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  • In the expression above, the output energy depends only on the difference in initial and final values of temperatures but in actual practice, ambient temperature as well as the initial and final temperature values also play the role in deciding the efficiency of the system, and this kind of qualitative effect can not be accommodated in the energy based approach.
  • In the equation above, the term within the parenthesis represents the exergy/energy radiation ratio, defined by for the first time by Petela and it represents the maximum energy available from radiation. This term has the significance similar to that of the Carnot efficiency for heat engines and its value can be larger than unity.During evaluating/projecting the performance of any thermal device, determining exergy, is the first goal. The parameters derived from the energy based approach does not provide complete information and are inadequate thermal performance indicators because their values can be misleadingly high or low depending on the temperature difference between source and sink, even though input energy condition may remain same. In other words, 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.
  • 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.
  • 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.
  • The environment is the natural referencestate in nature, which consists of an arbitrary amount of the “worthless” components. The matterconsidered in the definition of exergy can be a substance or any fieldmatter, e.g., radiation. In simple language, Exergy is a measure of the potential of the system to extract heat from the surroundings, as the system moves closer to the equilibrium with its environment. After the system and the surroundings reach equilibrium, the exergy becomes zero. It is a combination property of a system and its environment because unlike energy it depends on the state of both the system and the surrounding.

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  • 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 12/10/2013 2
  • 3. OBJECTIVE: TO PROPOSE and VALIDATE a QUANTIFIABLE THERMODYNAMICAL EXERGY/ENERGY NEXUS OUTPUT BETWEEN and THE TEMPERATURE DIFFERENCE 12/10/2013 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 12/10/2013 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 12/10/2013 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. 12/10/2013 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) 12/10/2013 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) 12/10/2013 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 12/10/2013 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 12/10/2013 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. 12/10/2013 14
  • 15. THANK YOU NAVEEN KUMAR VATS nkumar@iiitdm.ac.in 12/10/2013 15
  • 16. EXERGY ANALYSIS OF SOLAR BOX TYPE COOKER (SBC)  12/10/2013 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) 12/10/2013 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 12/10/2013 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) 12/10/2013 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 12/10/2013 23
  • 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 12/10/2013 26
  • 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.  12/10/2013 27
  • 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. 12/10/2013 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 12/10/2013 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 12/10/2013 30