Numerical Analysis of the Transient and Non-Isothermal Channel Flow of a Third-Grade Fluid with Convective Cooling

Abstract

We investigate the unsteady, non-isothermal, pressure driven channel flow of a third grade liquid subject to exothermic reactions. We assume temperature dependent fluid viscosity and also that the flow is subjected to convective cooling at the channel walls. The exothermic reactions are modelled via Arrhenius kinetics and the convective heat exchange with the ambient at the channel walls follows Newton’s law of cooling. The time-dependent, coupled, and nonlinear partial differential equations governing the flow and heat transfer problem are solved numerically using efficient, semi-implicit finite difference algorithms. The sensitivity of the fluid flow and heat transfer system to the various embedded parameters is explored.