(IJIRSE) International Journal of Innovative Research in Science & Engineering ISSN (Online) 2347-3207 Couette Flow Over A Deformable Permeable Bed S.Sreenadh 1,* , M.Krishnamurthy 2 , E.Sudhakara 3 and G.Gopi Krishna 4 1,2,3,4 Department of Mathematics, Sri Venkateswara University, Tirupati, 517502, India 1 *Address all correspondence to S.Sreenadh E-mail:profsreenadh@gmail.com Abstract-The flow of a viscous fluid over a thin deformable porous layer fixed to the solid wall of a channel is considered. The upper solid wall moves with constant velocity U 0. The flow in the deformable porous layer is governed by a modified Darcy law based on binary mixture theory. The flow over the deformable porous layer is governed by Navier-Stokes equations. The expressions for the displacement of the porous medium and the fluid velocity are obtained on solving the governing equations in the free flow and porous flow regions. The effects of various physical parameters such as f φ and η on the velocity and displacement are discussed in detail. When the thickness of the porous layer ε tends to zero and 1 f φ  , the results obtained reduce to the classical ones of Yuan [1] for the Couette flow between parallel plates. Keywords: Couette flow; deformable porous layer; permeable bed I. INTRODUCTION Viscous flow through and past deformable porous media has been studied experimentally by many researchers with a view to understand some practical phenomena such as transpiration colling and gaseous diffusion in arteriar walls. Most of the research works available deal with flow through rigid porous media. But when a biofluid flows in a physiological system, such as blood vessel there will be an interaction between free flow and tissue regions. Thus the study of flow through and past a deformable porous layer is necessitated. The study of deformation in porous materials with coupled fluid movement was initiated by Terzaghi [2] and later continued by Biot [3],[4],[5] and1956 into a successful theory of soil consolidation and acoustic propagation. Atkin and Craine (1976), Bowen (1980) and Bedford and Drumheller (1983) made important works on the theory of mixtures. Mow et al. (1984) developed a similar theory for the study of biological tissue mechanics. Using this theory arterial wall permeability is discussed by Jayaraman (1983). The same theory was also applied by Mow et al. (1985) and Holmes and Mow (1990) for the study of articular cartilages. Much of this analysis has been on one dimensional or purely radial compression without consideration of the influence of shear stresses on the deformable porous media. Barry (1991) discussed the flow of a viscous fluid past a thin deformable porous layer. Rajasekhara, Rudraiah and Ramaiah(1975) discussed the Couette flow over a naturally permeable bed. Ranganatha and Siddagangamma (2004) studied a mathematical model for the blood flow in arteries assuming the artery as a symmetric channel with solid walls attached by a thin deformable porous layer. The aim of the present study is to revisit the problem solved by Rajasekhara et al. (1975) for Couette flow over a deformable porous layer. The problem is solved analytically and the results are deduced and discussed. II. FORMULATION OF THE PROBLEM The geometry consists of a steady, fully developed Couette flow through a channel with solid walls at y L  and y h  and a porous layer of thickness L attached to the lower wall as shown in Fig.1. The flow region between the plates is divided into two layers. The flow region between the lower plate y L  and the interface 0 y  is termed as deformable porous region whereas the flow region between the interface 0 y  and the upper plate y h  is designated as free flow region. The fluid velocity in the free flow region