The phase-change heat conduction analysis during solidification processes by a hybrid generalized FDM

Abstract

Abstract In this paper, the single-domain enthalpy model is adopted for heat transfer analysis of phase change during solidification processes. The resulting second-order parabolic partial differential equations (PDEs) with varying thermophysical coefficients is numerically solved by a hybrid generalized finite difference method (GFDM) under mixed boundary conditions. The spatial derivatives in the PDEs are approximated by the Taylor series expansions combining with the moving-least squares technique. The temporal derivative is evaluated with a six-point symmetric difference by the classical Crank-Nicholson technique. The Newton-Raphson iteration method is used to solve the resulting nonlinear algebraic equations. Finally, the transient temperature field and the moving phase-change interface are obtained by analysing the nodal temperature distribution. Several examples are presented for verify the stability and effectiveness of this meshless method.