Transient Dean flow in a composite annular duct with porous walls partially filled with porous material

This work presents a semi-analytical solution of transient Dean flow in a composite annular duct with porous walls partially filled with porous materials. The flow is set up as a result of the imposed pressure gradient in the azimuthal $\left(\theta \right)$ direction while both the outer and the inner cylinders are fixed. The appropriate governing equations for the flow are rendered dimensionless and transformed using suitable techniques, the Laplace transform technique is further used to transform the partial differential equations into the total differential equation. The solution of the ODE is later transformed to the time domain using the well-known Riemann-sum approximation approach. To validate the accuracy of the numerical scheme deployed in this research, numerical comparison of the steady-state solution, and the values generated using the implicit finite difference on the transient state model is presented. Generally, higher dominance of clear fluid and fluid injection at the inner cylinder is found to enhance the fluid velocity at the fluid interface. It is also good to note that injection of fluid at the inner cylinder pose a decreasing influence on the flow with minimum or no effect near the point R = 1.7.