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 viscousdissipation (due to a high velocity gradient) on the steady flowof a viscous liquid in a symmetrically heated channel. The couplednonlinear differential equations arising in the planar Poiseuilleflow are not amendable to analytical solutions. Therefore,numerical solutions based on finite-difference scheme arepresented. The effects of various flow controlling parameters suchas temperature difference α, dimensionless pressuregradient, and the dimensionless viscous heating parameter δ on the dimensionless velocity and temperature are analyzed. Theanalysis reveals that when viscous heating parameter δ=0, we obtained zero solution for the dimensionless temperature.