NONLINEAR FERROCONVECTION IN A POROUS LAYER USING A THERMAL NONEQUILIBRIUM MODEL

The energy stability analysis of a thermoconvective magnetized ferrofluid saturating a porous medium with a thermal nonequilibrium model is performed by means of an integral inequality technique. The boundaries are assumed to be stress-free. An extended Brinkman model is used for the momentum equation, and a two field model is used for the energy equation, each representing the solid and fluid phases separately. The corresponding Euler-Lagrange equations of the variational problem enable us to define a sharp bound for the threshold of stability for a given class of initial disturbances. The linear stability theory is also employed, and a comparison of results obtained by both linear and nonlinear theories shows a difference in the stability boundaries and thus indicates that the subcritical instabilities are possible for ferrofluids. However, it is noted that for nonferrofluids, linear and nonlinear stability boundaries coincide. The effect of interface heat transfer coefficient, magnetic parameter M3, Darcy-Brinkman number Da, and porosity-modified conductivity ratio y' on the onset of convection and on the subcritical instability region has been investigated. An asymptotic analysis for both small and large values of interface heat transfer coefficient '1-C is also presented. Excellent agreement is found between the exact solutions and asymptotic solutions.