Boundary condition effects on ferro-thermal-convection in a ferrofluid-saturated porous layer with uniform volumetric energy sources

Abstract

This paper theoretically investigates the effects of different velocity, temperature and magnetic potential boundary conditions on the linear stability criteria of ferro-thermal-convection (FTC) in a layer of porous medium with uniformly distributed internal heat sources. The lower and upper boundaries are considered to be either rigid or free. At the lower boundary a thermally perfect insulator condition is used and at the upper boundary a general thermal boundary condition is appealed. 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 which is either the gravity thermal Rayleigh number Rt or the magnetic thermal Rayleigh number Rm. When both boundaries are insulating the expression for the critical eigenvalue is obtained using a regular perturbation technique. It is found that the critical Rt or Rm are high for rigid-rigid (R-R) boundaries and the least for free-free (F-F) boundaries. The influence of inverse Darcy number (Da−1), Biot number (Bi) and the Brinkman number (Λ) is to delay, while that of internal heating (N s) and the non-linearity of fluid magnetization (M3) is to speed up the onset of FTC in a porous medium. The previously published results are recovered as particular cases from the present study.