Internally heated Darcy-Brinkman-Bénard ferro-thermal-convection in a ferrofluid saturated porous layer: The influence of boundaries

Abstract

This paper theoretically investigates the effects of different velocity, temperature and magnetic potential boundary conditions on the linear stability criteria of three models of internally heated (IH) distributions on Brinkman-Benard ferro-thermal-convection (FTC) in a layer of porous medium with uniformly distributed internal heat sources. Here the system uses three IH configurations in the theoretical studies of FTC which is connected with three pairs of thermal boundary conditions: upper and lower surfaces of fixed temperature (IH1), upper and lower surfaces of insulating case (IH2), and an insulating lower surface with fixed temperature at the upper surface (IH3). The resulting thresholds are reported to three velocity boundary conditions like (i) lower and upper boundary no-slip (rigid-rigid, R-R), (ii) lower no-slip and upper free-slip (rigid-free, R-F), and (iii) lower and upper boundary free-slip (free-free, F-F). The principle of exchange of stabilities is valid and a Galerkin technique based on the weighted residual method (WRM) has been used in general to extract the critical eigenvalue of the gravity thermal M Rayleigh number and the magnetic thermal Rayleigh number.The governing parameters of the problem are viscosity ratio (Λ) and inverse of Darcy number (Da−1) effect is to stabilize the IH-FTC, while strength of magnetic number (M1) and non-1 M linearity of fluid magnetization (M3) effect is to destabilize the system. The model of IH2 advances the FTC compared IH1 and 3 IH3. In limiting cases, some previously published results are recovered from the present study.