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A numerical study on non-Fourier heat conduction model of phase change problem with variable internal heat generation

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A Correction to this article was published on 08 May 2023

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Abstract

In this study, the authors proposed one-dimensional non-Fourier heat conduction model applied to phase change problem in the presence of variable internal heat generation and this has been performed by finite element Legendre wavelet Galerkin method (FELWGM). We derived the stability analysis of the non-Fourier heat conduction model in our present case. The finite difference technique has been used to change the non-Fourier heat conduction model into an initial value problem of vector-matrix form and then we applied Legendre wavelet Galerkin method for the numerical solution of the present problem. The location of moving interface is analytically obtained under the steady-state condition. The effectiveness of the proposed numerical technique is verified through the experimental value of parameters which indicate promising results. In addition, the effect of Stefan numbers, internal heat generation, and its linear coefficient on the location of moving interface are discussed in detail and represented graphically.

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Acknowledgements

Jitendra, one of the authors, is grateful to C.S.I.R. (India) in the form of UGC Senior Research Fellowship vide Ref. No. 30-09-2015-433013 (i) RAC/RES/March.2016/S-8/ dated 29/8/2017 for this research work.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Jitendra & Jitendra Singh

  2. Department of Mathematical Sciences, IIT-BHU, Varanasi, 221005, India

    K. N. Rai

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Jitendra, Rai, K.N. & Singh, J. A numerical study on non-Fourier heat conduction model of phase change problem with variable internal heat generation. J Eng Math 129, 7 (2021). https://doi.org/10.1007/s10665-021-10143-1

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