2008c): Convection driven melting of anisotropic metals

Abstract

This paper numerically explores melting of a pure substance with the thermal conductivity of the solid phase, assumed to be anisotropic. A two-phase test case for such situations is deduced from the standard one-phase Gobin-Le Qué ré melting benchmark. The solution is presented for Prandtl number 0?02, Stefan number 0?01 and Rayleigh number 2?5610 4 which are specific for metals. Three cases are compared in terms of the terminal interface boundary position and average liquid fraction as a function of time for isotropic case and two distinctly oriented principal directions of the thermal conductivity tensor. The calculations have been performed by using the one-domain enthalpy formulation with artificial melting interval and the recently developed explicit local radial basis function collocation method (LRBFCM) which belongs to the entirely new generation of meshless methods. The results are not sensitive to the increased thermal conductivity of the solid phase in the direction parallel with the heated boundary but sensitive with the increase of the thermal conductivity of the solid phase in the direction perpendicular to the heated boundary