Thermal stability of a reactive viscous flow through a porous-saturated channel with convective boundary conditions

This study is devoted to investigate the thermal stability of a reactive viscous combustible fluid flowing steadily through a channel filled with a saturated porous medium. It is assumed that the system exchange heat with the ambient following Newton’s cooling law and the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The Brinkman model is employed and analytical solutions are constructed for the governing nonlinear boundary-value problem using a perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.