1. Quantifiable Dependence of Exergy
and Energy on Temperature
Difference
NAVEEN KUMAR VATS
IIITD&M KANCHEEPURAM, INDIA

2. OUTLINE:

OBJECTIVE

ENERGY and EXERGY

LOGARITHIMIC NEXUX

THEORETICAL PROJECTION

EXPERIMENTAL VALIDATION

CONCLUSION
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2

3. OBJECTIVE:
TO PROPOSE and VALIDATE a QUANTIFIABLE
THERMODYNAMICAL
EXERGY/ENERGY
NEXUS
OUTPUT
BETWEEN
and
THE
TEMPERATURE DIFFERENCE
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3

4. ENERGY and EXERGY
The energy gained by water in the vessel, kept inside the cooker, due
to rise in temperature can be considered as the output energy (Eo) of
the system and is mathematically given as
Eo
mcp (Tfi Tii )
The expression is only dependent on initial and final value of
temperatures and says nothing about the ambient temperature.
Output Energy
Mass
Heat Capacity of Water
Tii
T fi
2
Tam
Temperature Difference
Water temperature final
Water Temperature initial
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4

5. ENERGY and EXERGY
The exergy gained by water in the vessel kept inside the
cooker, or output exergy is given as
E Xo Eo mcpTam ln
Exergy Lost
T fi
Tii
mc pTam ln
Exergy Ratio
E0
;
T fi
Tii
mcp (T fi
Tii )
;
T fi
Eo mc pTam ln
Tii
T fi
mc pTam ln
Tii
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5

6. COOKING POWER STANDARD
Which
Formul
a?
100
90
Cooking Power (W)
80
y = -1.148x + 99.39
R² = 0.861
70
60
50
40
30
20
S
T
U
D
E
N
T
10
0
0
10
20
30
40
50
60
Temperature Difference (K)
Fig. 1: Cooking Power variation with Temperature
Difference
12/10/2013
Tii
T fi
2
Tam
6

7. EXERGY POWER STANDARD
Which
Formula
?
8
Exergy Power (W)
7
6
5
y = -0.005x2 + 0.421x - 1.243
R² = 0.923
4
3
2
1
0
0
10
20
30
40
50
Temperature Difference (K)
60
S
T
U
D
E
N
T
Fig. 2: Exergy Power variation with Temperature Difference
Naveen Kumar, G. Vishwanth, Anurag Gupta, An exergy based unified test
protocol for solar cookers of different geometries, Renewable Energy 44
(2012) 457-462.
12/10/2013
7

8. PROPOSED EXERGY/ENERGY NEXUS
X-Y
[N(
X+Y
X
- Z) + 1]Zln
2
Y
Provided X > Y > Z and 300 < Z < 320; Z < Y< 366; Y < X < 370 and X-Y < 12
Thus, considering X as Tfi, Y as Tii and Z as Tam, we get
T fi
Eo mc pTam ln
Tii
T fi
mc pTam ln
Tii
N
T fi
Tii
2
Tam
The constant (N) proposed herein = 0.0032 K-1 and it gives the
result within ~ 0.5% accuracy.
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8

9. EXERGY RATIO ANALYSIS
Exergy Ratio
0.2
y = 0.003x - 0.000
R² = 1
2 kg
0.15
0.1
0.05
0
0
10
20
30
40
50
60
Exergy Ratio
Temperature Difference (K)
0.2
y = 0.003x - 7E-05
R² = 1
2.5kg
0.15
0.1
Fig. 3:
Exergy Ratio
variation
with
Temperature Difference
for 2 kg and 2.5 kg load
of water in SBC during
full load test.
0.05
0
0
10
20
30
40
50
60
Temperature Difference (K)
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9

10. EXERGY RATIO ANALYSIS
Exergy Ratio
0.2
y = 0.003x - 0.000
R² = 1
5 kg
0.15
0.1
0.05
0
0
10
20
30
40
50
60
Temperature Difference (K)
Exergy Ratio
0.2
y = 0.003x + 0.000
R² = 0.999
20 kg
0.15
Fig. 4:
Exergy Ratio
variation
with
Temperature Difference
for SK-14 type (5 kg)
and Scheffler type (20
kg) solar cooker.
0.1
0.05
0
0
20
40
60
Temperature Difference (K)
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10

11. VALIDATION
Eureka
Right
8
Conventional Method
Exergy Power (W)
7
proposed Method
6
5
4
3
2
EXO
1
NmcpTam ln
T fi
Tii
T fi
Tii
2
Tam
0
0
10
20
30
40
Temperature Difference (K)
50
60
Fig. 5: Exergy Power variation with Temperature Difference for SBC
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11

12. VALIDATION
Eurek
a
Right
80
Cooking Power (W)
70
60
Conventional Method
50
40
Proposed Method
30
Eo Nmc p Tam ln
20
Twf
Twf Twi
Twi
2
Tam
mc pTam ln
Twf
Twi
10
0
0
10
20
30
40
50
60
Temperature Difference (K)
Fig. 6:
SBC
Cooking Power variation with Temperature Difference for
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12

13. DISCUSSION
Performance parameters (i.e. F2 and
Standardized
cooking
power
etc.)
determined through energy based approach
are more dependent on initial water
temperature and other ambient conditions
whereas performance indicators i.e. adjusted
quality factor etc. are almost independent of
the mass, ambient and initial load variations on
Naveen Kumar, Vishwanth G, Anurag Gupta. Effect oftemperature
exergy performance of solar box type cooker. Journal of Renewable and
value.

Sustainable Energy 2012;4: 053125.
12/10/2013
13

14. CONCLUSION

A new constant (N) governing the
mathematical aspect in heat transfer has
been found for the first time.

A new formula elucidating the dependence
of output heat energy on temperature
difference has been developed and
validated.

A new mathematical expression illustrating
the variations in output exergy on
temperature
difference
has
been
developed and validated.
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14

15. THANK YOU
NAVEEN KUMAR VATS
nkumar@iiitdm.ac.in
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15

16. EXERGY ANALYSIS OF SOLAR BOX TYPE
COOKER (SBC)

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16

17. EXERGY ANALYSIS OF SK-14 (DOMESTIC)
TYPE COOKER
Mass = 5.0kg
20
Exergy Power(W)
18.212
y = - 0.022346*x2 + 1.3556*x - 2.3466
R2 = 0.9811
data 1
quadratic
16
14
Maximum Power = 18.212 W
at Temperature Difference of
30.332 K
12
10
9.1062
8
Half Power = 9.1062 W
at Temperature Difference of
50.519 K and 10.145 K
6
4
2
5
10.145
15
20
25
30.332
35
40
T e m p e r a t12/10/2013 f f e r e n c e ( K )
ure Di
45
50.519
55
17

18. EXERGY ANALYSIS OF SK-14 (DOMESTIC)
TYPE COOKER
Mass=5.0kg
350
data 1
linear
Exergy Lost(W)
300
y = - 5.4072*x + 334.84
R2 = 0.9916
250
200
150
100
50
0
5
10
15
20
25
30
35
40
45
50
55
Temperature Difference(K)
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18

19. EXERGY ANALYSIS OF SCHEFFLER
(COMMUNITY) TYPE COOKER
Mass=20.0kg
60
y = - 0.071023*x2 + 4.1428*x - 4.6595
55.753
R2 = 0.8682
data 1
quadratic
Exergy Power(W)
50
40
Maximum Power = 55.753 W
at Temperature Difference of 29.165 K
27.877
Half Power = 27.877 W
at Temperature Difference of 48.977 K
and 9.354 K
20
10
0
5
9.354
15
20
25
29.165
35
40
T e m p e r a t u12/10/2013 f f e r e n c e ( K )
re Di
45
48.977
55
19

20. EXERGY ANALYSIS OF SCHEFFLER
(COMMUNITY) TYPE COOKER
Mass=20.0kg
1200
data 1
linear
Exergy Lost(W)
1000
y = - 19.485*x + 1132.7
R2 = 0.9916
800
600
400
200
0
5
10
15
20
25
30
35
40
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Temperature Difference(K)
45
50
55
20

21. EXERGY ANALYSIS OF PARABOLIC TROUGH
TYPE CONCENTRATING COOKER
Mass = 6.3kg
9
Exergy Power(W)
8
y = - 0.02581*x2 + 1.3361*x - 10.376
R2 = 0.6676
data 1
quadratic
6.9149
6
5
4
Maximum Power = 6.9149 W
at Temperature Difference of 25.883 K
3.4574
3
2
1
22
Half Power = 3.4574 W
at Temperature Difference of 14.308 K and 37.458 K
24
25.833
28
30
32
34
T e m p e r a t12/10/2013i f f e r e n c e ( K )
ure D
36
37.458
40
21

22. EXERGY ANALYSIS OF PARABOLIC TROUGH
TYPE CONCENTRATING COOKER
Mass=6.3kg
100
data 1
linear
Exergy Lost(W)
90
80
70
60
50
40
y = - 4.2007*x + 187.65
R2 = 0.8117
30
20
10
22
24
26
28
30
32
34
Temperature Difference(K)
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36
38
40
22

23. TABULATION
PRODUCT OF
PEAK EXERGY
HEAT LOSS
AND
QUALITY
COEFFICIENT
TEMPERATURE
FACTOR
(W/m2k)
DIFFERENCE
(W-K)
SOLAR
COOKER
GEOMETRY
PEAK
EXERGY
POWER
(W)
TEMPERATURE
DIFFERENCE AT
HALF POWER
(K)
SBC
6.46
46.2
298.5
5.24
0.123
SK-14
(DOMESTIC)
18.21
40.374
735.3
40.35
0.106
SCHEFFLER
(COMMUNITY)
55.75
39.62
2208.815
54.125
0.099
PARABOLIC
TROUGH
6.92
23.15
160.198
47.73
0.087
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24. SUMMARY AND CONCLUSION

An exergy based analysis is applied to solar cookers of different
designs based on the experimental data available and values of
proposed parameters are calculated for them.

Performance evaluation and test standards of solar cookers of
different geometries are discussed.

A unified test standard for solar cookers is proposed and
presented.
To establish a test standard for different types of solar
cookers, one may require more comprehensive testing and
data analysis. However, the proposed parameters may
stimulate the discussion and strengthen the case for exergy
12/10/2013
based test standards.
24

25. REFERENCES
[1] Mullick, S.C., Kandpal, T. C., Subodh Kumar, 1996. Testing of box-type solar cookers:
second figure of merit F2 and its variation with load and number of pots. Solar Energy
57(5), 409-413.
[2] BIS 2000. IS 13429 (part 3): 2000. Indian Standards Solar – Box Type- Specification Part 3
Test Method (First Revision) New Delhi: Bureau of Indian Standards.
[3] Funk, P. A., 2000. Evaluating the international standard procedure for testing solar
cookers and reporting performance, Solar Energy. 68(1), 1-7.
[4] S.C. Mullick, T. C. Kandpal and Subodh Kumar, ‘Thermal test procedure for a paraboloid
concentrator solar cooker’, Solar Energy, 46(3), 139- 144, 199.
[5] Petela, R., 2003. Exergy of undiluted thermal radiation. Solar Energy, 74, 469-488.
[6] Petela, R., 2010. Engineering Thermodynamics of Thermal Radiation for Solar Power
Utilization, McGraw-Hill, New York.
[7] Kaushik, S.C., Gupta, M. K., 2008. Energy and exergy efficiency comparison of
community-size and domestic-size paraboloidal solar cooker performance, Energy for
Sustainable Development. 3, 60-64.
[8] Ozturk, H.H., 2004. Experimental determination of energy and exergy efficiency of solar
parabolic-cooker. Solar Energy, 77, 67-71.
[9] Ozturk, H.H., 2007. Comparison of energy and exergy efficiency for solar box and
parabolic cookers. J. Energy Engg., 133(1), 53-62.
[10] Subodh Kumar, 2004. Thermal performance study of box type solar cooker from heating
characteristic curves. Energy Conversion & Management, 45, 127-139.
[11] Mullick, S.C., Kandpal, T. C., Saxena, A. K., 1987. Thermal test procedure for box-type
25
solar cookers. Solar Energy 39(4), 353-360. 12/10/2013

26. OUR APPROACH-EXERGY BASED APPROACH:
Exergy as defined by Szargut as follows:
Exergy of matter is the maximum work the matter could perform in
a reversible process in which the environment is used as the source
of worthless heat and worthless substances, if at the end of the
process all the forms of participating matter reach the state of
thermodynamic equilibrium with the common components of the
environment.
Accounts for:
 Temperatures of energy transfer
 Quantity of energy transfer
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27. Parameters
Peak exergy is the highest/maximum exergy output
power obtained through curve fitting by plotting the
graph between exergy output power and temperature
difference. This can be realistically considered as a
measure of its fuel ratings.
 The ratio of the peak exergy gained to the exergy lost at
that instant of time can be considered as the quality
factor of the solar cooker. A higher quality factor is
always desirable.
 The product of the temperature difference gap
corresponding to the half power points and the peak
exergy power can also considered to be another
benchmark indicator in this kind of analysis. Higher
temperature difference gap means the lesser heat
losses from the cooker.

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28. Cooker comparison

The cooker which attains higher exergy at higher
temperature difference is the better one. It has been
also noticed that the variation in the exergy lost with
temperature difference is more linear when temperature
of water varies in the range of 60oC to 95oC (see Fig.
2, 4, 6, 8). This range of temperature is also generally
used in calculation/determination of F2 (second figure of
merit), which is an important and well known
performance indicator for SBC [1, 12]. The amount of
heat energy at higher temperature is more valuable
than the same amount of heat energy at lower
temperature and in energy analysis it is not possible to
take into account such qualitative difference. The
exergy analysis is a more complete synthesis tool
because it account for the temperatures associated with
energy transfers to and from the cooker, as well as the
quantities of energy transferred, and consequently
provides a measure of how nearly the cooker
approaches ideal efficiency.
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28

29. 
mc p ( T fi Tii )
Cooking Power =
t

Temperature Difference =
; t Time duration / int erval
(Tw Ta )
mc p (T fi Tii )700
Standardized Cooking Power (Pst) =
Standardized Cooking
Power (W)

tI
60
50
At temperature difference of 50 0C
40
y = -0.665x + 73.04
R² = 0.894
30
20
Pst = 40 W; is the measure of its fuel
rating
10
0
0
20
40
Temprature Difference (oC)
60
Heat loss coefficient = 0.665/0.25 = 2.66
W/ oCm2
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29

30. F1
Tps Tas
Is
U Ls
1 Tw1 Ta
F1 (mc p ) w
F1
I
ln
1 Tw2 Ta
A
1
F1
I
1
F2
F ' CR
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30