Proceedings of the International Conference on Mechanical Engineering 2007 (ICME2007) 29- 31 December 2007, Dhaka, Bangladesh ICME07-TH-22 © ICME2007 1 TH-22 1. INTRODUCTION Roughened surfaces are encountered in several heat transfer devices such as flat plate solar collectors and flat plate condensers in refrigerators. Larger scale surface non-uniformities are encountered, for example, in cavity wall insulating systems and grain storage containers, room heater etc. The only papers to date that study the effects of such non-uniformities on the vertical convective boundary layer flow of a Newtonian fluid are those of Yao [1] and Yao & Moulic [2, 3]. Hossain and Pop [4] have also investigated the magneto-hydrodynamic boundary layer flow and heat transfer from a continuous moving wavy surface, while the problem of free convection flow from a wavy vertical surface in presence of a transverse magnetic field was studied by Alam et al. [5]. On the other hand, natural convection over a vertical wavy frustum of a cone has been studied by Pop and Na [6]. Natural convection heat and mass transfer near a vertical wavy surface with constant wall temperature and concentration in a porous medium has also been studied by Cheng [7]. Hossain and Rees [8] have investigated the combined effect of thermal and mass diffusion on the natural convection flow of a viscous incompressible fluid along a vertical wavy surface. Natural convection along a vertical wavy surface with uniform surface temperature in presence of heat generation has been studied by Molla et al. [9]. A medium is said to be optically dense if the radiation photon mean free path is very small compared with the characteristic dimension of the medium. This approximation, namely Rosseland or the diffusion approximation, was derived by Rosseland [10]. Several investigators had used the optically thick limit approximation. One of them, Cess [11] studied the interaction of thermal radiation with free convection heat transfer along a vertical flat plate. Yih [12] studied the effect of radiation on natural convection about a truncated cone. Following Cess [11], Hossain et al. [13-15] have analyzed the effect of radiation for the forced and free convection flow of an optically dense viscous incompressible fluid past a heated vertical plate, elliptic cylinder, and horizontal circular cylinder. Very recently, Molla et al. [16] have investigated the radiation effect on natural convection from an isothermal sphere. Here we have investigated the natural convection boundary layer flow over a vertical wavy surface in presence of thermal radiation effect. The boundary layer equations are solved by using implicit finite difference method [17, 18]. We have given our attention to the situation where the buoyancy forces assist the flow for various values of the radiation–conduction parameter or Planck number R d and the surface heating parameter θ w with Pr = 0.73. 2. FORMULATION OF THE PROBLEM The boundary layer analysis outlined below allows the shape of the wavy surface, () x ˆ σ to be arbitrary, but our detailed numerical work will assume that the surface ABSTRACT The effect of thermal radiation on a steady two-dimensional natural convection laminar flow of viscous incompressible optically thick fluid along a vertical wavy surface has been investigated. Using the appropriate variables; the basic equations are transformed into the local non-similarity boundary layer form and then solved employing the Keller-box scheme of finite difference method. Numerical results are presented by streamline, isotherms, velocity and temperature distribution of the fluid as well as the local heat transfer rate in terms of local Nusselt number and average rate of heat transfer for a wide range of Planck number R d and the surface heating parameter θ w . The present numerical result shows excellent agreement with the published results when the effect of thermal radiation was passed over. Keywords: Radiation effect, Natural convection, Vertical wavy surface RADIATION EFFECT ON NATURAL CONVECTION LAMINAR FLOW ALONG A VERTICAL WAVY SURFACE Md. Mamun Molla 1 , Azad Rahman 2 , Md. Manirul Alam Sarker 32 1 Department of Mechanical Engineering, University of Glasgow, Glasgow G12 8QQ, UK 2 Department of Natural Science, Stamford University Bangladesh, Dhaka, Bangladesh 3 Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka, Bangladesh * Corresponding Author: M.A. Sarker, Email: masarker@math.buet.ac.bd , Tel: +880-02-9665650/Ext 7948