18 quantifiable e xergy

Quantifiable Dependence of Exergy and Energy on Temperature Difference

NAVEEN KUMAR VATSIIITD&M KANCHEEPURAM, INDIA

ICA

ER

2013

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OBJECTIVE

ENERGY and EXERGY

LOGARITHIMIC NEXUX

THEORETICAL PROJECTION

EXPERIMENTAL VALIDATION

CONCLUSION

OUTLINE:IC

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2013

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TO PROPOSE and VALIDATE a

QUANTIFIABLE THERMODYNAMICAL

NEXUS BETWEEN EXERGY/ENERGY

OUTPUT and THE TEMPERATURE

DIFFERENCE

OBJECTIVE:IC

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2013

04/12/2023 4

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)( iifipo TTmcE

The expression is only dependent on initial and final value of temperatures and says nothing about the ambient temperature.

Mass

Heat Capacity of Water

Water temperature final

Water Temperature initial

Output Energy

ENERGY and EXERGY

am

fiii TTT

2Temperature Difference

ICA

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2013

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The exergy gained by water in the vessel kept inside the cooker, or output exergy is given as

;lnii

fiampoXo T

TTmcEE )(0 iifip TTmcE

ENERGY and EXERGY

ii

fiamp

ii

fiampo

T

TTmc

T

TTmcE

RatioExergyln

ln

;lnii

fiamp T

TTmcLostExergy

ICA

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2013

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Which Formul

a?

STUDENT

COOKING POWER STANDARD

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

90

100

f(x) = − 1.14824853935431 x + 99.3928787500462R² = 0.86181192721635

Temperature Difference (K)

Coo

kin

g P

ower

(W

)

Fig. 1: Cooking Power variation with Temperature Difference

am

fiii TTT

2

ICA

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2013

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Which Formula

?

STUDENT

EXERGY POWER STANDARD

0 10 20 30 40 50 600

1

2

3

4

5

6

7

8

f(x) = − 0.00577813434497074 x² + 0.421375549218065 x − 1.24297640745701R² = 0.923117067968509


Exe

rgy

Pow

er (

W)

Fig. 2: Exergy Power variation with Temperature Difference

ICA

ER

2013

Naveen Kumar, G. Vishwanth, Anurag Gupta, An exergy based unified test protocol for solar cookers of different geometries, Renewable Energy 44 (2012) 457-462.

04/12/2023 8

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

PROPOSED EXERGY/ENERGY NEXUS

amiifi

ii

fiamp

ii

fiampo

TTT

N

T

TTmc

T

TTmcE

2ln

ln

Y

X1]Zln +Z)-

2

Y+X[N( Y-X

The constant (N) proposed herein = 0.0032 K-1 and it gives the result within ~ 0.5% accuracy.

ICA

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2013

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EXERGY RATIO ANALYSIS

10 15 20 25 30 35 40 45 50 55 600

0.05

0.1

0.15

0.2f(x) = 0.003216805179662 x − 0.000102553643765338R² = 0.999999884135737


Exe

rgy

Rat

io

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

f(x) = 0.00319094219916681 x − 6.71061301296128E-05R² = 0.999999979076335


Exe

rgy

Rat

io

Fig. 3: Exergy Ratio variation with Temperature Difference for 2 kg and 2.5 kg load of water in SBC during full load test.

ICA

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2013

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EXERGY RATIO ANALYSIS

5 10 15 20 25 30 35 40 45 50 550

0.05

0.1

0.15

0.2

f(x) = 0.00329366457357344 x − 0.000438144206039243R² = 0.999999169795377


Exe

rgy

Rat

io

5 10 15 20 25 30 35 40 45 50 550

0.05

0.1

0.15

0.2

f(x) = 0.0032472924256667 x + 0.000703103877148323R² = 0.999949749519841


Exe

rgy

Rat

io

Fig. 4: Exergy Ratio variation with Temperature Difference for SK-14 type (5 kg) and Scheffler type (20 kg) solar cooker.

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VALIDATION

10 15 20 25 30 35 40 45 50 55 600

1

2

3

4

5

6

7

8

Conventional Method

proposed Method


Exe

rgy

Pow

er (

W)

Eureka Right

am

iifi

ii

fiampXO T

TT

T

TTNmcE

2ln

Fig. 5: Exergy Power variation with Temperature Difference for SBC

ICA

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2013

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VALIDATION

10 15 20 25 30 35 40 45 50 55 600

10

20

30

40

50

60

70

80

Conventional Method

Proposed Method


Coo

kin

g P

ower

(W

)

Eureka

Right

wi

wfampam

wiwf

wi

wfampo T

TTmcT

TT

T

TTNmcE ln

2ln

Fig. 6: Cooking Power variation with Temperature Difference for SBC

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2013

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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 temperature value.IC

AER

2013

Naveen Kumar, Vishwanth G, Anurag Gupta. Effect of load variations on exergy performance of solar box type cooker. Journal of Renewable and Sustainable Energy 2012;4: 053125.

04/12/2023 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.

ICA

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THANK YOU

NAVEEN KUMAR VATS

[email protected]

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PEAK EXERGY POWER =

QUALITY FACTOR ==

EXERGY TEMPERATURE DIFFERENCE GAP

PRODUCT = WK

HEAT LOSS COEFFICIENT = = 5.24 W/m2K

EXERGY ANALYSIS OF SOLAR BOX TYPE COOKER (SBC)

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5 10.145 15 20 25 30.332 35 40 45 50.519 552

4

6

8

9.106210

12

14

16

18.212

20

T e m p e r a t u r e D i f f e r e n c e ( K )

E x

e r

g y

P o

w e

r (

W )

M a s s = 5 . 0 k g

y = - 0.022346*x2 + 1.3556*x - 2.3466

R2 = 0.9811data 1 quadratic

Maximum Power = 18.212 Wat Temperature Difference of30.332 K

Half Power = 9.1062 Wat Temperature Difference of50.519 K and 10.145 K

EXERGY ANALYSIS OF SK-14 (DOMESTIC) TYPE COOKER

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5 10 15 20 25 30 35 40 45 50 550

50

100

150

200

250

300

350


E x

e r

g y

L o

s t

( W )

M a s s = 5 . 0 k g

y = - 5.4072*x + 334.84

R2 = 0.9916

data 1 linear

EXERGY ANALYSIS OF SK-14 (DOMESTIC) TYPE COOKER

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5 9.354 15 20 25 29.165 35 40 45 48.977 550

10

20

40

50

60

55.753

27.877


E x

e r

g y

P o

w e

r (

W )

M a s s = 2 0 . 0 k g

y = - 0.071023*x2 + 4.1428*x - 4.6595

R2 = 0.8682

data 1 quadratic

Maximum Power = 55.753 Wat Temperature Difference of 29.165 K

Half Power = 27.877 Wat Temperature Difference of 48.977 Kand 9.354 K

EXERGY ANALYSIS OF SCHEFFLER (COMMUNITY) TYPE COOKER

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5 10 15 20 25 30 35 40 45 50 550

200

400

600

800

1000

1200


E x

e r

g y

L o

s t

( W )

M a s s = 2 0 . 0 k g

y = - 19.485*x + 1132.7

R2 = 0.9916

data 1 linear

EXERGY ANALYSIS OF SCHEFFLER (COMMUNITY) TYPE COOKER

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22 24 25.833 28 30 32 34 36 37.458 401

2

33.4574

4

5

6

6.9149

8

9


E x

e r

g y

P

o w

e r

( W

)

M a s s = 6 . 3 k g

y = - 0.02581*x2 + 1.3361*x - 10.376

R2 = 0.6676

data 1 quadratic

Maximum Power = 6.9149 Wat Temperature Difference of 25.883 K

Half Power = 3.4574 Wat Temperature Difference of 14.308 K and 37.458 K

EXERGY ANALYSIS OF PARABOLIC TROUGH TYPE CONCENTRATING COOKER

04/12/2023 22

22 24 26 28 30 32 34 36 38 4010

20

30

40

50

60

70

80

90

100


E x

e r

g y

L o

s t

( W )

M a s s = 6 . 3 k g

y = - 4.2007*x + 187.65

R2 = 0.8117

data 1 linear

EXERGY ANALYSIS OF PARABOLIC TROUGH TYPE CONCENTRATING COOKER

04/12/2023 23

SOLAR COOKER

GEOMETRY

PEAK EXERG

Y POWER

(W)

TEMPERATURE

DIFFERENCE AT HALF POWER

(K)

PRODUCT OF PEAK EXERGY

AND TEMPERATU

RE DIFFERENC

E(W-K)

HEAT LOSS COEFFICIE

NT(W/m2k)

QUALITY

FACTOR

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(COMMUNI

TY)55.75 39.62 2208.815 54.125 0.099

PARABOLIC TROUGH 6.92 23.15 160.198 47.73 0.087

TABULATION

04/12/2023 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 based test

standards.

04/12/2023 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 solar cookers. Solar Energy 39(4), 353-360.

04/12/2023 26

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

OUR APPROACH-EXERGY BASED APPROACH:

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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.

04/12/2023 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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ervalint/durationTimet;t

)TT(mc iifip

tI

TTmc iifip

700)()( aw TT

25 30 35 40 45 50 550

10

20

30

40

50

60

f(x) = − 0.665193531706 x + 73.04742692605R² = 0.894438010048306

Temprature Difference (oC)

Sta

nd

ard

ize

d C

ook

-in

g P

ow

er

(W)

At temperature difference of 50 0C

Pst = 40 W; is the measure of its fuel rating

Heat loss coefficient = 0.665/0.25 = 2.66 W/ oCm2

Cooking Power =

Temperature Difference =

Standardized Cooking Power (Pst) =

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Lss

asps

UI

TTF

1

I

TT

F

I

TT

F

A

mcFCFF

aw

aw

wpR

2

1

1

112 1

1

11

ln)(

'

18 quantifiable e xergy

Technology

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