A numerical method based on integro‐differential formulation for solving a one‐dimensional Stefan problem

Abstract

A numerical method based on an integro-differential formulation is proposed for solving a one-dimensional moving boundary Stefan problem involving heat conduction in a solid with phase change. Some specific test problems are solved using the proposed method. The numerical results obtained indicate that it can give accurate solutions and may offer an interesting and viable alternative to existing numerical methods for solving the Stefan problem.

Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries

“…A good summary of the different models can be found in the monograph (Dybkov, 2010). There is also a class of problems in heat transfer that are analogous to such reaction controlled diffusion such as melting of ice and solidification (Reemtsen and Kirsch, 1984;Caldwell and Kwan, 2004;Ramos, 2005;Ang, 2008;Caldwell and Kwan, 2009).…”

A new approach to approximate solution of the Stefan problem with a convective boundary condition (Communicated by Corresponding Member Nikolai V. Pavlyukevich)

“…Точность приближенных решений проверяется на основе их сравнения с аналогичными численными решениями. В отличие от работы [8], в которой коэффициент теплообмена задается в виде функции ( ) / , h t h t = примем постоянство коэффициента теплообмена во времени и плавное изменение температуры среды по экспоненциальному закону [12].…”