COMPUTATION OF THE SOLIDIFICATION OF PURE METALS IN PLATE GEOMETRY USING THE GREENS-FUNCTION METHOD

In this study the Green's function technique has been used to solve th e solidification problem in plate geometry for three alternative types of boundary condition at the surface of the plate. With this method t he differential equation for heat conduction is transformed into an in tegral equation with line integrals, reducing in this manner the integ ration to a solution at the boundaries of the domain. The advantage is a considerable saving of computer time. Simple forms of boundary cond ition, that is constant values of temperature T-0, of heat flux densit y q(0), or of heat transfer coefficient it, are used, but the treatmen t can readily be extended to time dependent values. The rate laws for the advancement of the solidification front and for the evolution of s urface temperature (in the case of prescribed q(0) or h) are obtained and are presented in non-dimensional form. (C) 1998 Elsevier Science L td. All rights reserved.