24 Journal of Advanced Thermal Science Research, 2016, 3, 24-32 E-ISSN: 2409-5826/16 © 2016 Avanti Publishers Analysis of Entropy Generation in a Generalized Couette Flow between Two Concentric Pipes with Buoyancy Effect A. S. Eegunjobi 1 , O. D. Makinde 2 and A. P. Oluwagunwa 3,* 1 Department of Mathematics and Statistics, Namibia University of Science and Technology, Private Bag 13388, 13 Storch Street, Windhoek, Namibia 2 Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa 3 Department of Mathematics and Statistics, Rufus Giwa Polytechnic, Owo, Ondo State, Nigeria Abstract: Heat transfer and entropy generation analysis in buoyancy driven generalized Couette flow of variable viscosity fluid within the annulus of two concentric cylindrical pipes are theoretically investigated. It is assumed that the inner cylinder is fixed while the outer one is subjected to axial motion. The governing nonlinear equation models are obtained and solved numerically using shooting quadrature. The results for velocity and temperature profiles are utilized to compute entropy generation number and the Bejan number. Relevant results are displayed graphically and discussed quantitatively. Keywords: Generalized couette flow, concentric pipe annulus, variable viscosity, bouyancy force, heat transfer, entropy generation. 1. INTRODUCTION Couette flows occur either between two parallel flat plates or between concentric cylinders. Generalized Couette flow differs from couette flow due to the fact that pressure gradient is superimpose in the direction of the flow. These flows have many significance applications in engineering and industries such as MHD pumps, MHD generators, accelerators, flow meters and nuclear reactors, journal bearing, aerodynamic heating and metal extrusion. Makinde and Franks [1] investigated the effect of magnetic field on a reactive unsteady generalized couette flow with temperature dependent viscosity and thermal conductivity. Attia and Sayed-Ahmed [2] studied the unsteady MHD flow of an electrical conducting viscous incompressible non-Newtonian ocasson fluid bounded by two parallel non-conducting porous plates with heat transfer putting into consideration the Hall effects. Theuri and Makinde [3] conducted an analysis of the first and second law of thermodynamics on a temperature dependent viscosity hydromagnetic generalized unsteady Couette flow with permeable walls. Asghara and Ahmada [4] constructed the analytic solution for unsteady Couette flow in the presence of an arbitrary non-uniform applied magnetic field. Chinyoka and Makinde [5] investigated the transient problem of generalized Couette flow and heat *Address correspondence to this author at the Department of Mathematics and Statistics, Rufus Giwa Polytechnic, Owo, Ondo State, Nigeria; E-mail: petergunwa@gmail.com transfer in a reactive variable viscosity third grade liquid with asymmetric convective cooling. Eegunjobi and Makinde [6] numerically investigated the entropy generation rate in a transient variable viscosity Couette flow between two concentric pipes. A list of the key references in the vast literatures concerning Couette flow and generalized Couette flow are given in references [7-11]. In this paper, we consider the irreversibility analysis in a generalized Couette flow within the annulus of concentric pipes with buoyancy effect and variable viscosity. In the flow, the outer cylinder moves in the axial direction while the inner cylinder remains fixed. Mathematical formulation of the problem is given in section two while the entropy generation analysis is presented in section three. The models boundary value problem are tackled numerically using shooting quadrature coupled with Runge-Kutta-Fehlberg integration scheme. Relevant results are presented graphically and discussed quantitatively for velocity, temperature, skin friction, Nusselt number, entropy generation rate and Bejan number. 2. MATHEMATICAL MODEL The steady flow of an incompressible viscous fluid between two concentric cylindrical pipes separated by r 1 ! r 0 in a generalized Couette flow with the inner cylinder stationary and the outer cylinder moving is considered in the presence of buoyancy effect as shown in Figure 1.