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An analytical method for the solution of two phase Stefan problem in cylindrical geometry

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  • Khalid, Muhammad Zeeshan
  • Zubair, Muhammad
  • Ali, Majid

Abstract

Two phase Stefan problem was solved using analytical method in cylindrical domain. To solve governing equations Eigen conditions were formulated by using separation of variable technique. Eigenvalues of the eigencondition were obtained by applying corresponding boundary conditions for liquid and solid phase. Eigenvalues are graphically validated by using window size method in Mathematica. It is noted radial eigenvalues are free from imaginary values. Interface equation obtained from this method were solved and analyzed by varying the Stefan number and introducing the forced and natural convection. Conduction and convection heat transfer mechanism was studied and results obtained by varying thermal diffusivity, thermal conductivity and Stefan number were discussed. Natural convection effects were studied by introducing Rayleigh number and results showed Stefan number has significant effect than Rayleigh number during Phase transition process. Furthermore, eigen function expansion Method was compared with exact solution of Exponential Integral function method and results showed good agreement for Q = 1.

Suggested Citation

  • Khalid, Muhammad Zeeshan & Zubair, Muhammad & Ali, Majid, 2019. "An analytical method for the solution of two phase Stefan problem in cylindrical geometry," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 295-308.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:295-308
    DOI: 10.1016/j.amc.2017.09.013
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    References listed on IDEAS

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    1. Nina Boyarchenko & Sergei Levendorskiǐ, 2007. "The Eigenfunction Expansion Method In Multi‐Factor Quadratic Term Structure Models," Mathematical Finance, Wiley Blackwell, vol. 17(4), pages 503-539, October.
    2. Bechiri, Mohammed & Mansouri, Kacem, 2015. "Analytical solution of heat transfer in a shell-and-tube latent thermal energy storage system," Renewable Energy, Elsevier, vol. 74(C), pages 825-838.
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    Cited by:

    1. Xu, Minghan & Akhtar, Saad & Zueter, Ahmad F. & Alzoubi, Mahmoud A. & Sushama, Laxmi & Sasmito, Agus P., 2021. "Asymptotic analysis of a two-phase Stefan problem in annulus: Application to outward solidification in phase change materials," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    2. Kudryashov, Nikolay A., 2019. "Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 323-330.

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