A numerical study on three-dimensional conjugate heat transfer of natural convection and conduction in a dierentially heated cubic enclosure with a heat-generating cubic conducting body Man Yeong Ha*, Mi Jung Jung School of Mechanical Engineering, Pusan National University, San 30, Jangjeon-Dong, Kumjung-Ku, Pusan 609-735, South Korea Received 24 September 1999; received in revised form 10 February 2000 Abstract A comprehensive numerical study has been conducted to investigate three-dimensional, steady, conjugate heat transfer of natural convection and conduction in a vertical cubic enclosure within which a centered, cubic, heat- conducting body generates heat. The physical model considered here assumes that a temperature dierence exists across the enclosure (right cold wall and left hot wall) and the body generates a constant amount of heat. Under these conditions, the ¯ow inside the enclosure is driven by two temperature dierences: a temperature dierence across the enclosure and a temperature dierence caused by the heat source. A ratio of these two temperatures is a key parameter in this study. The steady, three-dimensional governing equations are written in a dimensionless form with dimensionless parameters that decide the heat transfer and ¯ow characteristics in this system. The analysis is conducted by observing variations of the velocity vectors, pathlines, and isotherms for dierent Rayleigh numbers and temperature-dierence ratios. The details of the three-dimensional ¯ow and isotherms are described in order to investigate the eects of three-dimensionalities on the ¯uid ¯ow and thermal characteristics in the enclosure. The variations of Nusselt numbers on the hot and cold walls are also presented to show the overall heat transfer characteristics inside the enclosure. 7 2000 Elsevier Science Ltd. All rights reserved. 1. Introduction An important class of natural convection heat transfer is that related to buoyancy-driven ¯ows moving within an enclosure. The heat transfer and ¯ow characteristics of natural convection in rec- tangular enclosures have attracted much research, due to their many practical engineering applications, such as in building insulation, solar energy collec- tion, cooling of heat-generating components in the electrical and nuclear industries, and ¯ows in rooms due to thermal energy sources[1±3]. There are two elementary classes of natural convection ¯ows in enclosures. The ®rst is a horizontal cavity with heating from below and with adiabatic vertical walls. Natural convection ¯ows in a horizontal cav- ity are characteristics of Rayleigh±Benard convection and of practical problems of electronic equipment International Journal of Heat and Mass Transfer 43 (2000) 4229±4248 0017-9310/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S0017-9310(00)00063-6 www.elsevier.com/locate/ijhmt * Corrensponding author. Tel.: +82-51-510-2440; fax: +82- 51-512-9835. E-mail address: myha@hyowon.pusan.ac.kr (M.Y. Ha).