Analysis of Heat Transfer in the Corroding Sidewall of a Furnace

A mathematical formulation is developed to calculate the rate of corrosion of a refractory sidewall of a furnace in the presence of free convection in the melt. The free-convection phenomena considered are caused by the dependence of the melt density on its temperature and composition. The formulation involves the statement of equations for heat conduction in the refractory wall and movement of the solid-melt interface. The governing equations and the boundary conditions are transformed into nondimensional forms, and the dimensionless parameters which characterize corrosion in the presence of free convection are identified. The equations are solved by using coordinate transformation and a finite-difference method. Calculated results are presented on the shape of the solid-melt interface, temperature distribution in the corroding wall, and the amount of cooling at the outside surface of the wall. The results show how free convection in the melt interacts with heat conduction in a refractory wall to determine the rate of corrosion of the wall.