Effect of finite walls thicknesses and thermal conductivities on the Rayleigh convection in a viscoelastic Jeffreys fluid layer

The problem of thermal convection in a viscoelastic Jeffreys fluid layer is extended to include the fluid layer thickness and that of the walls along with its thermal conductivities. The aim is to show the bridge between two familiar cases of thermal convection: insulating (constant heat flux) and perfect thermal conducting walls (fixed temperature).

Findings are related to more realistic conditions at which the convective motions in the fluid layer set in. These conditions are given by the Rayleigh, the wavenumber and the frequency of oscillation for fixed Prandtl number and fluid properties as the relaxation and retardation times. Convection in the fluid layer was investigated to determine curves of criticality for the Rayleigh number, the wavenumber and the frequency of oscillation against the thermal conductivities ratio (fluid/wall) for walls with small and large thicknesses. The role of the stress relaxation and retardation times is discussed from the point of view of the walls thermal and geometrical properties. Curves of criticality show that steady and oscillatory motions compete to destabilize the fluid layer. More results shall be discussed.