Natural Convection with Dissipative Heating

Abstract:

We derive a system of equations which models the motion of linear viscous fluids that undergo isochoric motions in isothermal processes but not necessarily isochoric ones in non-isothermal processes. The main point is that in contrast to the usual Oberbeck–Boussinesq approximation we do not neglect dissipative heating. We study Rayleigh–Bénard convection for our system and investigate existence, uniqueness and regularity of solutions and conditions for the stability of the motionless state.