The Prandtl–Darcy Convection in a Vertical Porous Layer may be Unstable with Internal Heating

Abstract

The stability of natural convection in an internally heated vertical porous layer confined between two impermeable boundaries which are kept at different constant temperatures is investigated. The momentum transfer is modeled by adopting Darcy’s law including time-dependent velocity term contribution. The conduction stream function and temperature fields are significantly altered due to internal heating, and the linear instability is analyzed 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 a uniform 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 internal heat source strength is to hasten the onset of instability, and the Prandtl–Darcy number is found to induct both destabilizing and stabilizing impact on the base flow.