Darcy-Benard-Oldroyd Convection in a Rotating Porous Layer with an Internal Heat Source

Abstract

This research examines the stability of an Oldroyd-B fluid within a horizontal porous layer, influenced by both an internal heat source and rotation. The energy equation incorporates a term for internal heat generation, and a modified Darcy-Oldroyd model that includes the Coriolis effect is used to describe momentum. To explore the impact of rotation, internal heat generation, and viscoelasticity on system stability, a linear stability analysis is performed. For nonlinear stability analysis, the normal mode method is combined with the Galerkin method of weighted residuals and the truncated Fourier series method. The Runge-Kutta-Gill technique is then applied to numerically solve the resulting system of nonlinear differential equations. The study investigates how various controlling parameters affect stability and convective heat transfer. It is observed that the initial conduction state transitions into convective motion. Key factors in initiating convection include the internal heat production coefficient and the stress-relaxation parameter. Conversely, rotation, the strain-retardation coefficient, and the heat-capacity ratio delay the onset of convection. The Vadasz number exhibits two distinct effects.