Finite Element Legendre Wavelet Galerkin Approch to Inward Solidification in Simple Body Under Most Generalized Boundary Condition

Abstract

his paper deals with a mathematical model describing the inward solidification of a melt of phase change material within a container of different geometrical configuration like slab, circular cylinder or sphere under the most generalized boundary conditions. The thermal and physical properties of melt and solid are assumed to be identical. To solve this mathematical model, the finite difference scheme is used to convert the problem into an initial value problem of vector matrix form and further, solving it using the Legendre wavelet Galerkin method. The results thus obtained are analyzed by considering particular cases when one might impose either a constant=time varying temperature or a constant=time varying heat flux or a constant heat transfer coefficient on the surface. The whole analysis is presented in dimensionless form. The effect of variability of shape factor, condition posed at the boundary, Stefan number, Predvoditelev number, Kirpichev number, and Biot number on dimensionless temperature and solid-layer thickness are shown graphically. Furthermore, a comparative study of time for complete solidification is presented.