Heat Transfer of Power-Law Fluids in Plane Couette–Poiseuille Flows with Viscous Dissipation. Issue 13 (19th July 2020) - Coelho, Paulo M.; Poole, Robert J.
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.