Flow of Temperature-dependent Viscous Fluid Between Parallel Heated Walls: Exact Analytical Solutions in the Presence of Viscous Dissipation

Abstract

We examine steady incompressible flow of viscous liquids between parallel heated walls of plane Couette device. The temperature of the upper and lower walls of the device are maintained at T = T_b and T = T₀ respectively. Of a particular interest are exact analytical solutions of the coupled non-linear differential equations resulting from plane Couette flow obtained for the temperature and velocity distributions respectively. The criterion for which the solutions are valid was determined by the temperature difference, α, between the upper and lower walls. The analysis reveals that the shear stress obtained at the walls exists when the temperature difference α> 0.