Heat transfer and banks formation in a slag bath with embedded heat sources

A study was conducted for the heat transfer and the formation of solid banks inside a bath of molten slag. This study is motivated by the need to predict the formation of a protective thermal barrier for the refractory brick walls inside smelting furnaces. A mathematical model for natural convection dominated solid liquid phase change with embedded heat sources is presented. A scale analysis is conducted yielding algebraic expressions for the steady-state minimal side bank thickness and location, molten volume fraction and average Nusselt number at the surface of the bath in terms of the Rayleigh number. The predictions of the scale analysis are validated with numerical results and their range of application are delineated.