This paper investigates the effect of non-Newtonian material effect on the thermal stability of a reactive fluid flow through a channel saturated with porous medium by using Brinkman model. Approximate solution of the dimensionless nonlinear ordinary differential equation governing the fluid flow is obtained by using Adomian decomposition method together with special Hermite--Pad\,e approximant. Effects of various non-Newtonian fluid parameters on both the velocity and temperature fields are constructed and discussed.