Rayleigh-Benard Convection With Second-Sound in a Viscoelastic Fluid-Filled High-Porosity Medium

The linear stability of the Rayleigh-Benard situation in a viscoelastic fluid occupying a high-porosity medium is investigated. The viscoelastic correction to Brinkman momentum equation is effected by considering the modified form of Jeffrey constitutive equation. Further, the non-classical Maxwell-Cattaneo heat flux has been used in place of the classical Fourier heat flux law. The results of the study reveal that the non-classical theory predicts finite speeds of heat propagation. The eigen value is obtained for free-free, isothermal boundary combinations and it has been observed that the critical Rayleigh number is less than the corresponding value of the problem governed by the classical Fourier law. The study finds application in progressive solidification of polymeric melts and solutions, and also in the manufacture of composite materials.