The International Conference on Advances in Renewable Energy (ICARE) was held at National Institute of Technology (NIT), Bhopal in June 2010. The topic of my presentation was: A simple procedure for estimating heat capacity and optical efficiency of solar box type cooker

1. A SIMPLE PROCEDURE FOR
ESTIMATING HEAT CAPACITY AND
OPTICAL EFFICIENCY OF SOLAR BOX
TYPE COOKER
Naveen Kumar, G.Vishwanath
Indian Institute of Information Technology
Design and Manufacturing (IIITD&M) , Kancheepuram
IIT Madras Campus
ICARE 2010 June 24, 2010

2. Outline
• Solar Box Type Cooker (SBC)
• Figures of Merit
• Optical Efficiency of a SBC
• Heat Capacity of a SBC
• Existing Methodology
• Proposed Methodology
• Experimental Data Analysis
• Result & Conclusion
ICARE 2010 June 24, 2010

3. Solar Box Type Cooker (SBC)
A solar thermal device, which is used at
domestic level mainly for boiling type of
cooking.
The optical efficiency and heat capacity of
the SBC are the two key parameters, which
determines effectiveness of SBC.
In order to evaluate the performance of the solar cooker for cooking, two figures
of merit (FOM) viz. F1 and F2, are generally calculated. [BIS Test Standards]
ICARE 2010 June 24, 2010

4. Figures of Merit (FOM)
F1 first FOM
F ' oe Tpz Taz
F1
F 'U LS Gs
F' : Heat exchange efficiency factor
F' : Optical efficiency
oe
It is a measure of the differential
temperature gained by the absorbing F 'U LS : Heat loss factor at stagnation
plate at a particular level of solar
insolation during no-load test. T pz : Plate temperature at stagnation
The value of F1 should be ≥ 0.11 ( as Taz : Ambient Temperature at stagnation
per BIS standards).
Gs : Solar Insolation at stagnation
ICARE 2010 June 24, 2010

5. Figures of Merit (FOM)
F2 second FOM
The second FOM,F2 is independent of climatic conditions and gives an
indication of heat transfer from absorbing plate to the water in the containers
kept on the plate. The value of F2 is generally determined using the equation:
( MC) w F1 ( MC) w 1 (Tw1 Tad ) / F1Gav
F2 F ' noe ln
( MC)' ( MC) w A(t w2 t w1 ) 1 (Tw2 Tad ) / F1Gav
( MC ) w: Heat Capacity of water
(MC)' : Heat Capacity of Interior Materials
A : Area of the plate
Tw1 : Temperature of water at time t w1 The value of F2 should be ≥ 0.4 (as per
: Temperature of water at time t w 2
Tw 2 BIS standards).
Tad : Ambient temperature
Gav : Average Solar Insolation
ICARE 2010 June 24, 2010

6. Optical Efficiency of SBC
Optical efficiency (F’noe) is the product of the transmittance of the
glazing of the SBC and the heat absorption coefficient of the bottom
plate.
A high optical efficiency is always desirable as it is corresponds to
high value of F1 i.e the first figure of merit.
Using the equation of first figure of merit, we can express optical
efficiency as:
Tpz Taz
F' oe F 'U LS F1 F 'U LS
Gs
ICARE 2010 June 24, 2010

7. Heat Capactity of SBC
( MC )' w ( MC )' ( MC ) w
Where (MC)’w is the heat capacity of the cooker and is equal to the sum of the
heat capacity of the cooker interior materials (MC)’ (to be found) and the heat
capacity of water (MC)w
For the given value of optical efficiency we can find heat capacity using
equation:
1 (MC)' 1
F2 F' oe (MC) w F' oe
ICARE 2010 June 24, 2010

8. Existing Methodology
Full load tests were conducted for different loads of water and the value of F2
was experimentally determined.
Heat capacity and optical efficiency were considered constant because the
duration of the experiment is apprx. 1.5 hour and temperature limits were
fixed.
The experimentally determined values of 1/F2 are then linearly plotted with
respect to heat capacity of the water of different loads filled in the vessel
1 (MC)' 1
F2 F' oe (MC) w F' oe
The optical efficiency and heat capacity of cooker materials are obtained
from the intercept and slope of the linear regression line achieved from the
plot [1].
1. Subodh Kumars, Estimation of design parameters for thermal performance evaluation
ICARE 2010 of box-type solar cooker, Renewable Energy. 30(2005)1117-1126 June 24, 2010

9. ,
Proposed Methodology
The rate of useful heat energy gained by water for an infinitesimal time dt during
full load testing of SBC is given by:
dTw dTw
( MC ) w AF oe GT U L (Tw Ta ) ( MC )
dt dt
Since the value of (MC)’ is un-known and will vary depending on the material
used in SBC, we are approximating this term by writing it in the form of unknown
heat loss coefficient (Us) and area (As).
dTw
(MC)' AsU s(Tw Ta )
dt
Thus the final equation is:
dTw
(MC) w AF [ oeG T U L (Tw Ta )] A s U s (Tw Ta )
dt
ICARE 2010 June 24, 2010

10. Proposed Methodology
Rearranging the final equation, we get:
dTw
( MC ) w AF U L AsU s (Tw Ta ) AF oe GT
dt
Comparing the above equation with Y= mX + C ; which is a straight line, we get
dTw
Y ( MC) w
dt
C AF oe GT X (Tw Ta ) m AF U L AsU s
Thus from the experimental data taken during full load test, we plot the cooking
power (Y) v/s temperature difference (X) and from the intercept and slope we
determine the value of optical efficiency and heat capacity respectively.
Optical Efficiency: F oe C /(AGT )
Heat Capacity: (MC) m C /(F1G T ) (Tw Ta )dt / dTw
ICARE 2010 June 24, 2010

11. Experimental Data Analysis
Variations in the cooking power Variations in the cooking power
with the temperature difference with the temperature difference of
of a SBC; Load = 2.5 Kg [1] a SBC; Load = 1.5 Kg [1].
Variations in the cooking
power with the
temperature difference of
a SBC; Load = 2Kg [1].
ICARE 2010 June 24, 2010

12. Results
CALCULATION TABLE:
Mass of water in kg Initial Temperature in °C Final Temperature in °C A sU s
(M) (Twi) (Twf) (W/K)
1.5 60.6 96.9 0.244
2 58.2 96.4 0.269833
2.5 62 95.4 0.184498
Comparison between calculated and expected values of the parameters:
Parameters Average Value Expected Value [1]
(Calculated)
Heat capacity of the solar 2257.1533 2252.86
cooker (MC) (J/°C)
Optical Efficiency (F’noe) 0.60847 0.6216
1. Subodh Kumars, Estimation of design parameters for thermal performance evaluation
ICARE 2010 of box-type solar cooker, Renewable Energy. 30(2005)1117-1126 June 24, 2010

13. Results
F2 PARAMETERS:
Mass of water F2cal F2exp | F2cal- F2exp| % difference
M
(kg)
1.5 0.4205 0.3743 0.0462 10.9869
2 0.4816 0.4931 0.0115 2.38787
2.5 0.5267 0.51239 0.01431 2.71691
ICARE 2010 June 24, 2010

14. Conclusion
A SIMPLE PROCEDURE FOR ESTIMATING THE
VALUE OF OPTICAL EFFICIENCY AND HEAT
CAPACITY OF A SOLAR BOX TYPE COOKER HAS
BEEN PROPOSED
ICARE 2010 June 24, 2010

15. If you have any queries then please send us a mail at
vatsnaveen@yahoo.co.in (Naveen Kumar)
vish777.2006@gmail.com (G.Vishwanath)