On some non-linear shear flows of non-Newtonian fluids

Abstract

In this paper we study two types of shear flows of non-Newtonian power law fluids. First, we investigate the unsteady flow induced by the motion of a slender cylindrical rod moving in the direction of its axis of symmetry through a conducting power law fluid in the presence of a magnetic field. Second, we study the flow of a power law fluid down an inclined porous plate moving in its own plane. For both types of flow we obtain exact similarity solutions in closed form for the initial-boundary value problem and the Cauchy problem for which the solution is of source-type. For the flow due to the cylinder motion we determine the effect of the coupling of the non-Newtonian fluid properties with the magnetic field. Similarly, for the flow down an inclined plate we address the coupling of the non-Newtonian rheology with the effect of the fluid loss through the porous plate.