Numerical simulation of natural convection in a horizontal enclosure with a heat-generating conducting body Jae Ryong Lee, Man Yeong Ha * School of Mechanical Engineering, Pusan National University, San 30, Chang Jeon Dong, Kum Jeong Gu, Pusan 609-735, Republic of Korea Received 17 July 2005; received in revised form 9 January 2006 Available online 22 March 2006 Abstract The physical model considered here is a horizontal layer of fluid heated below and cold above with heat-generating conducting body placed at the center of the layer. The dimensionless thermal conductivities of body considered in the present study are 0.1, 1 and 50. The dimensionless temperature difference ratios considered are 0.0, 0.25, 2.5 and 25. Two-dimensional solution for unsteady natural con- vection is obtained using an accurate and efficient Chebyshev spectral methodology for variety of Rayleigh number from 10 3 to 10 6 . Multi-domain technique is used to handle square-shaped heat-generating conducting body. The fluid flow, heat transfer and time- and surface-averaged Nusselt number are investigated for various ranges of Rayleigh number, thermal conductivity ratio and dimension- less temperature difference ratio. The results for the case of conducting body with heat generation are also compared to those without heat generation to see the effects of heat generation from the conducting body on the fluid flow and heat transfer in the enclosure. Ó 2006 Elsevier Ltd. All rights reserved. 1. Introduction Rayleigh–Be ´nard convection in a horizontal layer of fluid confined between two parallel plates, with the bottom plate heated and the top one cooled, has been well studied for over a century. It has been well established that for the isothermal boundary condition the horizontal layer of fluid becomes unstable above a Rayleigh number of 1708 and convective motion sets in the form of steady convective rolls of aspect ratio (width to height) of about 2 [1]. With increasing Rayleigh number the flow undergoes a sequence of instabilities and eventually transitions to a turbulent state above a Rayleigh number of about 10 7 [2,3]. The geometries that arise in engineering applications, however, are more complicate than a simple horizontal layer of convecting fluid. Ha et al. [4]. considered the prob- lem of natural convection in a square enclosure with isothermal top and bottom boundaries and various condi- tions of thermal boundary of interior body, and also, an aspect ratio effect of given enclosure with equi-spaced array of bodies was investigated by Lee et al. [5], in which they concluded that the transition of flow from quasi-steady up to unsteady convection depends on the presence of bodies and aspect ratio effect of the cell. However, a body considered was not calculated but trea- ted a rigid wall. In order to consider interior body, many numerical studies have conducted for couples of decades. One of the earliest systematic numerical investigations of this problem was by House et al. [6] who considered the influence of a centered conducting body on natural convec- tion within an enclosure. For given Ra and Pr, an existence of conducting body with thermal conductivity ratio less than unity makes heat transfer enhanced. Deng and Tang [7] defined a heat function to visualize the heat and fluid flow in an air filled square cavity over a wide range of Ra = 10 3 –10 6 , and those for conjugate natural convec- tion/heat conduction where the conduction effect of solid body on heat transfer is studied. Moreover, a phenomenon of free convection with another heat source is quite inter- esting and has been studied vigorously. Oh et al. [8] inves- tigated the steady natural convection processes when a 0017-9310/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2006.01.010 * Corresponding author. Tel.: +82 51 510 2440; fax: +82 51 512 9835. E-mail address: myha@pusan.ac.kr (M.Y. Ha). www.elsevier.com/locate/ijhmt International Journal of Heat and Mass Transfer 49 (2006) 2684–2702