Time-dependent Taylor-Couette Flow in an Annulus Partially Filled with Porous Material

The current investigation examines the time-dependent dynamics of fluid within a system composed of two coaxial rotating cylinders partially filled with clear fluid and fluid saturated with isotropic porous material of uniform permeability. The fluid motion is induced by the time-dependent exponential decay/growth boundary motion of the two cylinders. Through the utilization of the semi-analytical methodology, which incorporates the Laplace transform technique and the Riemann-sum approximation approach, a comprehensive examination is conducted on the interaction between the transparent fluid and the isotropic porous medium, as well as the influence of the time-dependent exponential decay or growth boundary condition on both surfaces. The results encompass the influence of different factors entering the dimensionless model. It is demonstrated that the velocity of the fluid in the area containing porous material is increased when the inner cylinder experiences exponential growth. The shear stress at both cylinders can be controlled by taking into account the suitable time-dependent exponential growth/decay at the surfaces.