Approximate analytical Solutions for the heat transfer in glass melting furnaces

Abstract

Temperatures and convections in glass melts are governed by coupled partial differential equations. These equations can, in general, only be solved by numerical methods. A considerable simplification of the partial differential equation for heat transport is possible under certain conditions. These conditions are frequently met in glass tanks. They allow the formulation of an ordinary differential equation for the heat transport with Solutions in the form of simple equations. These equations are analytical expressions of the vertical temperature profile in the glass melt. The Peclet number for the vertical flow component in the melt under the free surface appears to be the essential parameter in these expressions. It characterizes the combined heat transport by conduction and convection. However, flow velocity and thermal diffusivity vary strongly over the depth of the glass bath, thus rendering the Peclet number Position dependent. On this theoretical basis, it follows a detailed numerical and analytical study of the dependence of the vertical temperature profile on wall heat loss, primary recirculation and pull.