Analysis of Non-Newtonian Reactive Flow in a Cylindrical Pipe

In this paper, a mathematical investigation on the effect of convective cooling on a reactive third-grade fluid flowing steadily through a cylindrical pipe is performed. 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 simplified governing nonlinear equations of momentum and energy are obtained and solved using a special type of the Hermite–Padé approximation technique. The important properties of the overall flow structure including velocity field, temperature field, bifurcations, and thermal criticality conditions are discussed.