Convective instabilities in binary mixture ³He-⁴He in porous media

The present study attempts to simulate and analyze the Rayleigh-Bénard convection of superfluid mixture (³He-⁴He) kept in the sparsely packed porous medium with stress-free boundary conditions. Theoretically the linear and nonlinear analysis are carried out near the onset of stationary convection. The nonlinear governing equations describing the motion with the Darcy model, temperature and concentration fields are expanded as the sequence of non-homogeneous linear equations. These equations are solved by employing the Fourier analysis of perturbations in terms of the non-dimensional expansion parameter ε until O(ε⁸) as proposed by Kuo (1961). The flow field and heat transfer characteristics are analyzed for different control parameters arising in the system such as the Rayleigh number (R), the separation ratio (ψ), which is the coupling between the temperature and concentration fields, and the Lewis number (Le). Apart from streamlines and isotherms, the novel flow visualization technique for the heat flow patterns in terms of heatlines is derived and plotted. Also, the kinetic energy, potential energy, and minimum entropy generation are analyzed. The Nusselt number is found to be get enhanced as the values of R and ψ are increased whereas it gets inhibited as Le increases.