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Optimising the heat balance integral method in spherical and cylindrical Stefan problems

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  • Ribera, H.
  • Myers, T.G.
  • MacDevette, M.M.

Abstract

The Heat Balance Integral Method (HBIM) is generally applied to one-dimensional Cartesian heat flow and Stefan problems. The main reason for this being that solutions in spherical and cylindrical coordinates are less accurate than in Cartesian. Consequently, in this paper we examine the application of the HBIM to Stefan problems in spherical and cylindrical coordinates, with the aim of improving accuracy. The standard version as well as one designed to minimise errors will be applied on the original and transformed system. Results are compared against numerical and perturbation solutions. It is shown that for the spherical case it is possible to obtain highly accurate approximate solutions (more accurate than the first order perturbation for realistic values of the Stefan number). For the cylindrical problem the results are significantly less accurate.

Suggested Citation

  • Ribera, H. & Myers, T.G. & MacDevette, M.M., 2019. "Optimising the heat balance integral method in spherical and cylindrical Stefan problems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 216-231.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:216-231
    DOI: 10.1016/j.amc.2019.02.039
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    References listed on IDEAS

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    1. Sharma, Atul & Tyagi, V.V. & Chen, C.R. & Buddhi, D., 2009. "Review on thermal energy storage with phase change materials and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 13(2), pages 318-345, February.
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    1. Taler, Jan & Taler, Dawid, 2024. "Analysis of the possibility of reducing the heating time of thick-walled cylindrical components with holes," Energy, Elsevier, vol. 303(C).
    2. Taler, Dawid & Dzierwa, Piotr & Taler, Jan, 2020. "New method for determining the optimum fluid temperature when heating pressure thick-walled components with openings," Energy, Elsevier, vol. 200(C).
    3. 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).

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