Three-dimensional fluctuating Couette flow through the porous plates with heat transfer

Unsteady Couette flow of a viscous incompressible fluid between two horizontal porous flat plates is considered. The stationary plate is subjected to a periodic suction and the plate in uniform motion is subjected to uniform injection. Approximate solutions have been obtained for the velocity and the temperature fields, skin friction by using perturbation technique. The heat transfer characteristic has also been studied on taking viscous dissipation into account. It is found that the main flow velocity decreases with increase in frequency parameter. On the other hand, the magnitude of the cross-flow velocity increases with increase in frequency parameter. It is seen that the amplitude of the shear stress due to main flow decreases while that due to cross-flow increases with increase in frequency parameter. It is also seen that the tangent of phase shifts both due to the main and cross-flows decrease with increase in frequency parameter. It is observed that the temperature increases with increase in frequency parameter.