/glazed v-corrugated plate solar air heater Mahdi Hedayatizadeh a, *, Faramarz Sarhaddi b, Ali Safavinejad c, Faramarz Ranjbar d, Hossein Chaji e a

Faculty of Agriculture, University of Birjand, Birjand, Iran Shahid Nikbakht Faculty of Engineering, Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran Faculty of Engineering, Department of Mechanical Engineering, University of Birjand, Birjand, Iran d Faculty of Engineering, Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran e Agricultural and Natural Resources Research Center, Khorasan Razavi, Mashhad, Iran b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 July 2015 Received in revised form 4 November 2015 Accepted 11 November 2015 Available online xxx

The main objective of the present study is to perform an in-depth exergetic analysis of a double-pass/ glazed v-corrugated plate solar air heater based on exergy loss terms. Consequently, the detailed thermal modeling of the given air heater is carried out and validated with literature which shows good agreements. Through an exergy analysis performed with regard to internal/external exergy losses, the exergetic efficiency is optimized considering four independent variables of distance between the two adjacent glazings, height of v-corrugations, area of the heater and the total mass flow rate. Based on the simulation results, the maximum exergy efficiency of the given air heater was gained 6.27% corresponding to distance of 0.0023 m between glazings, corrugation height of 0.0122 m, heater area of 1.79 m2 and total air rate of 0.005 kg/s. Moreover, as an important conclusion, it was found that the internal exergy loss term originating from temperature difference between sun and absorber surface can be interpreted as the most destructive term in comparison to four other terms which accounted for 63.57% of the whole exergy losses at the point corresponding to maximum exergy efficiency. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Exergy efficiency Optimization V-corrugated plate Heater

1. Introduction Solar air heater can be an ideal choice for drying, space heating etc., as the warm air can be used directly, eliminating any need for an extra heat exchanger in the thermal system. But, it is essential to pay heed to the fact that solar air heaters suffer from low thermal performance due to low density, the small volumetric heat capacity and an inherently small heat conductivity of air. Hence, an improved design of a solar air heater may lead to a better thermal performance of the system [1] which could include different established methodologies such as the use of baffles/obstacles with different shapes and geometries on the surface of the absorber [2e4], varying the number of covers and flow passes [5,6], application of matrix [7,8], dual glassing [9,10], or corrugating the absorber surface of the heater [11e15]. Karim and Hawlader [16] examined flat plate, finned and v-corrugated absorber plates in * Corresponding author. Tel.: þ98 (56) 322 540 41 9; fax: þ98 (56) 322 540 50. E-mail addresses: [email protected] (M. Hedayatizadeh), [email protected] (F. Sarhaddi), [email protected] (A. Safavinejad), s. [email protected] (F. Ranjbar), [email protected] (H. Chaji). http://dx.doi.org/10.1016/j.energy.2015.11.046 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

single and dual-pass solar air heaters analytically and experimentally and reported a better performance with v-corrugated dualpass solar air heater. V-corrugating the absorber surface however increases pressure drop along flow channels of solar air heater which brings about more pumping power required and it necessitates application of an optimization method [17]. From the other side, it is demonstrated that exergy analysis derived from both first and second laws of thermodynamics is superior to energy analysis [10] and is a powerful tool in design, optimization, and performance evaluation of solar thermal systems which help identification of main sources of irreversibility (exergy losses) [18e20]. Ajam et al. [21] performed an exergetic optimization of solar air heaters and reported an extraordinary increase of the exergy efficiency according to the optimized parameters. Velmurugan and Kalaivanan [22] also studied four different models of solar air heaters analytically and experimentally from the energetic and exergetic points of views and reported the exergy and energy performance of wire mesh dual-pass solar air heater superior to those of roughened plate dual-pass, finned plate dual-pass and single-pass flat plate solar air heaters. Kalogirou [23] also applied the Artificial Neural-

800

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

Nomenclature Ah Aa Ad AR cp Dh

Heater area (L$W) (m2) Absorber surface area (2L$W for a ¼ 60) (m2) Total cross-section area of ducts (H2$W for a ¼ 60) (m2) Aspect ratio () Specific heat of air (J/kg K) Hydraulic diameter (m)

Ex G Gr H h Ir K L _ m _ M

Exergy rate (W) Solar irradiance (based on Ah) (W/m2) Grashof number () Thickness (m) Heat transfer coefficient (W/m2 K) Irreversibility (J) Thermal conductivity (W/m K) Length of heater (m) Total mass flow rate of air through heater (kg/s) _ divided by Ah (kg/m2 s) m _ divided by Ad (kg/m2 s) m Number of separate flow passages experienced by air in series through a collector array () Nusselt number () Pressure drop (Pa) Prandtl number () Rate of useful energy gain (W) Gas constant Reynolds number () Rayleigh number () Temperature (K) Heat loss coefficient (W/m2 K) Wind velocity (m/s) Width of heater (m)

,

M N Nu

DP Pr : qu R Re Ra T U Vw W

Networks and Genetic Algorithm (GA) to optimize a solar-energy system in order to maximize its economic benefits. S¸ahin [24] used GA to optimize a solar air heater and reported the algorithm as a successful method of optimization for enhancing the thermal performance of solar air collector. Nwosu [25] applied exergy-based optimization for sizing pin fins in design of an absorber in a solar air heater and his results indicated that high efficiency of the optimized fin improves the heat absorption of a solar air heater. Singh et al. [26] also performed an exergy based analysis of a solar air heater having discrete v-down rib roughness on absorber plate. They claimed that employing exergy analysis is suitable for design of rib roughened solar air heaters and also reported that there exist optimum roughness parameters of the discrete v-down rib for a given Reynolds number at which the exergetic efficiency gets maximum. Meanwhile, it is observed that most of exergy-related studies on solar air heaters have focused on net outlet exergy rates [27e29] for calculating exergy efficiency while in the present study, the exergy efficiency is formulated based on the rates of exergy losses to find the values of losses separately and to specify the term(s) which bring about the highest exergy deterioration rates for the given solar air heater. Afterwards, the exergetic efficiency function is fed to MATLAB software Genetic Algorithm with the aim of finding the highest achievable value with regard to four independent variables of distance between the two adjacent glazings, height of corrugations, area of the heater and the total mass flow rate. To the best of our knowledge, such a methodology has not been used for optimizing the operating and configuration

Greek letters Absorptivity, Thermal diffusivity (m2/s) & Opening angle for each v-shaped corrugation ( ) t Transmittivity s StefaneBoltzmann constant (W/m2 K4) b Volumetric thermal expansion coefficient (1/K) ε Emissivity n Dynamic viscosity (m2/s) q Tilt angle ( ) r Density of flowing air (kg/m3) ho Optical efficiency

a

Subscripts a Ambient ap Absorber plate bp Bottom plate c Convection des Destroyed ext External F1 Upper passage air flow F2 Lower passage air flow fin Final g1 Upper glass cover g2 Lower glass cover i Inlet ini Initial o Outlet opt Optical p Pump r Radiation s Sky sun Sun t Total TH Thermal

parameters of a double-pass/glazed v-corrugated (DPGVC)1 plate solar air heater through an exergy loss-based efficiency optimization procedure. 2. Theoretical analysis To perform an exergy analysis of the given DPGVC plate solar air heater, it is necessary to find the temperatures of different heater components. There for, it seems essential to perform a thermal analysis and develop energy balance equations for different elements of the heater. The given heater is made of two flat glass covers and a v-corrugated absorber plate with a well insulated back plate shown in Fig. 1. The v-corrugated plate geometry is formed by a set of equilateral triangles forming two passages above and below the absorbing plate. As seen in Fig. 2, two air streams which make up the total air flow are flowing steadily and simultaneously through the two separate channels to absorb heat from absorber. For thermal boundary conditions, the two top sides of the triangle are assumed uniform in temperature, but a constant heat flux boundary condition in the axial direction is assumed as far as the total heat transfer is concerned [30]. To model the v-corrugated plate air heater in the present study, a number of simplifying assumptions are made to lay the foundations without obscuring the basic physical situation.

1

Double-pass/glazed v-corrugated (DPGVC).

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

801

2.1.2. Lower glass cover Part of incident solar radiation passing through the upper glass cover is absorbed by the lower one and also a radiative exchange is expected to occur between the lower glazing and the absorber plate. Moreover, due to flow of air beneath the lower glazing, part of heat removed from absorber by upper passage flowing air is also assumed to be transferred to that glass cover:

 
 tg1 ag2 GAh þ hr;apg2 Tap  Tg2 Aa þ hc;f1g2 Tf1  Tg2 Ah

 ¼ hr;g2g1 þ hc;g2g1 Tg2  Tg1 Ah (2) 2.1.3. Upper flowing air stream The total amount of flowing air through the heater is divided in two streams i.e. one above and the other below the v-corrugated absorber surface. As mentioned above, part of heat absorbed by the v-corrugated plate is transferred to upper flowing air stream, hence:

Fig. 1. Three dimensional schematic of a DPGVC plate solar air heater.

    hc;apf1 Tap  Tf1 Aa ¼ q_ u1 þ hc;f1g2 Tf1  Tg2 Ah

(3)

where Tf1 and q_ u1 are the mean temperature of the upper air stream and the useful energy gain by air flowing through the above passage, defined by Tf1 ¼ (Tf1i þ Tf1o)/2 and _ p ðTf 1o  Tf 1i Þ=2, respectively while the total mass flow of q_ u1 ¼ mc air flowing through the heater is divided equally between the two channels.

Fig. 2. Front view of the heater and heat transfer coefficients shown with two air streams normal to the page.

These assumptions are as follows: 1. Thermal performance of heater is considered steady state. 2. There is a negligible temperature drop through the glass cover, the absorbing plate, and the back plate. 3. There is a two-dimensional heat flow through the back insulation. 4. The sky can be considered as a blackbody for longwavelength radiation at an equivalent sky temperature. 5. Loss through the up and back surfaces is to the same ambient temperature. 6. Dust and dirt on the heater and the shading of the absorbing plate are negligible. 7. Thermal inertia of heater components is negligible. 8. Operating temperatures of heater components and mean air temperatures in air passages are all assumed to be uniform. 9. Temperature of the air varies only in the flow direction. 10. All air passages are assumed to be free of leakage. 11. Thermal losses through the heater backs are mainly due to the conduction across the insulation and those caused by the wind and the thermal radiation of the insulation are assumed to be negligible [31].

2.1.4. Absorber plate Solar radiation passing through the two glazings intercepts the v-corrugations and increases its temperature. Hence, the heat transfer balance on absorber can be written as followings:

tg1 tg2 aap GAh

 
 ¼ hr;apg2 Tap  Tg2 Aa þ hc;apf 1 Tap  Tf1 Aa   þ hc;apf2 Tap  Tf 2 Aa   þ hr;apbp Tap  Tbp Aa (4)

2.1.5. Lower flowing air stream Air flowing beneath the absorbing surface also removes part of heat generated by incident radiation on the absorber. The temperature increase of the flowing air brings about thermal energy gain by the air stream while some of it is expected to be transferred to insulation:

    hc;apf2 Tap  Tf2 Aa ¼ q_ u2 þ hc;f2bp Tf2  Tbp Ah

(5)

where Tf2 and q_ u2 are the mean temperature of the lower air stream and the useful energy gain by air flowing through the lower pas_ p ðTf2o  Tf2i Þ=2, sage, defined by Tf2 ¼ (Tf2i þ Tf2o)/2 and q_ u2 ¼ mc respectively.

2.1. Energy balance 2.1.1. Upper glass cover The absorbed energy by the upper glass cover, from absorbed solar radiation and the lower glazing, is partly given to ambient and also dissipated to sky:



 ag1 GAh þ hr;g2g1 þ hc;g2g1 Tg2  Tg1 Ah

 ¼ hw Tg1  Ta Ah þ hr;g1s Tg1  Ts Ah

(1)

2.1.6. Back plate Heat loss through the insulation (back plate) is the last step considered through thermal modeling of heater components. Based on considering the two-dimensional heat flow through back plate, it can be written as:

v2 Tbp vx2

þ

v2 Tbp vz2

¼0

(6)

802

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

while x and z denote the directions along the length and thickness of the back plate accompanied by the following boundary conditions:

8 vTbp > > ¼0 < x ¼ 0; vx > > : x ¼ L; vTbp ¼ 0 vx


 hr;g1s ¼ sεg1 Tg1 þ Ts T2g1 þ T2s while Ts is the sky temperature and formulated as [33]:

Ts ¼ Ta  6

8 > >
vT > bp :z ¼ H ; k ¼ Ub Tbp  Ta 3 bp vz


  s T2g1 þ T2g2 Tg1 þ Tg2 ¼ 1 1 εg1 þ εg2  1

(15)

and the convective heat transfer coefficient for air trapped in an inclined enclosure is given by:

hc;g2g1 ¼ Nug1g2 2.2. Temperature determination of different air heater components Rearranging Eq. (1) up to Eq. (5) helps to find the component temperatures parametrically as follows:

Tg1

(14)

The radiative heat transfer coefficient between the two glass covers is also predicted by [34]:

and


 ag1 G þ hr;g2g1 þ hc;g2g1 Tg2 þ hw Ta þ hr;g1s Ts
 ¼ hr;g2g1 þ hc;g2g1 þ hw þ hr;g1s

(13)

k L

(16)

Such a Nusselt number is calculated by:

Nug1g2

(7)

#  "  1708  1708ðsin1:8·qÞ1:6 ¼ 1 þ 1:44 1  1 Ra·cosq Ra·cosq " #

1 Ra·cosq 3 þ 1 5830 (17)

Tg2 ¼

Tf 1


 tg1 ag2 GAh þ hr;apg2 Tap Aa þ hc;f1g2 Tf 1 Ah þ hr;g2g1 þ hc;g2g1 Tg1 Ah   hr;apg2 Aa þ hc;f1g2 þ hr;g2g1 þ hc;g2g1 Ah

_ p Ta þ hc;f1g2 Tg2 Ah hc;apf1 Tap Aa þ mc ¼ _ p þ hc;f1g2 Ah hc;apf1 Aa þ mc

Tap ¼

(9)

(8)

where q is the plate tilt angle of the heater and “*” symbol in the superscript means that only positive values of the terms in the square brackets are to be used. It is significant to know that the above correlation is valid for 0  q 75 .

tg1 tg2 aap GAh þ hr;apg2 Tg2 Aa þ hc;apf 1 Tf 1 Aa þ hc;apf 2 Tf 2 Aa þ hr;apbp Tbp Aa   hr;apg2 þ hc;apf1 þ hc;apf 2 þ hr;apbp Aa

(10)

The Rayleigh number, Ra, is the product of Gr and Pr:

Tf 2 ¼

_ p Ta þ hc;f2bp Tbp Ah hc;apf2 Tap Aa þ mc _ p þ hc;f2bp Ah hc;apf2 Aa þ mc

(11)

Ra ¼ Gr$Pr

(18)

and is given by


 gb Tg2  Tg1 H31 an

2.3. Heat transfer coefficients

Ra ¼

The convective heat transfer coefficient from the upper glass cover due to wind is given by [6]:

The recommended relation for inclination between 75 < q 90 is also given by:

hw ¼ 2:8 þ 3Vw

i h 1 1 Nug1g2 ¼ 1; 0:288ðAsinðqÞRaÞ4 ; 0:039ðsinðqÞRaÞ3

(12)

The radiative heat transfer coefficient from the upper glass cover to sky may be obtained by following formula [32]:

(19)

Max

(20)

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

where the subscript MAX indicates that at a given Ra, maximum of the three quantities separated by commas should be taken. In Eq. (20), “A” is the ratio of the thickness of enclosure, H1, to the height measured along either the heated or cooled boundary surface in the upslope direction [35]. The radiative heat transfer coefficient is given as below [32]:

hr;apg2 ¼

 
 sεg2 εap T2ap þ T2g2 Tap þ Tg2 εg2 þ εap  εap εg2

(21)

It is also assumed that hc;g2g1 ¼ hc;g1g2 and hr;g2g1 ¼ hr;g1g2 being already defined. Convective heat transfer coefficient between upper channel flowing air and absorber is calculated as followings [30]: Hollands and Shewen suggested that the Nusselt number, Nu, for an equilateral triangle arrangement can be expressed as

hc;apf1 ¼ Nuapf1

k Dh

(22)

803

  k ¼ 0:0015215 þ 0:097459Tf  3:3322  105 T2f  103 (28)   m ¼ 1:6157 þ 0:06523Tf  3:0297  105 T2f  106

(29)

while cp ¼ 1000 (J/kg K) can be assumed. Finally, the radiative heat transfer coefficient between absorber and back plates is calculated as follows:

hr;apbp ¼

   sεbp εap T2ap þ T2bp Tap þ Tbp εbp þ εap  εbp εap

(30)

and Ub as the bottom loss coefficient included in Eq. (6) is also given by [36].

 1  . Ub ¼ 1 hr;apbp þ hc;f2bp þ H3 =ki

(31)

while

Nuapf 1 ¼ 2:821 þ 0:063Re1

H2 n ; for Re1 < 2800; L

Nuapf 1 ¼ 1:9  106 Re1:76 þ 112:5 1

2.4. Pressure drop

(23) The pressure drop DP is found by the following relation [30]:

H2 n ; for 2800  Re1 L

Dp ¼ 12

 104 ; (24) and

H2 n ; for 104  Re1 L (25)

Reynolds number (Re) for the upper air passage is calculated by [30]:



_ m Ad



1 m1



2H2 3



¼

13:33 H þ 0:325 2 n Re L

(33)

for transient flow (2800  Re  104):

 105 ;

M D Re1 ¼ 1 h ¼ m1 _ 2m ¼ 3m1 W

(32)

while for laminar flow f is defined as (Re < 2800):

f¼

Nuapf 1 ¼ 0:0302Re0:74 þ 0:121Re0:74 1 1

_ 2  L 3 M f r H2

f ¼ 3:2104 Re0:34 þ 1:47Re0:19

(34)

and for turbulent flow (104 < Re < 105):

f ¼ 0:0733Re0:25 þ 0:255



_ 1 2H2 m m1 H2 W 3

H2 n L

H2 n L

(35)

2.5. Heater efficiency

(26) Convective heat transfer coefficient between absorber plate and lower passage air flow is also calculated by the same correlation as Eq. (22) provided that m1 is substituted by m2 in Eq. (26) till Re2 is achieved. Moreover, the convective heat transfer coefficients between upper channel flowing air and lower glass cover and also between lower channel flowing air and bottom plate are calculated the same as hc;apf1 and hc;apf 2 , respectively [12]. When the air temperature is in the range 280e470 K, the following empirical correlations are suggested to estimate the density, thermal conductivity and dynamic viscosity of air, respectively [12]:

The total useful thermal output of the given air heater is calculated by the following equation:

Q_ tu ¼ q_ u1 þ q_ u2

(36)

and the thermal efficiency of the present DPGVC plate solar air heater is given by [37e39]:

hTH ¼

Q_ tu GAh

 100

(37)

where G is the mean solar radiation falling on heater aperture. 2.6. Exergy analysis

r ¼ 3:91470:016082Tf þ2:9013105 T2f 1:9407108 T3f (27)

Exergy analysis is a useful method to establish strategies for the design and operation of solar air heaters where the optimal use of

804

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

energy is considered as an important issue [18]. In the exergy analysis some assumptions are made mentioned in literature [27,39,40]. The exergy flows are schematically shown in Fig. 3. The exergy balance for the solar air heater considered as the control volume can be written as followings [22]:

X

_ Ex i;net 

X

_ o;net ¼ Ex

X

_ Ex loss

(38)

where subscript “net”, represents the net exergy rates. The exergy efficiency of the solar air heater is also defined as the ratio of net output (desired) exergy rate to that of the net input:

P _ Exo;net hex ¼ P _ Ex i;net

(39)

Based on Eq. (39), the exergy efficiency of the solar air heater is a function of net outlet exergy rate and does not account for the exergy losses, i.e., it does not show the degree of importance of each loss item of exergy in the specified control volume. Hence, in the present study, calculation of exergy efficiency of the given air heater is done based on the items of exergy losses to reveal the importance of each source of loss on the exergy efficiency. Therefore, the exergy efficiency is calculated by:

P _ Ex hex ¼ 1  P loss _ Ex i;net

_ Ex loss ¼ ¼

X X

_ Ex loss;ext þ _ Ex loss;ext þ

X X

_ Ex loss;int _ Ex des

(42)

Exergy that goes out of control volume and cannot be used is called external exergy loss while the amount of exergy losses caused by flow friction, mixture of two kinds of liquids, etc. which do not go out of the control volume are called internal exergy losses (exergy destruction) [44]: The rates of exergy losses of the given solar air heater includes five terms [45];

2.6.2.1. External exergy loss terms  The first term is caused by optical losses in solar heater surface [46]:

"

#
 4 Ta 1 Ta 4 _ þ Exloss;opt ¼ GAh 1  aap tg1 tg2 1  3 Tsun 3 Tsun (43)  The second term is caused by heat loss from solar air heater to the surroundings [18,45,47]:

  Ta _ _ 1  ¼ Q Ex loss;Q loss loss Tap

 The net inlet exergy rate to solar air heater The net inlet exergy rate to solar air heater includes solar radiation intensity exergy rate [28]:

"

# 4 Ta 1 Ta 4 _ _ þ Exi;net ¼ Exsun ¼ GAh 1  3 Tsun 3 Tsun

X

(40)

2.6.1. Net inlet exergy rate

X

2.6.2. Rates of exergy losses It is the summation of the rate of external exergy losses from control volume and the rate of internal exergy losses (exergy destructions) in control volume [42,43]:

(41)

(44)

where Q_ loss is heat loss from solar air heater to the surroundings and is given by:


 Q_ loss ¼ UL Ah Tap  Ta

(45)

where UL ¼ Ub þ Ut ; where Tsun is the apparent sun temperature [41]. Ub, the bottom heat loss coefficient, has been given above and the top loss coefficient, Ut, can be calculated from the individual heat transfer coefficients using the following equation:

Ut ¼

1 1 1 þ þ hr;apg2 þ hc;fg2 hr;g2g1 þ hc;g2g1 hr;g1s þ hw

!1

(46) 2.6.2.2. Internal exergy loss terms (Destruction terms)  The first term is the exergy destruction rate due to the temperature difference between the sun and solar heater surface [46]:

"



4 Ta 1 Ta 4 _ þ a t t 1  ¼ GA Ex ap g1 g2 h desðTap Tsun Þ 3 Tsun 3 Tsun

# Ta  1 Tap (47) Fig. 3. Exergy flows in a solar air heater.

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

 The second term is the exergy destruction rate due to heat transfer from the heater surface to the working fluid at finite temperature difference [18]:

_ Ex desðTap Tf Þ ¼ GAh hTH Ta

1 1  Tf Tap

! (48)

where Tf ¼ (Tf1 þ Tf2)/2  The third term is exergy destruction rate due to air friction (pressure drop) in air ducts [46]:

_ 1 $P1 Ta m _ Ex desðfriction1 Þ ¼ rf1 Tf1

(49)

_ 2 $P2 Ta m _ Ex desðfriction2 Þ ¼ rf2 Tf2

(50)

2.6.3. Exergy efficiency Exergy efficiency of the given air heater is defined by Eq. (40). Substitution of Eqs. 41e50 into Eq. (40) results in exergy loss-based efficiency as follows:

hex

8 " >   Tap : "



4 Ta 1 Ta 4 þ þ GAh aap tg1 tg2 1  3 Tsun 3 Tsun !

# _ 1 DP1 Ta 1 1 Ta m þ GAh hTH Ta  1  þ Tf Tap Tap rf1 Tf1 9 # > = _ Ta m2 DP2 1 " # þ 



4 > rf2 Tf2 ; a a þ 13 TTsun GAh 1  43 TTsun (51)

3. Results and discussion 3.1. Validation of the simulation To find the temperatures of different elements of the given solar air heater, a simulation code including the above mentioned equations was developed in MATLAB software. But, as the preliminary step, it was essential to examine the simulation validity versus the results obtained from an experiment performed on an analogous system to that of this paper (DPGVC plate solar air heater). Fortunately, the experimental results are presented through literature by Sebaii et al. [36]. The values of some design and operating parameters given by Sebaii et al. [36] are summarized in Table 1 and the ones not mentioned are assumed (labeled

805

assumed). Hence, temperature variations of different components of the given solar air heater calculated by simulation are compared with their experimental values and also shown in the following figures (Figs. 4e6). Moreover, in order to compare the simulation results (labeled sim. in figures) with experimental ones (labeled exp. in figures), coefficient of determination (R2) and root mean square error (RMSE) are calculated [48] and summarized in Table 2. Fig. 4 depicts the graphical comparison made between the experimental and simulated temperatures of upper and lower glass covers. It is observed that simulated temperatures of both glass coverings follow the trend of their corresponding temperatures in experiment closely. Moreover, the high value of R2 and low value of RMSE (Table 2) both show that simulation is desirably able to predict the glass cover temperatures. The mean temperature differences between the experimental and the simulated results are found 1.02  C and 1.85  C for the upper and lower glass covers, respectively. Fig. 5 also reveals the trend of changes of air stream temperatures throughout a day from 8 AM till 8 PM. It is seen that simulation is predicting the temperatures of the two air streams approximately well (Table 2) while the mean temperature differences between the experimental and the simulated results are found 7.39  C and 3.4  C for the upper and lower air streams, respectively. Fig. 6 also shows that the simulation has the capability of estimating the temperatures of absorber and back plate with high R2 and low values of their RMSEs (Table 2). Hence, it may be concluded that simulation conducted above shows good agreements with its experiment and it has the potential to prognosticate the thermal behavior of the DPGVC plate solar air heater with mean temperature differences of 2.78  C and 1.99  C for the absorber and back plates, respectively. It is worth mentioning that the causes of errors may also be attributed to the following facts that:  Wind speed is considered constant in simulation while it is not in deed (experiment [36]) and as it has direct effect on heat loss coefficient, hence, part of the deviation may be related to;  Tilt angle of the heater has direct impact on the Nusselt number of the air confined between the two glass covers that has not been mentioned by literature [36] and it is there for assumed;  Solar radiation and ambient temperature values as significant inputs to simulation were extracted from their corresponding figures in literature [36] which may brings about decreases in precision; 3.2. Optimization problem 3.2.1. Genetic algorithm GA uses the techniques inspired by evolutionary biology such as inheritance, mutation, selection and crossover [49] and is one of the modern optimization techniques due to its evolutionary nature which can handle any kind of objective function and constraint without any mathematical requirement about the optimization problem while it is very effective at performing a global search (in probability) [50].

Table 1 Specifications of the DPGVC plate solar air heater based on Sebaii et al. [36] experimental test. Parameter

Value

Parameter

Value

Parameter

Value

Parameter

Value

aap ag

0.9 0.05 0.9 0.88

εbp

0.9 0.9 0.024 W/m K 60

Vw (assumed)

1 m/s 30 0.0203 kg/s 0.03 m

H2 H3 L W

0.05 m 0.04 m 1m 0.5 m

εap εg

tg

ki

a

q

_ m H1

806

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

Fig. 4. Comparison between the experimental and simulated temperatures of upper and lower glass covers.

Fig. 6. Comparison between the experimental and simulated temperatures of absorber and back plates.

Table 2 R2 and RMSE for temperatures of different elements of DPGVC plate solar air heater. Element

Error value

Upper glass cover Lower glass cover Upper passage air stream Absorber plate Lower passage air stream Back plate

R2

RMSE

0.97 0.98 0.96 0.98 0.98 0.99

1.40 2.27 8.98 3.61 4.06 2.26

procedure are shown in Table 3.while L and N (number of v-shaped corrugations) are not bounded pffiffiffiapparently, but considering the relations of L ¼ Ah/W and N¼ 3W=ð2H2 Þ, it is seen that these two parameters are implicitly bounded.

Fig. 5. Comparison between the experimental and simulated outlet temperatures of upper and lower air streams.

3.2.2. Formulation of the optimization problem Prior to feeding the developed simulation into MATLAB built-in optimizing toolbox, GA, it is essential to determine the objective function, relevant constraints and the range of variations (bounds) of independent parameters clearly. Hence, the exergy efficiency as the objective function is introduced to GA and the extreme limits of four independent parameters are specified as follows:

8 Maximize hex ¼ Eq:ð51Þ > > > > subject to < 0:001  H  0:2; > > 0:05  Ah  2; > > : _  0:05; 0:001  m while the linear/nonlinear equations of the simulation were all considered implicitly as the constraints of the problem. The environmental condition and design specifications of the solar heater and other constant parameters used through optimization

3.2.3. The results of optimization procedure Using constant values of parameters summarized in Table 3, the optimization procedure leads to the following optimum values of the objective function, the independent and dependent optimization parameters: hex ¼ 6.27%, H1 ¼ 0.0023 m, H2 ¼ 0.0122 m, _ ¼ 0:005 kg=s, Tg1 ¼ 318.36 K, Ah ¼ 1.79 m2, L ¼ 3.58 m, m Tg2 ¼ 350 K, Tap ¼ 359.77 K, Tf1 ¼ 352 K, Tf2 ¼ 354 K, Tbp ¼ 356.33 K, Ut ¼ 3.45 W/m2 K, Ub ¼ 0.58 W/m2 K, q_ u1 ¼ 261:71 W, q_ u2 ¼ 271:57 W , DP1 ¼ 25.49 Pa, DP2 ¼ 25.73 Pa, hTH ¼ 42.52 %. The variations of exergy efficiency and exergy loss terms each divided by exergy rate of solar radiation (net inlet exergy rate)

Table 3 Environmental conditions and design specifications of DPGVC plate solar air heater. Parameter

Value

Parameter

Value

aap ag

0.9 0.05 0.9 0.88 0.9 0.9 0.024 W/m K 0.04 m

W Tf1i ¼ Tf2i ¼ Ta Tsun G Vw

0.5 m 300 K 4350 K 700 W/m2 1 m/s 30 60

εap εg εbp

tg

ki H3

q a

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

versus mass flow rate of air through DPGVC plate solar air heater are shown in Fig. 7 while values of other three independent parameters of optimization are those of their optimum together with values of constant parameters brought in Table 3. As seen in Fig. 7 the exergetic efficiency of the given heater shows a sharply ascending trend of variations with mass flow rate to attain a maximum of 6.27% at 0.005 (kg/s) and starts a smoothly falling trend of changes with more increases in air flow rates. Hence, such a trend of variations in exergy efficiency reflects the importance of specifying the optimum value of air flow rate. Moreover, to study the exergy efficiency in detail, it is crucial to graph the variations of different exergy loss terms of the given heater versus mass flow rate to find the most and the least significant terms. On the other hand, for better comparison, their values are divided by that of net inlet exergy of the sun. As also seen in Fig. 7, the loss exergy terms can be generally divided in three groups with respect to their variations vs. air flow rate: The optical-related _ _ loss (Ex loss;opt =Exsun ) being constant, all the three destructive terms _ _ _ _ which show increases (Ex desðTap Tsun Þ =Exsun , ExdesðTap Tf Þ =Exsun and _ _ sun ) and the remaining one which has a declining Ex = Ex desðfrictionÞ _ _ trend of variation (Ex loss;Q loss =Exsun ) which springs from the heat _ losses. Furthermore, it is also observed that Ex desðTap Tsun Þ is the major source of exergy loss accounting for 63.54% of exergy losses at the optimum point which may be attributed to the fact that increase in mass flow rate is in parallel with more heat dissipation from heater while it results in absorber temperature decrease _ _ which brings about the increasing trend of Ex desðTap Tsun Þ =Exsun from 0.52 to 0.69 with air flow changes from 0.001 kg/s to 0.049 kg/s. The second important term is the optical related exergy loss term (28.91% of the total exergy losses) being independent of mass flow _ _ rate changes while decrease in Ex loss;Q loss =Exsun with mass flow rate may also be attributed to decreases in heater temperature and consequently the overall heat loss coefficient. On the other side, increase in mass flow rates has partly detrimental effects on quality of energy delivered by air heater as it also causes the pressure drop increases through v-shaped passages, seen by ascending trend of

807

_ _ Ex desðfrictionÞ =Exsun (Fig. 7) while the values of pressure related exergy loss are not comparable to other increasing terms (less than 0.8%). Studying the sole effect of heater area (Ah) on trend of variations of exergy efficiency is also shown in Fig. 8. It should be noticed that width of given air heater is kept constant (W ¼ 0.5 m), hence increasing heater area means increasing the length of heater. Exergy efficiency changes with heater area also show a peak which emphasizes on truly selected objective function for being fed to GA. Hence, elongating the given air heater beyond the optimum point (L ¼ 3.58 m) can causes the exergy efficiency commences to decline. Hence, the optimization procedure of the given heater helps significantly to save money and material along with higher exergy gains. The same as previous case, it is also needed to study the effect of heater area based on its effects on exergy loss terms (Fig. 8). Seeing Fig. 8, it is found that _ _ sun on contrary to the case of mass flow rate changes, Ex =Ex loss;Q loss

is the sole term which shows a continuously increasing trend of changes with heater area as the area increases causes more heat loss due to increasing absorber temperature and consequently _ _ more exergy loss while Ex loss;opt =Exsun is constant and _ _ ExdesðfrictionÞ =Exsun can also be considered constant within the _ _ specified ranges of heater area variations. Ex desðTap Tsun Þ =Exsun is continuously decreasing from 0.72 to 0.57 with heater area changes from 0.01 m2 to 3 m2. Such a descending trend may also be attributed to increases in absorber temperatures and finally _ _ Ex desðTap Tf Þ =Exsun term which shows declining trend exceeding 0.21 m2. The effect of height of v-corrugations on exergy efficiency of the given heater can also be a real matter as it has direct impact on pressure related exergy losses (Fig. 9). As seen in Fig. 9, lowering the v-corrugation height from 0.0122 m can noticeably decrease the exergy efficiency and such a graph (Fig. 9) can put much emphasis on the advantages of optimized heater upon the non-optimized ones for delivering higher quality levels of energy. Hence, feeding the design and environmental conditions to the given MATLAB

_ sun for the DPGVC plate solar air heater with mass flow rate. Fig. 7. Variations of exergy efficiency and exergy loss terms divided by Ex

808

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

_ sun for the DPGVC plate solar air heater with heater area. Fig. 8. Variations of exergy efficiency and exergy loss terms divided by Ex

code can bring the optimized values for the variables which are too effective in increasing the exergy efficiency of the v-corrugated solar air heater. For the present case of the study, the trend of _ sun is roughly variations of different exergy loss terms divided by Ex _ _ analogous to that of heater area case except for Ex desðTap Tsun Þ =Exsun. _ _ As also seen in Fig. 9, Ex desðTap Tsun Þ =Exsun is highest in comparison with others.

But, for observing the simultaneous effects of changes in air flow rate with heater area and air flow rate with corrugation height Figs. 10 and 11 are brought, respectively. As seen in Fig. 10, with small areas of the heater which equals the short lengths (as W is considered constant) it is recommended to have low rates of air flow rates and as the length of the heater increases, to keep the level of exergy efficiency of the given heater as high as

_ sun for the DPGVC plate solar air heater with v-corrugation height. Fig. 9. Variations of exergy efficiency and exergy loss terms divided by Ex

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

809

possible, it is also suggested to have more flow rates of air through ducts. Moreover, with small flow rates exergy efficiency has higher sensitivity with the size of heater area. Furthermore, it should be taken into consideration that variation of air flow rates through an experimental test is somehow easily achieved while the heater area is only easily changed through simulation. Hence, such a graph made by simulation and also the optimization applied to the present simulation can be a very useful way for finding a better configuration of the system. Fig. 11 also shows that for a given corrugation height, air flow rate should also be adjusted in such a way to bring the maximum exergy efficiency. Seeing Fig. 11 also shows that increase in height of corrugation accompanied by increase in air flow rates or vice versa, all show a peak pertaining to exergy efficiency while exceeding this optimum point will only deteriorate the exergy efficiency. Hence, for a given height a rate of air flow should be carefully investigated.

Fig. 12. Variations of exergy efficiency of DPGVC plate solar air with heater area and corrugation height.

Studying variations of both heater area and corrugation height on exergy efficiency is also shown in Fig. 12. Such a combination also shows a peak for exergy efficiency while as they are both design parameters they should be carefully measured in the first stages of air heater manufacturing for bringing about the highest achievable quantity for the objective function (functions).

4. Conclusions In the present paper the effects of air flow rate, heater area and height of v-corrugations on exergy efficiency of the given heater and also their exergy loss components were studied in detail. The simulation results show that: Fig. 10. Variations of exergy efficiency of DPGVC plate solar air heater with air flow rate and heater area.

 The simulation results were in good agreements with the experimental results of the literature;  Optimum values of 0.0122 m, 1.79 m2 and 0.005 kg/s obtained for the corrugation height, heater area and air flow rate, respectively, brought about the maximum exergy efficiency of 6.27% for the given double pass/glazed v-corrugated plate solar air heater;  Among the exergy loss terms, the one originating from temperature difference between sun and absorber had the most important role while accounted for 63.57% of the whole exergy losses at the point corresponding to maximum exergy efficiency;  Exergy efficiency calculation based on its constituting loss terms, help to find their significance and the place which bring about such an exergetic loss;  The optical related exergy loss term occupied the second position in comparison with three other remaining terms of exergy loss.  The magnitudes of other three exergy loss terms were not much noticeable.

Acknowledgements Fig. 11. Variations of exergy efficiency of DPGVC plate solar air heater with air flow rate and corrugation height.

The authors also warmly acknowledge University of Birjand, Faculty of Agriculture, for their support.

810

M. Hedayatizadeh et al. / Energy 94 (2016) 799e810

References [1] El-Sawi AM, Wifi AS, Younan MY, Elsayed EA, Basily BB. Application of folded sheet metal in flat bed solar air collectors. Appl Therm Eng 2010;30(8): 864e71. [2] Esen H. Experimental energy and exergy analysis of a double-flow solar air heater having different obstacles on absorber plates. Build Environ 2008;43(6):1046e54. it F. Experimental investigation of thermal performance of [3] Akpinar EK, Koçyig solar air heater having different obstacles on absorber plates. Int Commun Heat Mass Transf 2010;37(4):416e21. [4] Abene A, Dubois V, Le Ray M, Ouagued A. Study of a solar air flat plate collector: use of obstacles and application for the drying of grape. J Food Eng 2004;65(1):15e22. [5] Ramadan MRI, El-Sebaii AA, Aboul-Enein S, El-Bialy E. Thermal performance of a packed bed double-pass solar air heater. Energy 2007;32(8):1524e35. [6] Ho CD, Yeh HM, Wang RC. Heat-transfer enhancement in double-pass flatplate solar air heaters with recycle. Energy 2005;30(15):2796e817. [7] Fahmy MFM, Labib AM. Modeling and analysis of a matrix solar air heater. Energy Convers Manag 1991;31(2):121e8. [8] Kolb A, Winter ERF, Viskanta R. Experimental studies on a solar air collector with metal matrix absorber. Sol Energy 1999;65(2):91e8. [9] Prasad SB, Saini JS, Singh KM. Investigation of heat transfer and friction characteristics of packed bed solar air heater using wire mesh as packing material. Sol Energy 2009;83(5):773e83. [10] Alta D, Bilgili E, Ertekin C, Yaldiz O. Experimental investigation of three different solar air heaters: energy and exergy analyses. Appl Energy 2010;87(10):2953e73. [11] Hedayatizadeh M, Ajabshirchi Y, Sarhaddi F, Farahat S, Safavinejad A, Chaji H. Analysis of exergy and parametric study of a v-corrugated solar air heater. Heat Mass Transf 2012;48(7):1089e101. [12] Liu T, Lin W, Gao W, Xia C. A comparative study of the thermal performances of cross-corrugated and v-groove solar air collectors. Int J Green Energy 2007;4(4):427e51. [13] Kumar R, Rosen MA. Thermal performance of integrated collector storage solar water heater with corrugated absorber surface. Appl Therm Eng 2010;30(13):1764e8. [14] Ali AHH, Hanaoka Y. Experimental study on laminar flow forced-convection in a channel with upper V-corrugated plate heated by radiation. Int J Heat Mass Transf 2002;45(10):2107e17. [15] Naphon P. Heat transfer characteristics and pressure drop in channel with V corrugated upper and lower plates. Energy Convers Manag 2007;48(5): 1516e24. [16] Karim MA, Hawlader MNA. Performance investigation of flat plate, v-corrugated and finned air collectors. Energy 2006;31(4):452e70. rik K. Shape optimization for absorber plates of solar air [17] Kabeel AE, Me ca collectors. Renew Energy 1998;13(1):121e31. [18] Chamoli S, Thakur NS. Exergetic performance evaluation of solar air heater having V-down perforated baffles on the absorber plate. J Therm Anal Calorim 2014;117(2):909e23. [19] Rosen MA. Using exergy to assess regional and national energy utilization: a comparative review. Arab J Sci Eng 2013;38(2):251e61. [20] Yang B, Chen L, Ge Y, Sun F. Exergy performance optimization of an irreversible closed intercooled regenerative Brayton cogeneration plant. Arab J Sci Eng 2014;39(8):6385e97. [21] Ajam H, Farahat S, Sarhaddi F. Exergetic optimization of solar air heaters and comparison with energy analysis. Int J Thermodyn 2005;8(4):183. [22] Velmurugan P, Kalaivanan R. Energy and exergy analysis of solar air heaters with varied geometries. Arab J Sci Eng 2015;40(4):1173e86. [23] Kalogirou SA. Optimization of solar systems using artificial neural-networks and genetic algorithms. Appl Energy 2004;77(4):383e405. [24] S¸ahin AS¸. Optimization of solar air collector using genetic algorithm and artificial bee colony algorithm. Heat Mass Transf 2012;48(11):1921e8.

[25] Nwosu NP. Employing exergy-optimized pin fins in the design of an absorber in a solar air heater. Energy 2010;35(2):571e5. [26] Singh S, Chander S, Saini JS. Exergy based analysis of solar air heater having discrete V-down rib roughness on absorber plate. Energy 2012;37(1):749e58. [27] Bayrak F, Oztop HF, Hepbasli A. Energy and exergy analyses of porous baffles inserted solar air heaters for building applications. Energy Build 2013;57: 338e45. [28] Sabzpooshani M, Mohammadi K, Khorasanizadeh H. Exergetic performance evaluation of a single pass baffled solar air heater. Energy 2014;64:697e706. [29] Yadav S, Kaushal M. Exergetic performance evaluation of solar air heater having arc shape oriented protrusions as roughness element. Sol Energy 2014;105:181e9. [30] Hollands KGT, Shewen EC. Optimization of flow passage geometry for airheating, plate-type solar collectors. J Sol Energy Eng 1981;103(4):323e30. [31] Liu T, Lin W, Gao W, Luo C, Li M, Zheng Q, et al. A parametric study on the thermal performance of a solar air collector with a v-groove absorber. Int J Green Energy 2007;4(6):601e22. [32] Verma R, Chandra R, Garg HP. Parametric studies on the corrugated solar air heaters with and without cover. Renew Energy 1991;1(3):361e71. [33] Sukhatme K, Sukhatme SP. Solar energy: principles of thermal collection and storage. Tata McGraw-Hill Education; 1996. [34] Lin W, Gao W, Liu T. A parametric study on the thermal performance of crosscorrugated solar air collectors. Appl Therm Eng 2006;26(10):1043e53. [35] Garg HP. Advances in solar energy technology: Volume 1: Collection and storage systems, vol. 1. Springer Science & Business Media; 1987. [36] El-Sebaii AA, Aboul-Enein S, Ramadan MRI, Shalaby SM, Moharram BM. Investigation of thermal performance of-double pass-flat and v-corrugated plate solar air heaters. Energy 2011;36(2):1076e86. [37] Benli H. Experimentally derived efficiency and exergy analysis of a new solar air heater having different surface shapes. Renew Energy 2013;50:58e67. [38] Yeh HM, Ho CD, Hou JZ. The improvement of collector efficiency in solar air heaters by simultaneously air flow over and under the absorbing plate. Energy 1999;24(10):857e71. [39] Kurtbas I, Durmus¸ A. Efficiency and exergy analysis of a new solar air heater. Renew Energy 2004;29(9):1489e501. [40] Karsli S. Performance analysis of new-design solar air collectors for drying applications. Renew Energy 2007;32(10):1645e60. [41] Bejan A, Kearney DW, Kreith F. Second law analysis and synthesis of solar collector systems. J Sol Energy Eng 1981;103(1):23e8. [42] Kotas TJ. The exergy method of thermal plant analysis. Elsevier; 2013. [43] Wong KV. Thermodynamics for engineers. CRC Press; 2011. [44] Joshi AS, Tiwari A, Tiwari GN, Dincer I, Reddy BV. Performance evaluation of a hybrid photovoltaic thermal (PV/T)(glass-to-glass) system. Int J Therm Sci 2009;48(1):154e64. [45] Farahat S, Sarhaddi F, Ajam H. Exergetic optimization of flat plate solar collectors. Renew Energy 2009;34(4):1169e74. [46] Altfeld K, Leiner W, Fiebig M. Second law optimization of flat-plate solar air heaters part I: the concept of net exergy flow and the modeling of solar air heaters. Sol Energy 1988;41(2):127e32. [47] Bouadila S, Lazaar M, Skouri S, Kooli S, Farhat A. Energy and exergy analysis of a new solar air heater with latent storage energy. Int J Hydrogen Energy 2014;39(27):15266e74. [48] Hedayatizadeh M, Ajabshirchi Y, Sarhaddi F, Safavinejad A, Farahat S, Chaji H. Thermal and electrical assessment of an integrated solar photovoltaic thermal (PV/T) water collector equipped with a compound parabolic concentrator (CPC). Int J Green Energy 2013;10(5):494e522. [49] Davis L. Handbook of genetic algorithms, vol. 115. New York: Van Nostrand Reinhold; 1991. [50] Fahmy FH, Atia DM, El-Rahman NM, Dorrah HT. Optimal sizing of solar water heating system based on genetic algorithm for aquaculture system. In: Chemistry and chemical engineering (ICCCE), 2010 international conference on (pp. 221e226). IEEE; 2010, August.