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Solving heat conduction problems with phase-change under the heat source term approach and the element-free Galerkin formulation

Abstract : The present work has been conducted in order to introduce an alternative solution for heat transfer problems with phase-change and moving boundaries, via the element-free Galerkin (EFG) method. In this novel approach, the phase-change non-linearity is addressed under the heat source term methodology. For this purpose, the global weak-form of the internal energy balance for such a non-linear transient heat transfer problem has been developed by including the latent heat as a source vector. In order to prove the reliability of this approach, the EFG formulation has been adapted to the solution of a 1-D alloy solidification benchmark problem. The suitability and potentialities of this novel approach have also been depicted in the solution of a variable domain (moving boundary) solidification problem, by considering the start-up stage of a round billet steel continuous casting process as an applied example. Results have revealed that this technique can be successfully used to deal appropriately with the marked non-linearity related to the fusion latent heat release in heat transfer problems with phase change, and its straightforward implementation leads to both accurate and stable numerical results.
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Submitted on : Monday, May 23, 2022 - 10:21:12 AM
Last modification on : Tuesday, May 24, 2022 - 3:43:09 AM

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Juan Carlos Álvarez-Hostos, Erick Gutierrez-Zambrano, Joselynne Salazar-Bove, Eli Saúl Puchi-Cabrera, Alfonso D. Bencomo. Solving heat conduction problems with phase-change under the heat source term approach and the element-free Galerkin formulation. International Communications in Heat and Mass Transfer, Elsevier, 2019, 108, pp.104321. ⟨10.1016/j.icheatmasstransfer.2019.104321⟩. ⟨hal-03675401⟩

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