Download - 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
AER
2013
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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
ER
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
Temperature Difference (K)
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.
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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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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
Temperature Difference (K)
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
Temperature Difference (K)
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.
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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
Temperature Difference (K)
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
Temperature Difference (K)
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
Temperature Difference (K)
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
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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
Temperature Difference (K)
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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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.
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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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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
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
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
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 = 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
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
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
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 = 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
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22 24 26 28 30 32 34 36 38 4010
20
30
40
50
60
70
80
90
100
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
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
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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
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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.
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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.
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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.
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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)(
'