International Journal of Energy & Technology 3 (2) (2011) 1–13 1. INTRODUCTION The prediction of heat transfer from irregular surfaces is a topic of fundamental importance for some heat transfer devices, such as, flat plate solar collectors, flat plate condensers in refrigerators, double-wall thermal insulation, underground cable systems, electric machinery, cooling system of micro-electronic devices, natural circulation in the atmosphere, the molten core of the Earth, etc. In addition, roughened surfaces could be used in the cooling of electrical and nuclear components where the wall heat flux is known. Surfaces are sometimes intentionally roughened to enhance heat transfer. Process involving heat and mass transfer are often encountered in the chemical industry, in reservoir engineering connection with thermal recovery processes, and in the study of the dynamics of salty hot springs in the sea. In view of these applications, several authors have made investigations of the fluid flows over a wavy wall. Vajravelu and Sastri [1] have made an interesting analysis of the free convective heat transfer in a viscous incompressible fluid bounded by a long (when compared with the width of the channel) vertical wavy and a parallel flat wall. Later, Vajravelu [2] studied the combined free and forced convection in hydrodynamic flows in a vertical wavy channel with traveling thermal waves. Malashetty et al. [3] studied on magneto convective flow and heat transfer between vertical wavy wall and a parallel flat wall. Srinivas and Muthuraj [4] studied MHD flow with slip effects and temperature-dependent heat source in a vertical wavy porous space. It is necessary to study the heat transfer for more complex geometries because the prediction of heat transfer for irregular surfaces is a topic of great importance and irregular surfaces often occur in many applications. Recently several studies by Rathish Kumar et al. [5,6], Murthy et al. [7] and Kumar and Shalini [8] have been reported and were concerned with natural convection heat transfer in wavy vertical porous enclosures. It is now generally recognized that in industrial applications non-Newtonian fluids are more appropriate than Newtonian fluids. Numerous models were suggested for non-Newtonian fluids with their constitutive equations varying greatly in complexity. Already the class of flows for which an exact solutions is possible for Navier-Stokes equations that govern the flow of Newtonian fluids is rather restricted. This class further narrowed down for non-Newtonian fluids on account of the non-linear relationship between the stress and rate of strain at any point of the flow. Rheological properties of materials are specified in general by their real fluids especially those with low molecular weight, is described by Navier-Stokes theory. There are many complex fluids such as polymer solutions, soaps, blood, paints, certain oils and greases which are not well described by a Newtonian constitutive equation. FREE CONVECTION IN A VERTICAL DOUBLE PASSAGE WAVY CHANNEL FILLED WITH A WALTERS FLUID (MODEL B’) J. Prathap Kumar *,1 , J.C. Umavathi *,1 , Ali J. Chamkha ** and H. Prema *,3 * Department of Mathematics, Gulbarga University, Gulbarga 585 106, Karnataka, India p_rthap@yahoo.com 1 , jc_uma11@yahoo.com 2 , ashkptl@rediff.com 3 ** Manufacturing Engineering Department, The Public Authority for Applied Education and Training, Shuweikh 70654, Kuwait, achamkha@yahoo.com ABSTRACT The present analysis is concerned with the flow characteristics of fully developed free convection flow of a Walters fluid (Model B’) in a vertical channel divided into two passages (by means of a baffle) for two separate flow streams. Each stream has its own individual velocity and temperature fields. One of the walls of the channel is wavy while the other is flat and both walls are maintained at constant but different temperatures. The coupled non-linear partial differential equations governing the fluid motion in the channel have been solved by a linearization technique wherein the flow is assumed to consist of two parts; a mean part and a perturbed part. Exact solutions are obtained for the mean part and a perturbed part is solved using a long wave approximation. The velocity and temperature values are obtained and discussed for the various physical parameters such as the Grashof number, wall temperature ratio, viscoelastic parameter and x  at different positions of the baffle. The variation of the skin friction and the Nusselt number are given in tables for different governing parameters. It is found that the viscoelastic parameter, wave number and the amplitude parameter reduce the skin friction at the wavy wall while it remains invariant at the flat wall. In addition, the effect of wave number is found to decrease the rate of heat transfer at the wavy wall and increase at the flat wall. Keywords: Wavy vertical channel, baffle, Walters fluid International Journal of Energy & Technology www.journal-enertech.eu ISSN 2035-911X