Energy Based Volumetric Internal Heating on Bénard-Marangoni FTC in a Ferrofluid-Porous Saturated Layer: Effects of MFD Viscosity and Thermal Bounded Surfaces

A linear stability analysis of energy based volumetric internal heating on Bénard-Marangoni ferrothermal convection (FTC) in a ferrofluid (FF) porous saturated layer with effects of magnetic field dependent (MFD) viscosity and thermal bounded surfaces is investigated. The variation of the energy based modified critical Rayleigh number, gc R  , and the convection cell, c a , with rate of heat source, is calculated with a set of lower-rigid and upper-stress free (R-F) bounded surfaces. Using numerically the Galerkin technique (GT) and analytically the regular perturbation technique (RPT) it is possible to deduce the condition for the onset of FTC from a state of pure conduction. Here we find that the rate of internal heat source increases, gc R  decreases, showing that the system is destabilized, and c a increases, showing that the cells size become narrower. Numerical results are discussed in the table and graphically to reveal the details of stability characteristics for different physical parameters akin to MFD viscosity parameter, porous parameter, magnetic and