Solution of transient problems with steep gradients: novel front-tracking strategy

Abstract

A finite element collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. An efficient, parametrically convergent front-tracking procedure is developed based on a balance on a moving front, and the technique is applied and tested for the case of a gas-solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained here for Thiele modulus larger than 50 for the case of slab as well as spherical geometry and found to match the analytical solution when it exists (such as for slab geometry).