Couette flow with frictional heating in a fluid with temperature and pressure dependent viscosity

This study investigates the effects of variable viscosity and frictional heating on the laminar flow in a horizontal channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The wall at rest is thermally insulated, while the moving wall is kept at a uniform temperature. This investigation concerns fluids whose viscosity depends exponentially on the pressure and temperature. An appropriate approximation is introduced to analyze the interplay between the dependence of viscosity on the pressure and temperature and the viscous dissipation. It is shown that the nonlinear term in the equation for the balance of energy representing the frictional heating may lead to the existence of dual solutions of the boundary value problem for fixed values of the material parameters that characterize the fluid. The results obtained are compared with those predicted by the generalization of the Oberbeck–Boussinesq approximation for a fluid with pressure and temperature dependent viscosity. It is found that the results for the approximation carried out in this paper and those that stem from the Oberbeck–Boussinesq approximation are markedly different.