Stability of Penetrative Natural Convection in a Non-Newtonian Fluid-Saturated Vertical Porous Layer

Abstract

The stability of natural penetrative convection arising due to a uniform internal heat source in a vertical porous layer saturated with an Oldroyd-B fluid is investigated. The vertical walls of the porous layer are impermeable and maintained at different uniform temperatures. The energy stability analysis performed reveals that the system is unconditionally stable even in the presence of internal heating in the case of Newtonian fluids, while for viscoelastic fluids the base flow is found to be unstable. As the energy stability analysis of Gill type is unable to decide the stability of the system, the Galerkin method is used to solve the complex eigenvalue problem. The internal heating introduces asymmetry in the basic flow and amounts to the existence of different set of onset modes. The internal heating and stress relaxation parameter facilitates instability of the system while increasing strain retardation parameter discloses stabilizing effect on the system. Moreover, the critical Darcy–Rayleigh number, wave number and wave speed become invariant as Ns becomes large. The streamlines and isotherms presented herein demonstrate the development of complex dynamics at the critical state.