Modeling and asymptotic analysis of combustion of solid fuel deposited over an inert porous medium

Abstract

A simple mathematical model has been proposed for combustion of solid fuel deposited over an inert porous medium. The thermal nonequilibrium between the porous medium and gas is incorporated in the model considering two energy equations with different density, thermal conductivity and specific heat capacity for the porous medium and gas. A simple parameter "deposition of fuel" is newly introduced instead of fuel mass fraction to simplify the model. We employ large activation energy asymptotic to investigate the moving speed of the burning front of solid fuel for opposed flow combustion where the burning front (defined as the location of heterogeneous combustion takes place) propagates opposite to the direction of oxidizer (gas) flow velocity. During the analysis we consider all transport terms in the energy equations which have not been accomplished so far for heterogeneous combustion in an inert porous medium. We have successfully obtained an implicit analytical expression of the moving speed of the burning front including the other pertinent parameters such as deposition of solid fuel, porosity of the porous medium, thermal conductivity of the porous medium, gas flow velocity and the heat exchange coefficient between the porous medium and gas. The effects of variation of these parameters are discussed in terms of the moving speed of the burning front. Analytical solutions are found to be satisfactory in certain range of parameters based on the comparison with numerical solution provided by us. Additionally, the validity of the analytical result is also convinced by the past work done by Fatehi and Kaviany [3]. © 2012 by JSME.