THERMAL INSTABILITY OF VISCOELASTIC FLUIDS IN POROUS MEDIA

Based on the modified Darcy model, the status and progress in research of thermal instability of viscoelastic fluids in porous media are reviewed. By using the method of linear stability analysis, the effects of the geometry of porous media (i.e. horizontal porous layer, porous cylinder and porous cavity), thermal boundary conditions (i.e. bottom heated with constant temperature, bottom heated with constant heat flux, bottom with Newtonian heating and open top), flow model of viscoelastic fluids (i.e. modified Darcy-Jeffrey, Darcy-Brinkman-Oldroyd and Darcy-Brinkman- Maxwell models), local thermal non-equilibrium and rotation on the critical Rayleigh number of thermal instability of viscoelastic fluids can be calculated. By using the method of weakly non-linear analysis, the bifurcation from the basic state and the analytical solution of Nusselt number at the neighborhood of critical point can be obtained. By the numerical simulation method, the evolution of flow pattern as well as the variations of Nusselt number at high Rayleigh number can be revealed. It has been found that (1) the elasticity of viscoelastic fluids can destabilize the oscillatory convection; (2) the rotation effect and local thermal non-equilibrium effect can suppress the thermal instability of viscoelastic fluids; (3) at the neighborhood of critical point, the bifurcation from the basic state for stationary convection is supercritical, while the bifurcation for the oscillatory can be supercritical or subcritical, mainly depending on the values of viscoelastic parameters, Prandtl number and Darcy number; (4) with the increasing Rayleigh number, the flow pattern of thermal convection evolve from one-cell pattern into multi-cell roll pattern, and finally a chaotic pattern.