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Critical Concentration Ratio for Solar Thermoelectric Generators

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Abstract

A correlation for determining the critical concentration ratio (CCR) of solar concentrated thermoelectric generators (SCTEGs) has been established, and the significance of the contributing parameters is discussed in detail. For any SCTEG, higher concentration ratio leads to higher temperatures at the hot side of modules. However, the maximum value of this temperature for safe operation is limited by the material properties of the modules and should be considered as an important design constraint. Taking into account this limitation, the CCR can be defined as the maximum concentration ratio usable for a particular SCTEG. The established correlation is based on factors associated with the material and geometric properties of modules, thermal characteristics of the receiver, installation site attributes, and thermal and electrical operating conditions. To reduce the number of terms in the correlation, these factors are combined to form dimensionless groups by applying the Buckingham Pi theorem. A correlation model containing these groups is proposed and fit to a dataset obtained by simulating a thermodynamic (physical) model over sampled values acquired by applying the Latin hypercube sampling (LHS) technique over a realistic distribution of factors. The coefficient of determination and relative error are found to be 97% and ±20%, respectively. The correlation is validated by comparing the predicted results with literature values. In addition, the significance and effects of the Pi groups on the CCR are evaluated and thoroughly discussed. This study will lead to a wide range of opportunities regarding design and optimization of SCTEGs.

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References

  1. D. Mills, Sol. Energy (2004). doi:10.1016/S0038-092X(03)00102-6.

    Google Scholar 

  2. S.P. Sukhatme, Indian Academy of Sciences Chemical Sciences Proceedings (1997), pp. 521–53l.

  3. E. Zarza, L. Valenzuela, J. Leon, K. Hennecke, M. Eck, H.D. Weyers, and M. Eickoff, Energy (2004). doi:10.1016/S0360-5442(03)00172-5.

    Google Scholar 

  4. J. Schlaich, The Solar Chimney: Electricity from the Sun (Stuttgart: Edition Axel Menges, 1996), p. 12.

    Google Scholar 

  5. P.L. Geok, R. Affandi, A. Ghani, M. Ruddin, C.K. Gan, and J. Zanariah, Appl. Mech. Mater. (2015). doi:10.4028/www.scientific.net/AMM.785.576.

    Google Scholar 

  6. H. Xi, L. Luo, and G. Fraisse, Renew. Sustain. Energy Rev. (2007). doi:10.1016/j.rser.2005.06.008.

    Google Scholar 

  7. S. Priya and D.J. Inman, Energy Harvesting Technologies (New York: Springer, 2009), pp. 323–336.

    Book  Google Scholar 

  8. R. Amatya and R.J. Ram, J. Electron. Mater. (2010). doi:10.1007/s11664-010-1190-8.

    Google Scholar 

  9. D.K.C. MacDonald, Thermoelectricity: An Introduction to the Principles (New York: Dover, 2006), pp. 1–4.

    Google Scholar 

  10. A.I. Novikov, J. Eng. Phys. Thermophys. (2001). doi:10.1023/A:1016667129697.

    Google Scholar 

  11. Y. Cai, J. Xiao, W. Zhao, X. Tang, and Q. Zhang, J. Electron. Mater. (2011). doi:10.1007/s11664-011-1616-y.

    Google Scholar 

  12. K. Atik, Energy Sources Part A (2011). doi:10.1080/15567030903261873.

    Google Scholar 

  13. P. Li, L. Cai, P. Zhai, X. Tang, Q. Zhang, and M. Niino, J. Electron. Mater. (2010). doi:10.1007/s11664-010-1279-0.

    Google Scholar 

  14. B.R. Munson, D.F. Young, and T.H. Okiishi, Fundamentals of Fluid Mechanics, 1st ed. (New York: Wiley, 1990), pp. 388–393.

    Google Scholar 

  15. J.H. Lin, C.Y. Huang, and C.C. Su, Int. Commun. Heat Mass Transf. (2007). doi:10.1016/j.icheatmasstransfer.2006.12.002.

    Google Scholar 

  16. C.K. Ho, S.S. Khalsa, and G.J. Kolb, Sol. Energy (2011). doi:10.1016/j.solener.2010.05.004.

    Google Scholar 

  17. K.P. Bowman, J. Sacks, and Y.F. Chang, J. Atmos. Sci. (1993). 50(9), 1267–1278.

    Article  Google Scholar 

  18. K. Yamada, A. Yamaguchi, T. Takata, in 8th Japan Korea Symposium on Nuclear Thermal Hydraulics and Safety (2012) Paper no.: N8P1091.

  19. P.J. Marti and J.M. Pinazom, Int. J. Therm. Sci. (2003). doi:10.1016/S1290-0729(02)00038-8.

    Google Scholar 

  20. M.D. McKay, R.J. Beckman, and W.J. Conover, Technometrics (1979). doi:10.1080/00401706.1979.10489755.

    Google Scholar 

  21. J.C. Helton, J.D. Johnson, C.J. Sallaberry, and C.B. Storlie, Reliab. Eng. Syst. Saf. (2006). doi:10.1016/j.ress.2005.11.017.

    Google Scholar 

  22. J.C. Helton and F.J. Davis, Reliab. Eng. Syst. Saf. (2003). doi:10.1016/S0951-8320(03)00058-9.

    Google Scholar 

  23. J.A. Duffie and W.A. Beckman, Solar Engineering of Thermal Processes, 3rd ed. (New York: Wiley, 2006), p. 189.

    Google Scholar 

  24. R. Forristall, Report No. NREL/TP-550-34169, National Renewable Energy Laboratory, Colorado, October 2003.

  25. D.M. Rowe, Thermoelectrics Handbook (Boca Raton: CRC Press, 2006), pp. 1–4.

    Google Scholar 

  26. C.T. Hsu, G.Y. Huang, H.S. Chu, B. Yu, and D.J. Yao, Appl. Energy (2011). doi:10.1016/j.apenergy.2011.07.033.

    Google Scholar 

  27. T.M. Tritt and M.A. Subramanian, MRS Bull. (2006). doi:10.1557/mrs2006.44.

    Google Scholar 

  28. R.E. Walpole, R.H. Myers, S.L. Myers, and K. Ye, Probability and Statistics for Engineers and Scientists, 9th ed. (New York: Pearson, 2012), p. 407.

    Google Scholar 

  29. S.A. Klein, F.L. Alvarado. Engineering Equation Solver, http://www.fchart.com/ees/. Accessed 12 December 2015.

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Authors and Affiliations

  1. Solar Energy Lab, Mechanical Engineering Department, NED University of Engineering and Technology, University Road, Karachi, 75270, Pakistan

    Naveed ur Rehman & Mubashir Ali Siddiqui

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  1. Naveed ur Rehman
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  2. Mubashir Ali Siddiqui
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Correspondence to Mubashir Ali Siddiqui.

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ur Rehman, N., Siddiqui, M.A. Critical Concentration Ratio for Solar Thermoelectric Generators. J. Electron. Mater. 45, 5285–5296 (2016). https://doi.org/10.1007/s11664-016-4689-9

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  • DOI: https://doi.org/10.1007/s11664-016-4689-9

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