Flow of a Newtonian fluid in a symmetrically heated channel: Effect of viscosity and viscous dissipation

Abstract

This paper discusses the effect of viscosity and viscous dissipation (due to a high velocity gradient) on the steady flow of a viscous liquid in a symmetrically heated channel. The coupled nonlinear differential equations arising in the planar Poiseuille flow are not amendable to analytical solutions. Therefore, numerical solutions based on finite-difference scheme are presented. The effects of various flow controlling parameters such as temperature differenceα, dimensionless pressure gradient, and the dimensionless viscous heating parameterδon the dimensionless velocity and temperature are analyzed. The analysis reveals that when viscous heating parameterδ=0, we obtained zero solution for the dimensionless temperature.