Buoyancy Sustained by Viscous Dissipation

Abstract

The quasi-parallel regime of a Darcy–Boussinesq boundary-layer flow over a permeable vertical flat plate adjacent to a fluid saturated porous medium is considered. ‘Quasi-parallel’ means here a plane flow with a constant transversal velocity v=−v ₀ directed perpendicularly towards the vertical surface, where a lateral suction with the same velocity −v ₀ is applied. The plate is held at a constant temperature T _w which coincides with the ambient temperature T _∞ of the fluid. The heat released by viscous dissipation induces a density gradient in the fluid. Thus, although T _w=T _∞, a thermal convection occurs. The steady regime of this ‘self-sustaining buoyant flow’ has been examined in detail. Wall jet-like profiles with a continuous but finite spectrum of the momentum flow have been found. These self-sustaining buoyant jets show a universal behavior, that is, there exist certain length, velocity and temperature scales such that the flow characteristics become independent of the (constant) material properties of the fluid and the porous medium as well.