Heat Transfer of Power-Law Fluids in Plane Couette–Poiseuille Flows with Viscous Dissipation

Abstract

Analytical expressions for the velocity and temperature profiles, bulk temperature and Nusselt numbers, in a fully-developed laminar Couette–Poiseuille flow between parallel plates of a power-law fluid with constant, and distinct, wall heat fluxes, in the presence of viscous dissipation are deduced and presented. Both favorable and adverse pressure gradient cases were analyzed. The walls’ shear stresses ratio, which arises naturally when the dimensionless hydrodynamic solution is obtained, together with the fluid power-law index Brinkman number and the walls’ heat fluxes ratio are the independent variables in the heat transfer solutions. With the exception of Newtonian fluids, there are in general two distinct analytical solutions, one for positive and another for negative values of the walls’ shear stresses ratio. The existence of singular points are also observed, where for a given value of the power-law index, there are values of the walls’ shear stresses ratio for which the Nusselt number becomes independent of the Brinkman number. It was also found that in a Couette–Poiseuille flow, for each value of the power-law index there exists a certain negative value of the walls’ shear stresses ratio that makes the Nusselt numbers at both walls identically zero.

Notes on contributors

Paulo Coelho is an Assistant Professor at Universidade do Porto, Faculdade de Engenharia, Mechanical department. Current research interests comprise heat transfer with non-Newtonian fluids and heat treatment processes.

Rob Poole is currently the Head of Department of Mechanical, Materials and Aerospace Engineering within the School of Engineering at The University of Liverpool. He has a PhD in Mechanical Engineering from the same Institution and an undergraduate degree in Mechanical Engineering from Loughborough University. He currently holds an EPSRC fellowship (Complex Fluids & Rheology) and his research interests are primarily centered around the flow of complex fluids including both experimental and numerical approaches. In addition to investigating natural and forced convection effects on non-Newtonian fluids, including yield stress and power-law fluids such as in the current paper, he has investigated viscoelastic fluids in both laminar and turbulent flows including so-called purely-elastic flow instabilities and in “elastic” turbulence.