Energy and exergy analysis of hybrid micro-channel photovoltaic thermal module

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Solar Energy 85 (2011) 356–370 www.elsevier.com/locate/solener

Energy and exergy analysis of hybrid micro-channel photovoltaic thermal module Sanjay Agrawal ⇑, G.N. Tiwari Centre for Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India Received 7 January 2010; received in revised form 12 October 2010; accepted 16 November 2010 Available online 17 December 2010 Communicated by: Associate Editor S.C. Bhattacharya

Abstract In this communication, an attempt has been made to evaluate energy and exergy analysis of a hybrid micro-channel photovoltaic thermal (MCPVT) module based on proposed micro-channel solar cell thermal (MCSCT) under constant mass flow rate of air in terms of design and climatic parameter. The performance in terms of overall annual thermal and exergy gain and exergy efficiency of microchannel photovoltaic thermal module have been evaluated by considering four weather conditions for different climatic conditions of India. Further analysis has also been carried out for single channel photovoltaic thermal (SCPVT) module and the results of microchannel photovoltaic thermal module and single channel photovoltaic thermal module have been compared. On the basis of numerical computations, it has been observed that an overall annual thermal and exergy gains have been increased by 70.62% and 60.19% respectively for MCPVT module for Srinagar climatic conditions. Similar observations have been made for Bangalore, Jodhpur and New Delhi. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Exergy; Micro-channel; Hybrid photovoltaic thermal module

1. Introduction Several theoretical and experimental studies of hybrid photovoltaic thermal systems are available in the literature. Among the first, Kern and Russell (1978) have given the design and performance of water and air cooled hybrid PVT collector and they found that the hybrid collector systems are attractive in small buildings that have substantial heating loads. The passively cooled photovoltaic panels are best suited for structures located in regions where yearround air conditioning and small, low-grade, thermal energy demands predominate. Hendrie (1979) has presented a theoretical model on PVT systems using conventional thermal collector techniques. Florschuetz (1979) has suggested an extension of Hottel–Willer model to analyze steady state combined photovoltaic thermal collector ⇑ Corresponding author. Tel.: +91 9911428863; fax: +91 11 26591251.

E-mail address: [email protected] (S. Agrawal). 0038-092X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2010.11.013

with simple modification of conventional parameters of the original model by assuming a linear correlation between efficiency of solar cell array and its temperature over its operating temperature range. Raghuraman (1981) has given numerical methods for predicting the performances of liquid and air PVT flat plate collectors. Cox and Raghuraman (1985) have studied air type hybrid systems and made use of computer simulation to optimize the design of flat PVT solar air collector in order to increase the solar absorption and reducing the infrared emittance. Lalovic (1986) has proposed a novel transparent type of a-Si cell as a low cost improvement of hybrid systems. Bhargava et al. (1991) and Prakash (1994) have studied the effect of air mass flow rate, air channel depth, length and fraction of absorber plate area covered by solar cells on single pass air heater. They concluded that the solar cell efficiency was marginally improved while an average thermal efficiency of about 50–70% for water heating and 17–51% for air heating was obtained. Garg and Agarwal

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

357

Nomenclature Ac b d Cf dx dt h ho hi hb I(t) K L N m_ f Q_ u T T U

area of solar cell, m2 width of the micro-channel, m depth of micro-channel, m specific heat of air, J/kg K elemental length, m elemental time, s heat transfer coefficient, W/m2 K heat transfer coefficient from solar cell to ambient through glass cover, W/m2 K heat transfer coefficient from solar cell to flowing air, W/m2 K heat transfer coefficient from flowing air to ambient, W/m2 K incident solar intensity, W/m2 thermal conductivity, W/mK length, m number of micro-channel solar cell thermal (MCSCT) air mass flow rate in micro-channel, kg/s useful heat, W temperature, K average temperature, K overall heat transfer coefficient, W/m2 K

(1995) presented the first simulation study of the PVT aircooling flat plate collector. Sopian et al. (1996) have proposed at university of Miami a new design of double pass PVT collector which can produce more heat, while simultaneously having a productive cooling effect on the cell. Loferski et al. (1998) have given the result for a hybrid system with air circulator. Jones and Underwood (2001) have studied the temperature profile of a photovoltaic (PV) module in non steady state condition. They conducted experiments for cloudy as well as clear day condition for analysis. The photovoltaic module is employed for directly converting solar energy into electricity. The remaining thermal energy available with PV module increases its temperature and hence electrical efficiency decreases. If thermal energy associated with PV module is removed then its electrical efficiency can be improved. The carrier of thermal energy associated with the PV module can either be air or water. The integrated arrangement for utilizing the thermal energy as well as electrical energy with PV module is referred to as the hybrid photovoltaic thermal system. Performance analysis of a PVT system can be carried out either in terms of energy or exergy. Tripanagnostopoulos et al. (2002) studied an integrated unglazed hybrid PVT system with a booster diffuse reflector with the horizontal roofing of a building and concluded that the system yields distinctly clear higher electrical and thermal outputs. Sandnes and Rekstad (2002) observed that the hybrid PVT system concept must be used for low temperature thermal

v go V npv b0

velocity of air, m/s efficiency at standard test condition (I(t) = 1000 W/m2 and Ta = 25 °C) velocity of fluid (air) flowing inside of channel, m/s number of rows of micro-channel solar cell thermal (MCSCT) temperature coefficient of efficiency, 1/K

Greek letters a absorptivity b packing factor g efficiency q density, kg/m3 Subscripts a ambient air air in the duct c solar cell eff effective f fluid(air) fi inlet fluid fo outgoing fluid

applications and for increasing their electrical efficiency. Bosanac et al. (2003) have defined energy efficiency as the total energy yield for a year and the results are calculated from the first law of thermodynamics and exergy efficiency as the total exergy yield per year. According to Coventry and Lovegrove (2003), exergy (sometimes called availability) has been defined as the maximum theoretical useful work obtainable from system as it returns to equilibrium with the environment. Chow (2003) has analyzed the PVT water collector with a single glazing in transient conditions, consisted of tubes, in thermal contact with the flat plate on account of metallic bond. It has been observed that the electrical efficiency is increased by 2% at the mass flow rate of 0.01 kg/s due to decrease in temperature of solar cell of PV module. Temperature dependence of open circuit voltage, intensity dependence of the efficiency and thermo photovoltaic conversion efficiency has been discussed by Wu¨rfel (2009). Zondag et al. (2003) and Chow (2003) have given reasons for reduction of the electrical efficiency of the PV module. They are packing factor (PF) of PV module, ohmic losses between two consecutive solar cells and the temperature of the module. It has been found that an overall electrical efficiency of the PV module can be increased by increasing the packing factor (PF) and reducing the temperature of the PV module by using the thermal energy associated with the PV module. Nelson (2003) has described basic physics of semiconductors in photovoltaic devices, physical models of solar cell operation, character-

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

a

Air outlet

d=500 µm

m

istics and design of common types of solar cell and approaches to increasing solar cell efficiency. Tiwari and Sodha (2006) have developed a thermal model of integrated photovoltaic and thermal solar (IPVTS) water/air heating system. They observed that an overall thermal efficiency of IPVTS system for summer and winter conditions is about 65% and 77%, respectively. Tiwari and Sodha (2006) have validated the theoretical and experimental result for photovoltaic (PV) module integrated with air duct for composite climate of India. They concluded that an overall thermal efficiency of PVT system is significantly increased due to utilization of thermal energy from PV module. Thermal photovoltaic solar hybrid system for efficient solar energy conversion has been discussed by Vorobiev et al. (2005) and it has been found that thermal photovoltaic solar hybrid systems offer unexplored possibilities to increase the efficiency of solar to electric energy conversion. The possibility of generating electricity and heat energy from a commercial PV module adopted as a PVT air solar collector with either forced or natural airflow in the channel was demonstrated by Tonui and Tripanagnostopoulos (2007). Nayak and Tiwari (2008) have made exergy analysis of integrated photovoltaic thermal (IPVT) water heater under constant flow rate. They observed that an overall exergy and thermal efficiency of IPVT is maximum at the hot water withdrawal flow rate of 0.006 kg/s. Dubey and Tiwari (2009) have made detailed analysis of thermal energy, exergy and electrical energy yield by varying number of collectors by considering four weather conditions. Dubey et al. (2009) have developed an analytical expression for electrical efficiency of PV module with and without flow as function of climatic and design parameter and found that glass to glass PV module with duct gives higher electrical efficiency as well as higher outlet air temperature i.e. it gives higher thermal efficiency. Performance analysis of a hybrid photovoltaic–thermal integrated system has also been done by Radziemska (2009) who presented the concept of exergy analysis for evaluation of the PVT systems which is very useful tools for the improvement and costeffectiveness of the system. Energy and exergy analysis have been done by Agrawal and Tiwari (2010) for building integrated photovoltaic thermal system which is fitted on the rooftop with an effective area of 65 m2. It is capable of annually producing the net electrical and thermal exergies of 16209 kWh and 1531 kWh respectively. In this paper, a photovoltaic solar cell with micro-channel (Fig. 1a) which is encapsulated in between solar cell and tedlar is considered for the study. Such system has been proposed and will be referred as hybrid micro-channel solar cell thermal (MCSCT). In order to obtain maximum electrical and thermal efficiency, a series and parallel combination of MCSCT have been considered which is referred as micro-channel photovoltaic thermal (MCPVT) module as shown in Fig. 2. An overall annual gain in energy, exergy and exergy efficiency of the MCPVT module have been evaluated by considering four types of weather conditions for four different

b= 0. 12

358

Solar cell Tedlar

L=0.12 m

Micro-channel

Air inlet

b

Fig. 1. (a) View at A of Fig. 2 proposed micro-channel solar cell thermal (MCSCT). (b) Air flow pattern over elementary area bdx of proposed micro-channel solar cell thermal (MCSCT).

A

Fig. 2. Micro-channel PVT module (nine rows each having four cells in series are connected in parallel).

cities (Srinagar, Bangalore, Jodhpur and New Delhi) in India. These cities are classified under the four different climatic condition of India. The four types of weather conditions are defined as, Type a (clear days): The ratio of daily diffuse to daily global radiation is less than or equal to 0.25 and sunshine hours greater than or equal to 9 h. Type b (hazy days): The ratio of daily diffuse to daily global radiation is between 0.25 and 0.50 and sunshine hours between 7 and 9 h. Type c (hazy and cloudy days): The ratio of daily diffuse to daily global radiation is between 0.50 and 0.75 and sunshine hours between 5 and 7 h.

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

Type d (cloudy days): The ratio of daily diffuse to daily global radiation is greater than or equal to 0.75 and sunshine hours less than or equal to 5 h. The monthly average data of solar radiation for different climatic conditions was obtained from Indian Metrological Department (IMD), Pune. 2. System description The present study has been carried out on the proposed single hybrid micro-channel solar cell thermal (MCSCT) as shown in Fig. 1a. The proposed solar cell having dimension 0.12 m length and 0.12 m breadth has been considered. The solar cell have effective area of 0.0144 m2 with micro-channel of depth 500 lm below the solar cell. In the proposed design of MCSCT the channel is between cell and tedlar due to which the thermal resistance of tedlar is eliminated unlike conventional PV module in which there is tedlar thermal resistance between PV module and flowing air. There is provision for the inlet and outlet air to flow through the micro-channel of solar cell as shown in Fig. 1b. For the analysis, PVT module of nine rows, each having four cells with micro-channel in series, are connected in parallel as shown in Fig. 2, have been considered. If the outlet of one micro-channel solar cell thermal (MCSCT) is connected to the inlet of another MCSCT, then it is referred as series connection. If the inlet and outlet of each micro-channel solar cell thermal are same, then it is referred as parallel connection. The hybrid MCPVT module based on micro-channel solar cell thermal (MCSCT) has been analyzed in terms of an overall energy, exergy and exergy efficiency. The result has also been compared with result of photovoltaic thermal (PVT) module with single channel of Dubey et al. (2009), which will be referred as single channel photovoltaic thermal (SCPVT) module with same (micro depth) flow rate. 3. Thermal modeling In order to write the energy balance equation of MCSCT, the following assumptions have been made:  One dimensional heat-conduction is good approximation for the present study.  There is no temperature gradient along the thickness of solar cell.  The specific heat of air remains constant.  Heat capacity of solar cell is neglected.  The system is in quasi-steady state.  The ohmic losses in the solar cell are negligible.  There is stream line flow of air through the micro-channel at small flow rate.  Packing factor (b) is unity. Fig. 1 shows the cross sectional view of PV cell with micro-channel and an elemental area bdx of MCSCT.

359

Following Tiwari and Sodha (2006), the energy balance equation for solar cell can be written as ½ac IðtÞbdx ¼ ½ho ðT c  T a Þbdx þ hi ðT c  T f Þbdx þ gc IðtÞbdx 3 2 3 Rate of solar Rate of heat loss from 6 7 6 7 4 energy available 5 ¼ 4 top surface of solar cell 5 on solar cell to ambient 2 3 2 3 Rate of heat transfer Rate of 6 7 6 7 þ 4 from solar cell to 5 þ 4 electrical energy 5 flowing fluid i:e: air produced

ð1Þ

2

From Eq. (1), the expression for solar cell temperature is Tc ¼

ac IðtÞ  gc IðtÞ þ ho T a þ hi T f ho þ hi

or Tc ¼

aeff IðtÞ þ ho T a þ hi T f ho þ hi

ð2Þ

where aeff = (ac  gc) Energy balance for air flowing in the micro-channel of MCSCT for elemental area bdx is given by dT f hi ðT c  T f Þbdx ¼ m_ f C f dx þ hb ðT f  T a Þbdx dx 2 3 2 3 Rate of heat transfer The mass flow 6 7 6 7 4 from solar cell to 5 ¼ 4 rate of flowing 5 flowing fluid i:e: air fluid i:e: air 2 3 Rate of heat transfer 7 6 þ 4 from flowing fluid to 5 ambient

ð3Þ

where m_ f ¼ qLdV Solving Eqs. (2) and (3) with initial condition at x = 0, i.e. Tf = Tfi; one gets     hp aeff bU L x Tf ¼ IðtÞ þ T a 1  exp þ T fi m_ f C f UL   bU L x  exp ð4Þ m_ f C f At, x = L, Tf = Tfo, the outlet air temperature of microchannel solar cell thermal (MCSCT), one gets     hp aeff bU L L T fo ¼ IðtÞ þ T a 1  exp þ T fi m_ f C f UL   bU L L  exp ð5Þ m_ f C f The average air temperature over the length of air below micro-channel solar cell thermal (MCSCT) is obtained with help of Eq. (4) as Z 1 L Tf ¼ T f dx L 0

360

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

or

3.2. Energy analysis 

Tf ¼

hp aeff UL

 3 2  LL 1  exp bU m_ f C f 5 IðtÞ þ T a 41 

 3 2 LL 1  exp bU m_ f C f 5 þ T fi 4

bU L L m_ f C f

bU L L m_ f C f

ð6Þ

The energy analysis is based on the first law of thermodynamics, and the expression for total thermal gain can be defined as, P X X Q_ u;electrical Q_ u;thermal þ ð12Þ Q_ u;total ¼ gcpower where

For a number of MCSCT connected in series, the outlet temperature of first MCSCT will be the inlet for second MCSCT, the outlet temperature of second MCSCT will be the inlet for the third and so on. Hence for a system of N number of MCSCT connected in series, the outlet air temperature from Nth, MCSCT can be expressed in terms of Tfi. The outlet air temperature of N number of MCSCT connected in series is derived as     hp aeff NbU L L T foN ¼ IðtÞ þ T a 1  exp þ T fi m_ f C f UL   NbU L L  exp ð7Þ m_ f C f The rate of useful thermal energy obtained for npv row of MCPVT module Q_ U ;N ¼ npv  m_ f C f ðT foN  T fi Þ

ð8Þ

or      hp aeff _QU ;N ¼ npv  m_ f C f 1  exp NbU L L IðtÞ þ T a  T fi m_ f C f UL ð9Þ

3.1. Instantaneous electrical efficiency Electrical efficiency of solar cell depends on solar cell temperature is given by Schott (1985) and Evans (1981) and it is expressed as g ¼ go ½1  bo ðT c  T o Þ

ð10Þ

An expression for temperature dependent electrical efficiency of hybrid micro-channel solar cell thermal as function of design as well as climatic parameter can be obtained as   aeff IðtÞ hi hp aeff IðtÞ g ¼ g o 1  bo  ðT o  T a Þ þ ho þ hi U L ðho þ hi Þ  9  9 8 8 NbU L L = LL = < 1  exp NbU < 1  exp m_ f C f m_ f C f hi þ 1 NbU L L NbU L L : ; : ; ðh þ h Þ o i m_ f C f m_ f C f   T a  T fi Þ ð11Þ

Q_ uN Q_ u;thermal ¼ 1000

ð13Þ

Overall thermal gain from a PVT system = thermal energy collected by the PVT system + (electrical output /gcpower). where, gcpower is the electric power generation efficiency conversion factor of a conventional power plant for India. This is so because electrical energy is a high-grade form of energy which is required for operation of DC motor. This electrical energy has been converted to equivalent thermal energy by using electric power generation efficiency conversion factor as 0.20–0.40 for a conventional power plant, Huang et al. (2001) and it depends on quality of coal, usual the value of this factor is taken as 0.38 for conversion. 3.3. Exergy analysis The exergy of a thermodynamic system is the maximum work that can be done by the system when undergoes reversible processes that bring the system into complete thermodynamic equilibrium with a defined reference environment. Exergy is always destroyed when a process involves a temperature change. This destruction is proportional to the entropy increase of the system together with its surroundings. The destroyed exergy has been called anergy. Exergy analysis identifies the location, magnitude and the source of thermodynamic inefficiencies in a system. This information, which can not be provided by other means (e.g., energy analysis), is very useful for the improvement and cost-effectiveness of the system. The exergy analysis is based on the second law of thermodynamics, which includes accounting the total exergy inflow, exergy outflow and exergy destructed from the system. The general exergy balance for a micro-channel PVT module can be written as, X X X _ in  _ out ¼ _ dest Ex Ex Ex ð14Þ or, X

_ in  Ex

X X _ thermal þ Ex _ electrical Þ ¼ _ dest ðEx Ex

and X X X _ out ¼ _ thermal þ _ electrical Ex Ex Ex where

ð15Þ

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

"    4 # _ in ¼ Ac  N  IðtÞ  1  4  T a þ 1  T a ; Petela ð2003Þ ð16Þ Ex Ts Ts 3 3   _ thermal ¼ Q_ U ;N 1  T a þ 273 and Ex ð17Þ T fo þ 273   _ electrical ¼ g  A  IðtÞ ð18Þ Ex 1000

where A is area of module and Ts is the Sun temperature in Kelvin. The Exergy efficiency of MCPVT module is defined by Hepbasli (2008) as follows:   _ out Ex gEX ¼  100 ð19Þ _ in Ex 4. Methodology The climatic data, namely solar radiation and ambient air temperature have been obtained from Indian Metrological Department (IMD), Pune (see Table 2). The hourly variation of solar radiation and ambient air temperature for a typical day of Srinagar has been shown in Fig. 3. 4.1. Energy analysis

4.1.1. Annual thermal gain I. The rate of useful thermal energy for configuration as explained in system description are obtained using Eq. (9) considering N equal to four and putting, npv equal to nine for configuration . II. Daily thermal gain in kWh of a–d type weather have been calculated using Eq. (13). III. Monthly thermal gain in kWh have been calculated by multiplying daily thermal output and no. of clear days in a month of a–d type weather of MCPVT module.

Solar intensity, W/m 2

6

600

5 500

4

400

3

300

2 1

200

It Ta

100

0 -1

Ambient temperature, 0C

7

700

8:00

IV. Annual thermal gain has been calculated by summing the monthly thermal gain of a–d type weather of MCPVT module. V. An overall annual thermal gain has been evaluated using Eq. (12) 4.1.2. Annual electrical gain I. MCSCT based electrical efficiency of MCPVT module have been calculated for configuration as explained in system description using Eq. (11) considering N equal to four based on hourly solar radiation, ambient temperature and cell temperature. II. Daily electrical energy generated in kWh of a–d type weather of MCPVT module have been calculated by Eq. (18). III. Monthly electrical output have been calculated by multiplying daily electrical energy generated and no. of clear days in a month of a–d type weather of MCPVT module. IV. An annual electrical output have been calculated by summing the monthly electrical output of a–d type weather. 4.2. Exergy analysis

Annual electrical, thermal output and exergy can be obtained as follows:

0

361

-2 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

Time (Hours) Fig. 3. Hourly variation of solar intensity and ambient temperature for the month of January.

I. Daily exergy equivalent of thermal output has been calculated from Eq. (17). II. Monthly output exergy has been calculated by multiplying daily exergy output and no. of clear days in a month of a–d type weather. III. Annual output exergy has been calculated by summing the monthly input exergy of a–d type weather. IV. As electrical output of MCPVT module is a form of exergy, overall annual exergy of MCPVT module is obtained by Eq. (15) 4.3. Exergy efficiency Exergy efficiency has been calculated by following steps: I. Firstly daily input exergy of a–d type weather have been calculated using Eq. (18). II. Monthly input exergy has been calculated by multiplying daily exergy input and no. of clear days in a month of a–d type weather. III. Annual input exergy have been calculated by summing the monthly input exergy of a–d type weather. IV. Daily exergy output of a–d type weather have been evaluated by using Eqs. (15), (17) and (18). V. Monthly output exergy have been calculated by multiplying daily exergy output and no. of clear days in a month of a–d type weather. VI. Annual output exergy have been calculated by summing the monthly input exergy of a–d type weather. VII. An overall exergy efficiency has been calculated by using Eq. (19).

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S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370 Table 1 Design parameters of micro-channel solar cell thermal (MCSCT). Parameters

Values

cf J/kg K ho W/m2 K hi W/m2 K hb W/m2 K Kc W/mK Lc m ac b0 1/K gc m_ f kg/s v m/s V m/s dm Ac m2 q kg/m3

1012 5.7 + 3.8  v 2.8 + 3  v 1 0.039 0.0003 0.9 0.0045 0.15 .000036 1.5 0.5 0.0005 0.0144 1.29

5. Results and discussions The values of various design parameter of MCSCT are given in Table 1.The hourly variation of solar intensity and ambient temperature for a typical day in the month of January for Srinagar has been shown in the Fig. 3. Following the above mentioned methodology, Eqs. (2), (5) and (11) have been computed by using Matlab 7 for evaluating the hourly variation of solar cell, the outlet air temperature and solar cell electrical efficiency of micro-channel photovoltaic thermal (MCPVT) module at different depth of micro-channel for the month of January of Srinagar. The results have been shown in Fig. 4. It is observed that the electrical efficiency decreases with increase of solar cell and the outlet air temperature and vice-versa with decrease of solar cell and the outlet air temperature. These results are in accordance with the result reported by earlier researcher, Zondag et al. (2003). It has also been observed that the solar cell temperature and the outlet air temperature are maximum and electrical efficiency is minimum between 12:00 and 13:00 h. One can also observe that solar cell electrical efficiency, outlet air temperature is higher and solar cell temperature is lower at micro-channel depth (d) of 500 lm in comparison to that of micro-channel depth 1000 and 1500 lm. Hence for better performance of MCPVT, micro-channel depth 500 lm has been taken for further calculations. The monthly thermal energy, exergy and electrical energy gain are evaluated by using Eq. (9), (15) and (18). The computation has been carried out by considering the four type weather condition (a–d type) of Srinagar. For MCPVT and SCPVT modules, the monthly variation of an overall thermal energy gain (kWh) for four type of weather condition of Srinagar have been shown in Fig. 5. It is seen that the maximum and the minimum overall thermal energy gain for both the cases are obtained during May and December month respectively. It is also seen that monthly variation of overall thermal energy gain of

MCPVT module is higher than SCPVT module as expected. This is due to decrease in heat transfer coefficient from solar cell to flowing air by eliminating the tedlar thermal resistance and because of change in air flow pattern due to partition of single channel into combination of proposed micro-channel solar cell thermal as shown in Fig. 2. An overall thermal energy gain for MCPVT and SCPVT modules are 42.96 kWh and 24.39 kWh in the month of May and 19.45 kWh and 12.41 kWh in month of December respectively. This concludes that the monthly overall thermal energy gain in case of MCPVT module is higher than SCPVT module. The monthly variation of overall exergy gain (kWh) for Srinagar has been shown in Fig. 6. It is clear that the maximum and the minimum overall exergy gain for both the case are obtained during May and December month respectively. In this case too, the monthly variation of overall exergy gain of MCPVT module is higher than SCPVT module. Monthly overall exergy efficiency has been evaluated with help of Eqs. (15)–(19) of MCPVT and SCPVT module of Srinagar. Monthly variation of overall exergy efficiency of a–d type weather of Srinagar of MCPVT and SCPVT modules have been shown in Figs. 7 and 8 respectively. Monthly overall exergy efficiency for both the cases (MCPVT and SCPVT module) has been shown in Fig. 9 for comparison. It has been observed that the monthly overall exergy efficiency of MCPVT module is maximum (18%) in month of January and minimum (15.8%) in the month of June while in case of SCPVT module, an overall exergy efficiency is maximum (12.48%) in month of December and minimum (9.38%) in month of June. On the basis of above result it is concluded that MCPVT module give higher overall exergy efficiency than SCPVT module. The similar analysis of monthly overall thermal energy, exergy gain and exergy efficiency for rest three different cities of India (Bangalore, Jodhpur and New Delhi) have been evaluated. On the basis of monthly analysis, annual analysis have been carried out for all four cities .The comparison chart of overall annual thermal and exergy gain considering the four type of weather condition for four different cities of India (Srinagar, Bangalore, Jodhpur and New Delhi) taking both the case (MCPVT and SCPVT module) is shown in Figs. 10 and 11 respectively. The detailed analysis shows that the maximum overall annual thermal gain (434.09 kWh in case of MCPVT module and 249.64 kWh in case of SCPVT module) and overall exergy gain (152.96 kWh in case of MCPVT module and 93.57 kWh in case of SCPVT module) is obtained for the Bangalore and minimum overall annual thermal gain (377.43 kWh in case of MCPVT module and 221.20 kWh in case of SCPVT module) and overall exergy gain (132.91 kWh in case of MCPVT module and 82.97 kWh in case of SCPVT module) for the Srinagar .It can be seen that the annual overall thermal and exergy gain for all four cities of MCPVT module are higher than SCPVT module. The comparison graph of overall exergy efficiency for four different cities of India taking both the case (MCPVT

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

363

Table 2 Measured average hourly global radiations (W/m2) on horizontal surface, number of days fall under different weather conditions and the average ambient temperature (°C) for different places in India (Source: IMD, Pune). Month Solar radiation Time

January

February March

April

May

June

July

August

September October

November December

2

(a) Bangalore: (i) Measured average hourly global radiations for “type a” Global 8 am 181.04 208.59 230.90 269.44 309.26 9 am 412.80 428.66 493.29 536.80 558.34 10 am 617.39 655.05 736.69 780.56 753.70 11 am 781.10 821.46 926.62 963.89 905.56 12 pm 855.07 911.99 1034.14 1046.88 969.91 1 pm 866.49 910.10 1029.51 1048.96 963.89 2 pm 788.35 859.22 936.92 956.25 878.70 3 pm 637.26 716.03 779.28 772.22 743.52 4 pm 429.83 500.63 561.69 550.00 538.43 5 pm 201.69 262.00 323.03 274.65 290.28

weather 277.77 511.11 698.61 823.61 861.12 826.38 850.00 737.50 444.44 319.44

condition 276.16 528.47 686.57 815.97 865.74 836.34 821.07 652.78 437.04 290.51

(W/m ) 274.54 545.84 674.54 808.33 870.37 846.29 792.13 568.05 429.63 261.57

279.17 541.66 758.34 908.34 986.11 926.39 920.84 537.50 477.77 256.94

249.54 501.94 720.51 864.72 934.40 914.91 862.55 602.36 435.60 231.02

208.33 453.89 664.17 798.89 875.28 870.56 796.39 640.83 425.83 200.00

142.54 376.59 589.52 750.79 828.25 837.62 771.43 619.92 408.57 185.79

(a) Bangalore: (ii) Measured average hourly global radiations for “type b” Global 8 am 159.82 178.04 194.27 235.99 249.91 9 am 392.66 400.95 429.51 479.40 475.93 10 am 615.48 604.51 626.39 699.30 688.43 11 am 774.11 748.09 788.02 852.78 828.89 12 pm 794.25 818.75 872.57 941.55 878.80 1 pm 796.23 827.52 864.41 948.38 854.44 2 pm 745.63 689.24 775.52 850.93 769.17 3 pm 609.72 583.85 581.42 669.44 653.98 4 pm 411.71 410.85 412.50 487.27 457.04 5 pm 196.73 192.01 229.34 245.60 253.52

weather 217.13 432.25 646.61 757.72 827.32 824.69 752.93 560.65 414.04 220.83

condition (W/m2) 241.67 212.78 443.21 431.11 624.07 652.22 779.32 752.22 776.85 835.56 756.17 796.67 710.80 730.56 604.01 558.89 419.75 422.22 259.88 227.22

261.11 405.56 716.67 825.00 866.67 669.44 611.11 450.00 372.22 213.89

223.61 416.67 665.27 859.03 919.45 850.00 750.00 683.34 447.23 215.28

139.24 376.39 614.93 721.53 767.36 777.08 718.75 530.21 400.00 148.61

128.31 344.71 584.39 735.45 772.75 725.66 658.20 490.61 317.20 130.95

(a) Bangalore: (iii) Measured average hourly global radiations for Global 8 am 124.31 125.00 185.42 153.70 9 am 311.81 347.22 345.14 344.44 10 am 484.72 534.26 547.92 560.19 11 am 665.97 710.19 780.55 775.00 12 pm 561.80 624.07 870.14 807.40 1 pm 610.41 825.00 674.31 789.81 2 pm 609.72 662.04 486.81 697.22 3 pm 485.42 459.26 371.53 720.37 4 pm 256.94 327.78 259.03 516.67 5 pm 160.42 130.56 184.03 233.33

“type c” weather condition (W/m2) 203.47 202.38 189.77 172.68 384.26 408.34 356.00 372.69 551.85 583.73 504.97 518.52 702.32 617.46 574.27 694.45 860.88 782.94 692.54 635.65 832.41 715.87 697.51 700.46 690.97 650.79 605.70 646.30 532.87 468.25 557.02 485.65 394.68 353.97 389.18 346.30 230.79 200.00 199.42 185.19

182.41 425.92 638.89 747.22 745.37 765.74 637.04 542.59 409.26 218.52

181.95 378.47 582.64 652.78 650.00 644.45 700.00 484.72 340.97 115.28

112.78 290.00 435.00 590.56 593.33 641.67 430.56 414.44 279.45 98.33

85.77 284.37 499.65 572.92 526.04 535.42 496.18 406.94 300.35 105.56

(a) Bangalore: (iv) Measured average hourly global radiations for Global 8 am 101.39 133.33 152.43 177.95 9 am 270.37 350.00 355.32 397.80 10 am 481.02 577.78 479.05 478.06 11 am 446.76 616.67 533.45 576.79 12 pm 366.20 422.22 537.96 623.84 1 pm 423.61 500.00 534.37 589.76 2 pm 431.48 511.11 540.39 594.85 3 pm 412.50 583.33 463.19 488.54 4 pm 235.65 338.89 297.34 328.18 5 pm 166.20 233.33 176.85 182.18

“type d” weather condition (W/m2) 203.47 182.54 141.67 165.08 440.27 344.44 331.25 282.54 477.08 476.98 446.88 450.79 620.14 546.03 494.10 519.84 709.72 636.11 482.29 651.98 645.14 633.73 481.25 603.57 649.31 564.29 485.42 508.33 513.89 471.03 345.83 400.79 359.03 253.18 299.31 291.67 187.50 117.46 154.86 148.81

150.00 222.22 308.33 419.44 522.22 480.56 438.89 427.78 258.33 77.78

110.52 204.33 377.54 424.28 541.03 426.54 481.90 350.45 107.89 58.73

81.67 108.89 361.11 522.22 666.67 525.00 408.33 361.11 104.44 47.22

69.44 190.74 384.26 276.85 310.19 347.22 351.85 241.67 132.41 99.07

Type of days

January February March

April

May

June

(a) Bangalore: (v) Number of days fall in different weather condition a 7 8 9 9 7 b 16 11 11 10 13 c 6 7 8 9 8 d 2 2 3 2 3

July

August September October

8 11 8 3

7 13 7 4

June

July

6 11 10 4

8 10 9 3

November December 7 10 11 3

6 10 12 2

7 10 12 2

Month Solar radiation Time

January

(a) Bangalore: (vi) Average ambient 8 am 16.00 9 am 16.00 10 am 16.00

February March temperature 17.60 17.10 16.60

April

May

for different months (°C) 18.50 21.80 20.80 18.50 21.60 20.80 18.50 21.60 20.80

21.70 21.80 20.80

21.60 21.10 20.80

August 21.30 21.10 20.70

September October 21.30 20.80 20.60

21.40 21.40 21.50

November December 16.70 16.70 16.40

16.50 16.50 15.40

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S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

Table 2 (continued) Month Solar radiation Time 11 am 12 pm 1 pm 2 pm 3 pm 4 pm 5 pm

January 15.90 16.50 18.40 21.30 23.50 25.80 25.00

February March 16.60 17.10 19.60 23.20 25.90 28.20 29.60

(b) Jodhpur: (i) Measured average hourly global Global 8 am 129.75 200.73 9 am 330.27 414.62 10 am 506.54 591.27 11 am 632.93 713.56 12 pm 691.90 776.19 1 pm 690.68 776.85 2 pm 626.45 711.90 3 pm 503.24 587.70 4 pm 332.81 410.58 5 pm 130.03 196.63

18.50 20.00 22.90 25.20 26.90 29.70 31.20

April 21.60 21.60 24.30 26.90 29.70 32.50 33.20

May 20.80 20.90 22.40 24.10 26.00 27.30 28.10

June 20.80 21.50 22.50 24.00 25.50 26.10 27.20

July 20.70 20.70 20.50 21.40 23.10 25.50 26.50

August

September October

November December

20.80 20.80 22.40 23.80 25.50 26.80 28.20

20.60 20.80 22.80 23.30 24.30 26.30 28.10

21.80 21.90 22.70 22.90 22.90 24.00 24.10

16.40 17.20 20.10 21.40 22.90 24.40 24.90

15.30 15.70 20.00 22.30 23.50 24.10 24.60

radiations for “type a” weather condition (W/m2) 286.48 343.28 378.15 398.61 399.89 337.71 494.82 549.00 574.17 576.39 578.23 526.88 676.60 723.33 735.65 716.67 718.96 682.14 787.82 823.56 843.70 817.13 819.74 787.82 845.99 886.72 896.11 883.33 886.16 848.20 853.37 893.56 900.28 891.67 894.52 854.90 787.29 826.95 844.26 845.37 848.08 801.73 669.12 717.33 729.17 732.87 735.21 687.31 490.60 550.94 568.33 574.07 575.91 524.33 275.37 338.94 369.54 389.35 390.60 324.73

275.52 475.52 645.31 755.90 810.24 815.28 755.38 639.41 472.74 258.86

208.82 405.64 582.35 694.04 752.94 754.98 695.26 571.41 407.27 201.14

138.47 332.69 494.86 607.73 666.39 671.67 617.13 497.82 336.57 139.95

120.90 299.79 462.20 577.78 639.18 637.33 582.91 460.27 300.55 110.98

(b) Jodhpur: (ii) Measured average Global 8 am 108.95 9 am 290.68 10 am 460.31 11 am 583.43 12 pm 649.01 1 pm 639.41 2 pm 571.52 3 pm 444.30 4 pm 279.71 5 pm 99.25

hourly global radiations for “type b” weather condition 177.66 256.97 325.96 358.36 360.76 356.67 376.71 460.98 527.81 548.83 543.36 533.00 553.31 630.16 701.79 710.64 682.64 660.55 672.75 750.62 810.22 817.98 786.07 778.78 738.24 813.49 865.71 877.08 838.19 845.33 734.22 820.64 870.90 880.94 847.01 838.00 665.13 757.05 797.49 817.05 802.13 785.78 525.00 640.78 685.45 706.93 694.62 691.56 357.86 465.21 514.52 547.98 544.23 534.11 161.11 252.69 313.03 358.98 360.55 351.78

(W/m2) 318.75 496.53 644.56 731.13 809.72 825.93 774.88 662.50 492.36 311.11

268.38 474.95 641.77 736.41 796.77 794.85 740.40 612.78 443.18 260.50

204.26 402.73 566.20 675.23 727.04 735.14 678.98 549.63 388.06 190.28

126.53 310.88 476.57 587.45 644.44 649.72 600.19 473.52 319.26 130.09

89.39 263.89 429.20 550.54 611.69 616.51 550.15 428.70 264.31 90.28

(b) Jodhpur: (iii) Measured average Global 8 am 62.15 9 am 207.99 10 am 337.85 11 am 410.42 12 pm 462.50 1 pm 545.49 2 pm 491.32 3 pm 370.49 4 pm 232.29 5 pm 83.33

hourly global radiations for “type c” weather condition 133.33 192.86 256.60 294.44 320.20 326.39 300.93 356.35 486.81 465.74 444.45 430.76 494.44 495.64 584.03 601.85 613.89 592.26 611.11 595.24 729.17 690.74 714.65 686.31 510.18 687.30 821.18 767.59 787.63 730.36 577.78 677.38 753.82 739.81 788.64 706.15 516.67 620.64 719.10 714.81 711.87 646.03 320.37 482.15 650.00 646.30 653.54 585.71 220.37 352.38 498.26 475.00 527.53 480.16 110.19 186.91 314.24 295.37 337.88 298.02

(W/m2) 278.03 445.71 580.30 685.35 762.12 740.15 680.56 564.90 453.79 259.34

280.56 412.96 526.85 627.32 733.33 767.13 740.74 604.17 411.11 251.85

91.67 184.72 287.50 618.05 688.89 680.55 558.33 513.88 398.61 176.38

77.78 205.56 356.94 422.23 581.95 531.95 473.62 293.06 231.94 106.94

56.95 208.80 272.68 457.41 468.52 463.43 425.00 331.02 199.54 75.00

(b) Jodhpur: (iv) Measured average Global 8 am 50.46 9 am 182.87 10 am 319.91 11 am 422.69 12 pm 427.78 1 pm 396.76 2 pm 463.89 3 pm 368.52 4 pm 277.32 5 pm 120.83

hourly global radiations for “type d” weather condition 53.70 119.44 125.42 186.32 247.22 105.00 204.63 166.66 175.00 327.78 480.56 231.67 337.04 373.61 392.29 387.81 383.33 315.00 531.48 433.33 455.00 495.56 536.11 397.78 475.00 340.27 357.29 505.04 652.78 500.56 437.96 415.27 436.04 584.68 733.33 546.67 488.89 556.95 584.79 479.89 375.00 471.67 387.03 431.94 453.54 289.27 125.00 315.56 315.74 191.66 201.25 252.01 302.78 239.44 177.78 84.72 88.96 195.87 302.78 187.22

(W/m2) 159.03 291.67 314.58 468.05 451.39 461.11 579.86 506.94 343.06 165.97

152.78 330.56 391.67 475.00 537.04 474.07 392.59 312.04 269.45 116.67

183.33 377.78 533.33 538.89 666.67 647.22 583.33 425.00 305.56 144.44

76.39 248.61 302.77 369.44 304.17 362.50 352.77 288.89 158.34 56.95

47.22 161.11 302.78 313.89 380.56 355.56 438.89 350.00 238.89 63.89

Type of days

January February March

April

May

June

(b) Jodhpur: (v) Number of days fall in different weather condition a 7 9 11 11 9 b 14 13 13 15 17 c 8 5 6 3 4 d 2 2 1 1 1

July 7 18 4 1

August September October 6 16 6 3

5 18 5 3

5 17 6 2

November December 6 13 10 2

5 6 11 14 11 9 3 2 (continued on next page)

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

365

Table 2 (continued) Month Solar radiation Time

January

(b) Jodhpur: (vi) Average 8 am 9 am 10 am 11 am 12 pm 1 pm 2 pm 3 pm 4 pm 5 pm

ambient temperature for different 13.40 16.90 22.50 12.80 15.90 21.70 11.90 15.80 21.30 11.60 15.60 21.30 11.70 15.60 21.90 10.50 17.10 25.30 14.30 19.60 29.80 19.40 22.60 32.30 21.70 25.10 33.80 24.20 26.10 34.30

February March

April

May

months 24.00 23.80 23.30 23.30 23.30 24.50 26.60 29.70 31.80 32.50

June

(°C) 31.10 30.20 29.50 29.40 29.80 31.10 32.70 33.90 35.50 36.80

31.90 32.20 32.60 32.70 33.20 34.80 36.00 37.10 33.80 40.00

(c) New Delhi: (i) Measured average hourly global radiations for type “a” Global 8 am 132.99 180.29 266.77 368.14 406.31 9 am 355.56 403.58 488.94 588.48 608.84 10 am 554.69 594.44 671.21 767.81 776.26 11 am 680.73 729.39 804.33 888.32 897.98 12 pm 726.74 786.02 866.93 941.01 956.82 1 pm 733.85 792.03 869.28 944.12 950.51 2 pm 656.08 728.58 803.15 878.68 886.62 3 pm 500.00 584.23 665.33 746.90 761.37 4 pm 311.46 391.22 483.01 568.30 580.81 5 pm 106.42 178.23 264.10 348.61 372.48

weather 436.67 637.22 802.22 915.00 951.67 946.11 882.78 765.56 611.67 420.00

(c) New Delhi: (ii) Measured average hourly global radiations for Global 8 am 119.58 186.67 300.45 413.11 9 am 332.50 425.84 540.22 635.55 10 am 516.25 609.59 733.78 808.89 11 am 650.41 752.50 872.45 936.00 12 pm 708.75 813.75 933.11 999.55 1 pm 723.33 822.50 938.89 982.22 2 pm 650.41 758.33 869.55 901.34 3 pm 498.75 603.75 713.55 751.11 4 pm 315.00 408.33 522.89 557.55 5 pm 110.84 183.75 288.89 332.22

type “b” 439.11 641.34 794.45 898.45 947.55 936.00 852.22 722.22 540.22 340.89

July

November December

21.80 21.50 21.00 20.60 21.90 26.40 29.80 33.60 34.30 35.10

15.40 15.30 15.90 15.90 16.30 21.50 25.50 27.70 30.00 30.90

17.50 17.00 16.00 16.00 16.00 16.00 18.80 22.00 24.80 25.60

condition (W/m2) 367.36 333.59 587.04 528.54 737.27 674.49 831.71 820.20 881.48 868.18 896.53 807.83 820.60 766.67 753.24 658.08 569.68 477.78 373.15 305.81

277.96 501.30 682.04 809.07 869.07 855.19 779.81 656.48 483.89 270.19

168.75 364.58 565.28 694.45 761.80 756.25 686.11 543.75 362.50 152.08

121.46 316.04 485.35 609.97 664.01 657.45 587.37 454.17 274.62 84.09

93.12 275.27 443.25 565.87 621.83 618.39 553.31 426.19 253.97 68.78

weather condition (W/m2) 433.34 398.66 366.89 641.34 592.22 551.78 794.45 751.11 713.55 912.89 840.66 832.00 999.55 936.00 881.11 996.66 907.11 881.11 912.89 837.78 808.89 808.89 707.78 687.55 635.55 554.66 505.55 416.00 352.45 317.78

277.34 499.78 687.55 788.66 837.78 860.89 800.22 667.34 462.22 265.78

260.00 442.00 598.00 693.34 728.00 702.00 615.34 465.11 283.11 98.22

153.11 332.22 470.89 574.89 606.66 563.34 491.11 352.45 193.55 86.66

86.66 280.22 456.45 580.66 629.78 635.55 566.22 424.66 228.22 63.55

(c) New Delhi: (iii) Measured average hourly global radiations for Global 8 am 71.11 117.78 197.78 288.89 9 am 235.55 284.45 366.66 453.34 10 am 360.00 420.00 513.34 582.22 11 am 457.78 522.22 613.34 677.78 12 pm 515.55 562.22 664.45 724.45 1 pm 515.55 562.22 662.22 720.00 2 pm 462.22 506.66 602.22 664.45 3 pm 353.34 384.45 497.78 564.45 4 pm 217.78 266.66 353.34 420.00 5 pm 71.11 111.11 188.89 233.34

type “c” weather condition (W/m2) 361.11 358.33 333.33 297.50 566.67 555.56 530.67 490.00 708.33 727.78 642.66 597.50 841.67 816.67 744.00 700.00 894.44 833.33 778.67 702.50 872.22 861.11 762.66 702.50 805.56 763.89 722.67 630.00 666.67 688.89 602.67 540.00 513.89 538.89 469.33 430.00 322.22 333.33 280.00 282.50

261.25 456.53 617.50 691.39 730.97 752.09 712.50 575.28 414.30 255.97

195.83 365.56 496.11 587.50 624.06 608.39 514.39 383.83 229.77 73.11

66.66 206.66 333.34 415.55 444.45 453.34 406.66 313.34 177.78 62.22

66.66 216.00 365.34 482.67 544.00 522.66 448.00 341.34 200.00 58.67

(c) New Delhi: (iv) Measured average hourly global radiations for Global 8 am 51.20 94.30 169.75 266.75 140.11 188.61 331.42 441.89 503.44 10 am 237.11 247.89 479.61 600.86 11 am 301.78 291.00 552.36 716.72 12 pm 379.92 369.14 590.08 773.30 1 pm 379.92 412.25 627.80 757.14 2 pm 328.72 374.53 568.53 689.78 3 pm 261.36 299.08 463.45 541.58 4 pm 161.67 204.78 307.17 425.72 5 pm 45.80 88.92 161.67 239.80 Type of days January February March April May

“type d” weather condition (W/m2) 304.12 235.12 262.50 208.47 350.12 397.50 358.89 287.50 623.56 454.88 515.00 440.70 702.78 595.44 587.50 530.41 761.56 672.12 605.00 572.64 764.12 682.34 615.00 588.47 621.00 631.22 517.50 562.09 529.00 536.66 445.00 496.11 426.78 426.78 347.50 348.34 255.56 281.12 232.50 195.28 June July August September

155.00 237.66 425.00 557.50 585.00 585.00 530.00 442.50 350.00 187.50 October

110.84 184.00 375.66 488.12 503.44 511.12 454.88 339.88 237.66 113.75 November

63.88 176.95 273.44 375.66 444.66 477.88 424.22 337.34 198.33 66.44 December

2 3 10 17

26.40 26.50 26.50 26.50 28.20 29.10 29.60 30.60 32.60 32.60

September October 23.30 23.20 23.20 23.20 23.20 24.90 26.80 29.50 31.70 32.40

(c) New Delhi: (v) Number of days fall in different type of days for New Delhi a 3 3 5 4 4 3 b 8 4 6 7 9 4 c 11 12 12 14 12 14 d 9 9 8 5 6 9

26.40 25.70 25.70 25.70 25.70 25.90 26.30 27.00 28.10 28.60

August

2 3 7 19

7 3 10 10

5 10 13 3

6 10 12 2

54.45 272.22 356.61 397.45 405.61 359.34 239.55 141.55 52.72

3 7 13 8

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S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

Table 2 (continued) Month Solar radiation Time

January

February March

(c) New Delhi: (vi) Average monthly 8 am 7.90 9 am 7.90 10 am 7.90 11 am 6.60 12 pm 6.40 1 pm 7.70 2 pm 10.60 3 pm 13.00 4 pm 15.00 5 pm 16.50

April

ambient temperature (oC) for 9.20 15.80 25.00 9.10 15.90 25.00 8.90 15.90 25.00 8.80 15.80 25.10 8.90 16.60 25.90 11.40 19.90 27.60 15.10 22.80 30.30 18.30 26.20 31.70 20.10 27.00 33.20 21.60 28.90 34.40

May

June

July

August

September October

each month for New Delhi from IMD, 30.80 26.50 26.10 24.30 30.80 26.30 26.10 24.30 30.10 26.30 26.20 24.30 30.60 26.50 26.30 24.30 31.80 27.30 26.60 24.40 33.80 29.90 28.00 25.50 35.30 31.40 28.40 25.60 36.60 32.20 29.30 26.00 37.60 33.60 30.40 26.40 38.50 34.30 32.20 27.10

November December

Pune 27.90 27.90 27.90 28.30 28.90 30.60 32.30 33.50 33.90 35.50

21.00 21.00 20.50 20.50 22.70 25.00 28.30 30.50 31.60 32.70

17.00 16.70 16.50 16.00 16.20 20.50 25.00 27.60 28.50 29.60

9.60 9.10 8.90 8.70 9.40 13.10 16.80 19.30 20.90 21.70

(d) Srinagar: (i) Measured average Global 8 am 73.61 9 am 252.78 10 am 455.56 11 am 545.84 12 pm 577.78 1 pm 572.22 2 pm 511.11 3 pm 418.06 4 pm 227.78 5 pm 43.06

hourly global radiations for “type a” weather condition 69.79 221.53 373.06 408.52 434.92 408.89 284.72 461.57 594.31 633.52 634.52 626.11 481.60 665.74 776.53 793.52 796.43 788.06 647.22 800.70 880.56 915.74 904.76 888.89 732.99 891.43 932.50 981.67 951.19 950.28 747.57 905.79 931.81 975.74 963.89 958.89 688.20 841.67 870.70 913.70 919.84 850.55 562.50 703.71 735.69 783.89 795.24 727.78 356.60 498.15 531.11 560.56 626.19 550.55 127.08 245.37 283.06 344.81 417.46 317.78

(W/m2) 289.58 542.71 711.11 831.60 885.42 903.47 843.75 745.49 534.38 293.40

291.25 492.78 668.47 784.30 842.71 832.57 760.69 612.71 400.49 196.11

179.42 379.32 544.75 661.83 719.34 702.06 622.53 479.84 290.84 94.86

66.67 272.22 452.78 558.33 652.78 622.22 563.89 380.56 216.67 25.00

30.55 213.89 360.19 485.19 543.52 513.89 470.37 362.04 201.85 52.78

(d) Srinagar: (ii) Measured average Global 8 am 25.70 9 am 165.51 10 am 315.05 11 am 421.53 12 pm 463.66 1 pm 473.38 2 pm 457.18 3 pm 361.81 4 pm 216.43 5 pm 52.55

hourly global radiations for “type b” weather condition 86.11 146.43 266.88 359.83 366.03 316.58 250.00 369.05 464.96 547.76 572.49 555.69 474.31 556.75 676.28 733.98 755.88 713.58 719.44 661.51 826.92 857.91 919.23 892.03 812.50 769.05 858.55 893.16 878.53 888.80 811.81 816.67 811.32 880.66 888.94 844.88 750.00 665.87 673.29 711.65 808.60 769.77 585.41 535.72 446.37 355.13 542.84 590.17 359.03 351.98 390.17 318.70 419.07 438.24 70.83 184.53 184.83 206.31 222.60 258.29

(W/m2) 267.13 538.89 671.29 864.82 899.08 800.82 730.93 637.50 457.41 293.98

250.82 463.40 636.77 742.16 761.93 761.44 694.77 527.29 334.80 157.35

168.98 364.82 525.00 639.58 693.06 677.78 593.29 448.61 266.43 81.25

46.20 184.35 339.72 462.50 518.52 521.20 473.89 357.59 203.52 58.80

33.33 202.78 277.78 341.67 525.00 544.44 491.67 327.78 155.56 27.78

condition 188.89 344.44 372.22 505.56 541.67 711.11 577.78 508.33 263.89 225.00

(W/m2) 177.43 320.14 387.85 532.64 529.17 622.22 559.73 443.06 290.28 180.21

165.97 295.83 403.48 559.72 516.66 533.33 541.67 377.78 316.67 135.42

133.33 211.11 258.33 427.78 702.78 636.11 433.33 202.78 94.44 50.00

33.33 155.56 289.81 399.38 428.70 400.00 367.28 255.86 124.69 32.10

39.75 158.48 238.50 295.91 304.76 242.92 260.59 169.61 88.34 23.85

hourly global radiations for “type d” weather condition 56.95 77.78 127.78 177.78 186.11 194.44 168.06 205.56 241.67 277.78 263.89 250.00 279.17 369.44 394.44 419.44 369.44 319.44 286.81 391.67 188.89 489.45 511.39 533.33 364.58 366.67 550.00 733.33 611.11 488.89 323.61 283.33 933.33 933.33 708.33 483.33 287.50 319.00 583.33 883.33 655.55 427.78 221.53 246.50 427.78 655.56 590.28 325.00 100.00 144.44 119.44 94.44 184.72 275.00 42.36 47.22 77.78 108.34 141.67 175.00

(W/m2) 163.89 191.67 449.44 544.44 688.33 593.89 569.44 375.00 197.22 116.67

41.67 100.00 219.44 438.89 641.67 575.00 491.67 341.67 277.78 88.89

39.45 129.16 294.44 406.94 527.78 483.33 405.56 312.50 188.89 60.56

37.22 158.33 369.44 375.00 413.89 391.67 319.44 283.33 100.00 32.22

25.00 112.22 225.00 438.89 531.11 491.67 388.89 304.44 105.56 16.67

(d) Srinagar: (iii) Measured average hourly global radiations for “type c” weather Global 8 am 23.89 35.48 51.39 208.33 204.34 204.85 9 am 90.00 123.89 94.44 352.08 360.42 217.52 10 am 191.67 230.67 151.39 592.36 474.48 323.26 11 am 271.67 338.09 281.94 622.22 550.35 380.51 12 pm 306.67 399.70 434.72 783.34 668.76 447.54 1 pm 377.78 396.53 408.33 603.47 651.74 574.04 2 pm 359.44 392.25 475.00 604.86 600.35 600.71 3 pm 383.33 321.33 390.28 576.39 574.99 500.37 4 pm 155.56 157.83 226.38 331.25 284.38 293.83 5 pm 30.00 38.83 72.22 188.89 229.34 268.86 (d) Srinagar: (iv) Measured average Global 8 am 29.63 9 am 148.15 10 am 258.89 11 am 351.85 12 pm 361.11 1 pm 300.00 2 pm 286.11 3 pm 171.30 4 pm 80.56 5 pm 20.37 Type of days

January February March

April

May

June

(d) Srinagar: (v) Number of days fall in different weather condition a 5 7 8 10 13 b 17 14 17 17 15

July 11 12

August September October 7 17

6 18

14 12

November December 12 12

5 3 14 8 (continued on next page)

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367

Table 2 (continued) Type of days

January February March c d

7 2

April

May

3 3

2 1

4 3

June

July

2 1

4 3

May

June

August September October 4 3

3 4

November December

3 2

5 2

8 3

19 1

Month Solar radiation Time

January

February March

April

(d) Srinagar: (vi) Average ambient temperature for different months 8 am 0.20 4.50 3.80 11.90 9 am 0.50 4.30 3.10 11.60 10 am 0.80 3.90 2.70 11.40 11 am 0.80 4.00 2.50 11.40 12 pm 0.90 4.00 3.30 11.70 1 pm 0.10 3.90 6.50 13.70 2 pm 1.60 4.90 9.50 14.80 3 pm 2.70 6.30 12.10 15.90 4 pm 4.50 7.30 13.00 17.10 5 pm 6.40 7.80 14.30 18.80

(°C) 17.30 16.80 16.00 16.10 17.60 18.30 19.50 20.70 23.90 24.60

July

21.20 20.70 20.20 20.30 22.50 24.40 26.60 28.40 29.20 30.30

19.20 19.20 18.60 18.80 19.60 20.40 20.40 21.40 21.60 21.50

August 19.40 19.40 19.40 19.30 19.30 20.30 20.80 22.80 24.80 25.30

September October 13.00 12.80 12.40 12.30 12.40 13.80 14.40 16.10 18.50 19.60

November December

6.30 5.80 5.40 5.20 6.40 9.00 11.50 14.50 16.90 18.60

2.10 1.60 1.50 1.20 1.20 3.50 6.00 10.00 12.30 13.60

1.40 1.40 1.30 0.90 0.80 2.30 4.20 5.30 6.70 7.70

17

120

T c , at d=500 µm T c , at d=1000 µm

16

80 15 60 14 40

Cell efficiency, %

Temperature, oc

100

13

20

T c , at d=1500 µm T fo , at d=500 µm T fo , at d=1000 µm T fo , at d=1500 µm T fi , at d=500, 1000, 1500 µm ηe , at d=500 µm ηe , at d=1000 µm

0 8:00

12 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00

ηe , at d=1500 µm

Time (Hours) Fig. 4. Hourly variation of cell temperature, outlet air temperature, inlet air temperature and cell efficiency for the month of January.

and SCPVT module) is shown in Fig. 12. It has been observed that an overall exergy efficiency of MCPVT module for all four cities are higher than SCPVT module and it

Single channel PVT module Micro-channel PVT module

Overall monthly exergy gain (KWh)

overall monthly thermal energy gain (KWh)

Micro-channel PVT module 50 45 40 35 30 25 20 15 10 5 0

is further to be noted that for both cases (MCPVT and SCPVT modules), the overall exergy efficiency are higher for the Srinagar city . An overall monthly exergy efficiency of MCVT module varies between 15.83% and 18.03% and for SCPVT module it varies between 9.38% and 12.33% for the Srinagar.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month of Year Fig. 5. Monthly variation of overall thermal energy gain by considering a–d type weather condition of micro-channel PVT module and single channel PVT module of Srinagar.

18 16 14 12 10 8 6 4 2 0

Single channel PVT module

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month of Year Fig. 6. Monthly variation of overall exergy gain by considering a–d type weather condition of micro-channel PVT module and single channel PVT module of Srinagar.

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

Overall exergy efficiency, %

368 19

Weather conditions a type

18

b type c type

17

d type 16

Including all

15 Jan Feb Mar Apr May Jun

Jul

Aug Sep Oct Nov Dec

Month of Year

Overall exergy efficiency, %

Fig. 7. Monthly variation of overall exergy efficiency by considering a–d type weather condition of micro-channel PVT module of Srinagar. 14

Weather conditions a type

13

b type

12

c type

11

d type 10

Including all

9 8 Jan Feb Mar Apr May Jun

Jul

Aug Sep Oct Nov Dec

Month of Year

Overall monthly exergy efficiency, %

Fig. 8. Monthly variation of overall exergy efficiency by considering a–d type weather condition of single channel PVT module of Srinagar.

19 18 17 16 15 14 13 12 11 10 9 8 Jan Feb Mar

Overall monthly exergy efficiency of microchannel PVT module) Overall monthly exergy efficiency of single Channel PVT module)

Apr May Jun

Jul

Aug Sep Oct

Nov Dec

Month of year

Micro-channel PVT module 500

Single Channel PVT module

450 400 350 300 250 200 150 100 50 0 Srinagar

Banglore

Jodhpur

New Delhi

City Fig. 10. Annual overall thermal energy gain for four different cities of India by considering a–d type weather condition of micro-channel PVT module and single channel PVT module.

Overall annual exergy gain (KWh)

Overall annual thermal gain (Kwh)

Fig. 9. Monthly overall exergy efficiency by considering a–d type weather condition of Srinagar of micro-channel PVT module and single channel PVT module.

Micro channel PVT module 180 160 140 120 100 80 60 40 20 0

Single Channel PVT module

Srinagar

Banglore

Jodhpur

New Delhi

City Fig. 11. Annual overall exergy gain for four different cities of India by considering a–d type weather condition of micro-channel PVT module and single channel PVT module.

S. Agrawal, G.N. Tiwari / Solar Energy 85 (2011) 356–370

369

Overall exergy efficiency, %

20 Srinagar MCPVT Module Banglore MCPVT Module Jodhpur MCPVT Module New Delhi MCPVT Module Srinagar SCPVT Module Banglore SCPVT Module Jodhpur SCPVT Module New Delhi SCPVT Module

18

16

14

12

10

8 Jan Feb Mar Apr May Jun

Jul

Aug Sep Oct Nov Dec

Month of Year Fig. 12. Monthly variation of overall exergy efficiency for four different cities by considering a–d type weather condition of micro-channel PVT module and single channel PVT module.

6. Conclusions The following conclusions have been drawn:  An overall annual thermal gain of the proposed MCPVT module has been increased by 70.62%, 73.88%, 74.05% and 72.59% over SCPVT module for Srinagar, Banglore, Jodhpur and New Delhi Indian climatic conditions respectively.  An overall annual exergy gain of the proposed MCPVT module has been increased by 60.19%, 63.47%, 62.41% and 60.47% over SCPVT module for Srinagar, Banglore, Jodhpur and New Delhi Indian climatic conditions respectively.  An overall annual exergy efficiency of the proposed MCPVT module has also been increased by 57.61%, 63.19%, 61.08% and 58.43% over SCPVT module for Srinagar, Banglore, Jodhpur and New Delhi Indian climatic conditions respectively. Acknowledgments The authors are thankful to Dr. Arvind Tiwari for his idea of analyzing micro-channel solar cell thermal. The authors are also thankful to the Indian Meteorology Department (IMD), Pune for providing the hourly radiation and ambient temperature data of different city in India. Appendix A. In modeling equations, we used following relations for defining the design parameters, which are shown in Table 1. aeff ¼ ðac  gc Þ m_ f ¼ qLdV ho ¼ 5:7 þ 3:8  v hi ¼ 2:8 þ 3  v



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