Fundamental J. Thermal Science and Engineering, Vol. 1, Issue 2, 2011, Pages 83-99 Published online at http://www.frdint.com/ : es phras and Keywords porous medium, oscillating plate, periodic solution, Darcy number. * Corresponding author Received November 10, 2011 © 2011 Fundamental Research and Development International OSCILLATORY FLOW OF VISCOUS FLUID IN A HORIZONTAL CHANNEL FILLED WITH POROUS MATERIAL ABIODUN O. AJIBADE * and STEPHEN ISHAYA Department of Mathematics Ahmadu Bello University Zaria, Nigeria e-mail: olubadey2k@yahoo.com Abstract The flow of viscous fluid in a horizontal channel filled with porous material is considered. The motion of the fluid is induced by one of the channel boundaries moving in its own plane with a sinusoidal variation of velocity. An analytic solution describing the flow is obtained by solving the partial differential equation in dimensionless form. The expressions for the velocity and skin-friction are derived using the method of substitution in the momentum balance equation that is used to describe the flow. The response of velocity and skin-friction to the different governing parameters is fully discussed with the aid of graphs. It is interesting to remark that fluid velocity increases as the Darcy number increases. Also, as the ratio of effective viscosity to that of the fluid viscosity increases, fluid motion responds with an increase in velocity within the channel. 1. Introduction The motion of viscous fluid caused by the sinusoidal oscillation of flat plate is termed as Stokes’ second problem (Schlichting [1]). The study of this type of flow is not only of fundamental theoretical interest but it also occurs in many applied