A unified treatment of the direct contact melting processes in several geometric cases

Abstract This paper presents a theoretical study of direct contact melting processes for three geometries: the flat plate, the cylindrical wall and the spherical wall. Governing equations that include both fluid inertia terms and heat convection terms are solved analytically and numerically. It is shown that transport for the three geometries is essentially governed by one common equation system, and that the results for all three cases can be expressed as one basic solution for inertialess flow and as a perturbation solution for the full equations with inertia. Using a similarity transformation, the equations for inertialess flow are reduced to a system of ordinary differential equations in one independent variable. It is shown that there exists an exact solution to this system, and it can be obtained without using any approximate method or numerical technique. Comparison of the numerical and perturbation solutions with inertia to the exact solution results for inertialess flow indicates that the effect of the inertia terms is so small that they can be neglected over almost the entire practical range of Prandtl number.