Axisymmetric Flow Through a Cylinder with Porous Medium

The present work is a struggle to establish a mathematical appearance of the conduct of axisymmetric fluid flow in a moving cylinder confined in a porous medium. The fluid is assumed to be flowing through the annular region formed between two concentric smooth cylinders for the case when the outer cylinder is kept fixed while the inner cylinder is assumed to be moving with a constant velocity along the axial direction and is also assumed to be rotating with a constant angular velocity with reference to the centre line along the axial axis. Firstly, the conducting equations of motion are obtained in the form of a system of coupled non-linear partial differential equations with corresponding boundary conditions. The system is then transformed into a new set of coupled non-linear ordinary differential equations using a set of suitable similarity transformation. The problem is then solved using the fourth order numerical technique, the Runge-Kutta-Shooting method. The concluding results are derived for non- dimensional coupled differential equations. In the end the results are graphically presented and the behaviour of porosity parameter over the fluid flow is examined. The observed results indicated that with increasing values of the Reynolds’s numbers the non-dimensional linear and axial velocities also increases.