Non-isothermal flow of a Bingham fluid with pressure and temperature dependent viscosity

Abstract

In this paper we investigate the non-isothermal flow of a Bingham fluid whose viscosity and yield stress depend on temperature and pressure. We consider two situations: in the first one we assume that the buoyancy effects are dominant and influence the development and evolution of the unyielded plug. In this case the governing equations are obtained via the Oberbeck–Boussinesq approximation which is derived using a perturbative approach. We show that within this approximation the heat generated by viscous friction can be safely neglected. In the second situation we assume that the frictional heating effects are dominant and influence the flow via the viscosity and yield stress that depend on temperature. For both situations we investigate the simple unidirectional flow between plates subjected to given thermal conditions. We derive the equations for the steady fully developed flow and we determine the exact position of the yield surfaces separating the yielded and the unyielded domain. We also show some plots to assess the effects due to the dependence of the rheological parameters on the temperature and pressure.