The Prandtl-Darcy convection in a vertical porous layer may be unstable with internal heating

Abstract

Abstract The stability of buoyant flow in a vertical porous layer with the inclusion of time-dependent velocity term in the momentum equation is investigated. The buoyant flow is simultaneously induced by a uniformly distributed internal heat source and by the temperature gradient due to differentially heated impermeable porous layer boundaries. The conduction stream function and temperature fields are significantly altered due to internal heating and the linear instability is analysed through a study of normal mode perturbations on the base flow. The neutral stability curves and the critical Darcy-Rayleigh number for the onset of instability are evaluated by solving the stability eigenvalue problem numerically. It has been established that the volumetric heat source and the Prandtl-Darcy number reinforce together in initiating the instability of the base flow under certain conditions despite their isolation presence evidences stability for all infinitesimal perturbations. Although the effect of increasing internal heat source strength is to hasten the onset of instability, the flow is destabilized by decreasing and stabilized by increasing the Prandtl-Darcy number in some intermediate range of its value.