Rapid melting and solidification of surface due to stationary heat flux

Abstract

A general two-dimensional computer heat flow model is developed in an oblate spheroidal coordinate system for rapid melting and subsequent solidification of the surface of a semiinfinite solid subjected to a high intensity heat flux over a circular region on its bounding surface. Generalized numerical solutions are presented for an aluminum substrate subjected to both uniform and Gaussian heat flux distributions. Temperature distributions, melt depth and geometry, and melting and solidification interface velocities are calculated as a function of applied heat flux, radius of the circular region, and time. It is shown that the important melting and solidification parameters are a function of the product of the absorbed heat flux, q, and the radius of the circular region, a. General trends established show that melt depth perpendicular to the surface is inversely proportional to the absorbed heat flux for a given temperature at the center of the circular region. Dimensionless temperature distributions and the ratio of liquid-solid interface velocity to absorbed heat flux,R/q, as a function of dimensionless melt depth remain the same if the productqa is kept constant, whileq anda are varied. For a given total power absorbed melting and solidification parameters are compared for uniform and Gaussian heat flux distributions. For a given temperature at the center of the circular region both melt depth and width are smaller for the Gaussian distribution while temperature gradients and interface velocities are larger.