Articles

Green’s function solution for transient heat conduction in annular fin during solidification of phase change material

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  • 1. Faculty of Mechanical Engineering, University of Tabriz, Tabriz 5166616471, Iran;
    2. Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, L1H 7K4 Oshawa, Ontario, Canada;
    3. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran 159163411, Iran

Received date: 2011-10-08

  Revised date: 2011-12-15

  Online published: 2012-10-10

Abstract

The Green’s function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.

Cite this article

A. H. MOSAFFA;F. TALATI;M. A. ROSEN;H. BASIRAT-TABRIZI . Green’s function solution for transient heat conduction in annular fin during solidification of phase change material[J]. Applied Mathematics and Mechanics, 2012 , 33(10) : 1265 -1274 . DOI: 10.1007/s10483-012-1620-x

References

[1] Kraus, A. D., Aziz, A., and Welty, J. Extended Surface Heat Transfer, Wiley, New York (2001)
[2] Cheng, C. Y. and Chen, C. K. Transient response of annular fins of various shapes subjected toconstant base heat fluxes. Journal of Physics D: Application Physics, 27, 2302-2306 (1994)
[3] Campo, A. and Rodriguez, F. Approximate analytic temperature solution for uniform annular finsby adapting the power series method. International Communications in Heat and Mass Transfer,25, 809-818 (1998)
[4] Koonprasert, S. and Sangsawang, R. Analytical solution and symbolic computation for the temperaturedistribution of the annular fin under fully wet-surface condition. Proceedings of InternationalConference of Numerical Analysis and Applied Mathematics, Vol. 1048, American Instituteof Physics, New York, 324-327 (2008)
[5] Sharqawy, M. H. and Zubair, S. M. Efficiency and optimization of straight fins with combined heatand mass transfer—an analytical solution. Applied Thermal Engineering, 28, 2279-2288 (2008)
[6] Aziz, A. and Rahman, M. M. Thermal performance of a functionally graded radial fin. InternationalJournal of Thermophysics, 30, 1637-1648 (2009)
[7] Cole, K. D., Tarawneh, C., and Wilson, B. Analysis of flux-base fins for estimation of heat transfercoefficient. International Journal of Heat and Mass Transfer, 52, 92-99 (2009)
[8] Malik, M. Y. and Rafiq, A. Two-dimensional fin with convective base condition. Nonlinear Analysis:Real World Applications, 11, 147-154 (2010)
[9] Lamberg, P. and Sirén, K. Analytical model for melting in a semi-infinite PCM storage with aninternal fin. Heat and Mass Transfer, 39, 167-176 (2003)
[10] Lamberg, P. Approximate analytical model for two-phase solidification problem in a finned phasechangematerial storage. Applied Energy, 77, 131-152 (2004)
[11] Shatikian, V., Ziskind, G., and Letan, R. Numerical investigation of a PCM-based heat sink withinternal fins. International Journal of Heat and Mass Transfer, 48, 3689-3706 (2005)
[12] Talati, F., Mosaffa, A. H., and Rosen, M. A. Analytical approximation for solidification processesin PCM storage with internal fins: imposed heat flux. Heat and Mass Transfer, 47, 369-376 (2011)
[13] Wilson, D. G. and Solomon, A. D. A Stefan-type problem with void formation and its explicitsolution. IMA Journal of Applied Mathematics, 37, 67-76 (1986)
[14] Alexiades, V. and Solomon, A. D. Mathematical Modelling of Melting and Freezing Processes,Hemisphere Publishing Corporation, Washington, D. C. (1993)
[15] Ozisik, M. N. Heat Conduction, 2nd ed., Wiley, New York (1993)
[16] Carslaw, H. and Jaeger, J. Conduction of Heat in Solids, 2nd ed., Oxford University Press, London(1959)
[17] Lamberg, P. and Sirén, K. Approximate analytical model for solidification in a finite PCM storagewith internal fins. Applied Mathematical Modelling, 27, 491-513 (2003)
[18] Incropera, F. P., DeWitt, D. P., Bergman, T. L., and Lavine, A. S. Fundamental of Heat andMass Transfer, 6th ed., Wiley, New York (2007)

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