A one-phase Stefan problem with size-dependent thermal conductivity and moving phase change material under the most generalized boundary condition

Abstract

In the current paper, we analyzed a one-phase moving boundary problem that includes a size-dependent thermal conductivity and a moving phase change material under the most generalized boundary condition. A numerical solution to the problem is obtained via heat balance integral method (HBIM) with an approximation of the quadratic temperature profile. In particular, numerical results are compared against the exact solution and previous work and found to be closed. The effect of dimensionless problem parameters on temperature profile and moving melting interface are shown in figures. The physical behavior of these parameters shows that the melting interface enhanced growing for a large value of either Stefan number, Péclet number or Kirpichev number while it deterred with increasing the Nusselt number. A comparative study between moving boundary problem with size-dependent thermal conductivity and moving PCM, moving boundary problem with constant thermal conductivity and moving PCM, and standard problem is presented in each kind of boundary conditions. We also found that the second kind flux boundary condition is physically more realistic for the melting process than the first and third kind temperature boundary condition for a moving boundary problem with size-no independent thermal conductivity and moving PCM. For limiting value of the Nusselt number ((Formula presented.)), we found a unique λ with the Stefan number and Péclet number. © 2022 Informa UK Limited, trading as Taylor & Francis Group.