Thermal convection of a viscoelastic fluid in a fluid-porous system subjected to a horizontal plane Couette flow

• Thermal convection in a two-layer system with viscoelastic fluids is studied firstly.
• Transverse mode due to Couette flow is studied as well as longitudinal one for viscoelastic fluids.
• The transverse mode may be the preferred mode in the case of viscoelastic fluids.

Thermal convection in superposed fluid and porous layers saturated with viscoelastic fluids subjected to a horizontal plane Couette flow is investigated. Transverse mode generated by the shear flow, whose axis of convection roll is normal to the base flow, is studied as well as longitudinal mode whose axis is parallel to the base flow. Numerical results show that the neutral curves of both modes are bimodal when the depth ratio of the fluid layer to the porous layer is proper. We found that longitudinal mode is influenced by the depth ratio only. However, the neutral curves of transverse mode change with the variations of the depth ratio, the Reynolds number, the Prandtl number, the stress relaxation time and the strain retardation time. It is also found that the increase of the depth ratio leads to a more unstable system, while the increases of Reynolds number and Prandtl number make the system more stable. Meanwhile, the system is more unstable with a larger stress relaxation time and a smaller stain retardation time. Our results show that for viscoelastic fluids the transverse mode can be the preferred mode with proper values of the parameters, which will never happen in the case of Newtonian fluids.