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

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 R_t or the magnetic thermal Rayleigh number R_m. When both boundaries are insulating the expression for the critical eigenvalue is obtained using a regular perturbation technique. It is found that the critical R_t or R_m 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.