RUN-UP FLOW OF OLDROYD (1958) TYPE VISCO-ELASTIC LIQUID THROUGH POROUS MEDIUM UNDER THE INFLUENCE OF MAGNETIC FIELD IN A LONG CIRCULAR CYLINDER

摘要

In the present problem Laplace transform technique has been applied to analyze the run-up flow of Oldroyd (1958) type visco-elastic liquid through porous medium under the influence of magnetic field in a long right circular cylinder. The motion is initially generated by constant pressure gradient down the tube length. When the flow is fully developed, the pressure gradient is suddenly withdrawn where as the wall of the cylinder is impulsively started simultaneously. Expressions for velocity field, flow rate and the shear stress on the wall has been obtained. The results for Kuvshiniski visco-elastic, Rivlin Ericksen visco-elastic and ordinary viscous fluid flows are also deduced as the limiting cases. If porous medium is withdrawn, all corresponding results for viscous and various types of visco-elastic liquids can be determined.