Thermal stability of a reactive viscous flow through a porous-saturated pipe

Purpose - This paper aims to examine the steady-state solutions of a strongly exothermic reaction of a viscous combustible fluid in a cylindrical pipe filled with a saturated porous medium under Arrhenius kinetics, neglecting reactant consumption. Design/methodology/approach - The problem is formulated in terms of a non-linear differential equation. Approximate solution of this problem is obtained using a regular perturbation technique. A bifurcation study is performed using a special type of Hermite-Pade approximation method in order to determine the thermal criticality conditions. Findings - The steady-state thermal ignition criticality conditions as well as the solution branches was obtained accurately. It was found that a reduction in porous medium permeability will facilitate the early appearance of thermal ignition, hence, improving the effectiveness of engineering equipments like the catalytic converter used in an automobile's exhaust system. Practical implications - A very useful source of information for researchers on the subject of thermal combustion in porous media. Originality/value - This paper illustrates the effect of permeability parameter on steady-state thermal ignition criticality conditions in a porous medium.