Effect of thermal modulation on the onset of convection in a viscoelastic fluid saturated porous layer

The effect of thermal modulation on the onset of convection in a horizontal, anisotropic porous layer saturated by a viscoelastic fluid is investigated by a linear stability analysis. Darcy's law with viscoelastic correction is used to describe the fluid motion. The perturbation method is used to find the critical Rayleigh number and the corresponding wavenumber for small amplitude thermal modulation. The stability of the system characterized by a correction Rayleigh number is calculated as a function of the thermal and mechanical anisotropy parameters, the viscoelastic parameters and the frequency of modulation. It is found that the onset of convection can be delayed or advanced by the factors represented by these parameters. The results of the problem have possible implications in mantle convection.