Time Estimate for the Incipient Surface Melting of Regular-Shaped Metals Receiving Uniform Heat Flux Inside a Metal Melting Furnace

This article addresses the continuous heating of regular-shaped metals (large plate, long cylinder, and sphere) at ambient temperature placed in a metal melting furnace. Under the assumption of temperature-independent thermophysical properties of the metal, the heat conduction problem entails to unsteady one-dimensional (1D) heat conduction with a boundary condition of uniform heat flux. Based on the exact, analytic spatiotemporal temperature distributions for the regular-shaped metals, the objective of this study is to construct simple predictive formulas so that engineers can estimate the incipient melting of these metals when heated continually. The time at which melting at the metal surface is initiated, tmelt, corresponds to setting the surface temperature, Tsur, equal to the melting temperature, Tmelt. The analysis will be done under the premises of two asymptotic solutions: one a “large-time” solution and the other a “short-time” solution. A collection of six formulas of simple form for predicting the melting time, tmelt, will be developed for those regular-shaped metals (large plate, long cylinder, and sphere).