A note on the thermal stability of a reactive non-Newtonian flow in a cylindrical pipe

Abstract The effect of variable viscosity and viscous dissipation on the thermal stability of a one-step exothermic, reactive non-Newtonian flow in a cylindrical pipe was considered assuming negligible reactant consumption. The governing equations; momentum and energy equations, which are coupled due to the dissipative term in the energy equation, were solved by closed-form and approximate techniques respectively. We obtained closed-form solutions for the momentum equation via the Homotopy analysis method(HAM), while the resulting energy equation was analysed for thermal stability via the variational technique. Parametric analysis of the solutions were conducted on the dimensionless velocity ( v ( r )), the critical Frank-Kamenetskii parameter( δ cr ) and the critical temperature( θ cr ) and expressed graphically and in tabular forms.