DARCY–BENARD–MARANGONI FERROCONVECTION WITH INTERNAL HEAT GENERATION

Abstract

The onset of Darcy–Benard-Marangoni penetrative convection in a horizontal ferrofluid-saturated porous layer  of high permeability of practical importance is investigated by employing the Brinkman–Forchheimer– Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity  in the presence of a uniform applied vertical magnetic field. The lower boundary is taken to be rigid and isothermal and the upper surface is free and subject to the general thermal condition.  The critical eigen values are obtained numerically, in general, using Galerkin method. However, closed form solution is also obtained using regular perturbation technique for insulated boundaries. The stability of the system is found to be dependent on the dimensionless internal heat source strength Ns, permeability parameter and the ratio of effective viscosity to fluid viscosity.   It is observed that the increase in the value of permeability parameter is to delay while increase in the value of internal heat source strength is to hasten the onset of Darcy–Benard-Marangoni ferroconvection in a fluid saturated porous layer.

 

Keywords - Volumetric heat source; ferroconvection;  Effective viscosity