Wavelet based numerical approach of non-classical moving boundary problem with convection effect and variable latent heat under the most generalized boundary conditions

Abstract The major goal of this article is to analysis a mathematical model of a non-classical one-dimensional moving boundary problem in the presence of convection effect when one surface subjected to the most generalized boundary conditions. The control function describes the cooling and heating effect depends on the evolution of heat flux at x = 0 . The thermo-physical properties are assumed to be constant while latent heat depends on the position of moving interface and its velocity. The parameters affecting the thermal behaviour of the melting process in various enclosures, i.e. the effect of Peclet number, control function, variable latent heat, heat flux and convecting heat transfer coefficient on the moving interface and temperature distribution are comprehensively investigated by the Legendre wavelet Galerkin computational method. In specific cases the Legendre wavelet Galerkin method is used for the numerical solution when surface is subjected to the first kind boundary condition with constant latent heat and thus the results obtained are compared with Turkyilmazoglu (2018) results and found in good compliance. Further when latent heat is variable, the present numerical solution obtained is compared with exact solution and are found in high accuracy and good flexibility.