NATURAL CONVECTION IN A SQUARE CAVITY WITH SPATIAL SIDE-WALL TEMPERATURE VARIATION Nawaf H. Saeid Department of Mechanical Engineering, Curtin University of Technology, Sarawak, Malaysia Yusli Yaacob School of Mechanical Engineering, University of Science Malaysia, Pulau Penang, Malaysia Laminar natural convection in a two-dimensional square cavity filled with a pure air (Pr ¼ 0.71) is studied numerically in the present article with nonuniform side-wall tempera- ture. The heated vertical wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, which is higher than the cold side-wall temperature, while the top and the bottom walls are adiabatic. A finite-volume method is used to solve numerically the nondimensional governing equations in the vorticity–stream function formulation. The effects of the amplitude and the wave number of the heated side-wall temperature variation on the natural convection in the cavity are investigated. It is found that the average Nusselt number varies based on the hot-wall temperature. It increases with an increase in the ampli- tude, while the maximum average Nusselt number occurs at the wave number of k ¼ 0.7 for Rayleigh number range 10 3  Ra  10 6 . It is found that the values of maximum fluid circulation occur at a similar wave number, which produces maximum heat transfer for small values of Ra, while it occurs at higher values of wave number at high Ra. INTRODUCTION Laminar natural convection in enclosures has received considerable attention in the last several decades due to its effect on thermal performance in many engin- eering applications. The applications include the operation of solar collectors, cool- ing of electronic equipment, hot- and chilled-water storage tanks, ovens, furnaces, and many others. Much research work, both theoretical and experimental, has been done on the convective heat transfer processes in two-dimensional enclosures, where the common model is the square or rectangular enclosure heated horizontally or vertically. The details of the natural-convection theory in enclosures has been presented in books by Minkowycz et al. [1], Yang [2], Pop and Ingham [3], and Bejan [4], among others. The model commonly used consists of a cavity with the vertical walls maintained at Received 28 March 2005; accepted 8 August 2005. Address correspondence to Nawaf H. Saeid, Department of Mechanical Engineering, Curtin University of Technology, Sarawak Campus, CDT 250, 98009 Miri, Sarawak, Malaysia. E-mail: n h saeid@yahoo.com 683 Numerical Heat Transfer, Part A, 49: 683–697, 2006 Copyright # Taylor & Francis Group, LLC ISSN: 1040-7782 print=1521-0634 online DOI: 10.1080/10407780500359943