In,. .I. Hear Mass Transfer. Vol. 35, No. 7, pp. 1645-1657, 1992 00174310/92$5.00+0.00 Printed in Great Britain 0 1992 Pergamon Press Ltd On naturalconvection in a singleand two zone rectangular enclosure T. G. KARAYIANNIS Institute of Environmental Engineering, South Bank Polytechnic, 103 Borough Road, London SE1 OAA, U.K. and M. CIOFALO and G. BARBARO Dipartimento di Ingegneria Nucleare, Universita di Palermo, Viale delle Scienze, 90128 Palermo, Italy zyxwvutsrqpon (Received 29 May 1991 and in final form 15 July 1991) Abstract-Convective heat transfer was investigated numerically for rectangular enclosures both undivided and dividedin two zonesby a vertical partition, and havingopposite isothermal walls at different temperatures. The aspect ratio was varied from 0. I to 16 and the Rayleigh number from 3.5 * lo3 to 3.5 (non-partitioned enclosures) and from I .O * 10’ to1.6 * 10’ (partitioned enclosures). The thickness and conductivity of the partition were varied. The end wall thermal boundary conditions were adiabatic or LTP (Linear Temperature Profile). The continuity, momentum and energy equations for a 2-D laminar steady flow were solved under the Boussinesq approximation by using a finite-difference method and the SIMPLECpressure-velocity coupling algorithm. Grid-independent results indicate thatthe reduction in the Nusselt number caused by a thin central partition can be predicted within a few per cent (in the range investigated) by assuming the partition to be isothermal, i.e. infinitely conducting. The finite conductivity of the partition causes a temperature distribution along its length, resulting in an increase in Nu which depends on Rayleigh number, aspect ratio and end wall thermal boundary conditions. zyxwvutsrqponmlkj 1. INTRODUCTION HEAT TRANSFER by natural convection in rectangular enclosures, such as the one shown in Fig. l(a), is an area of considerable engineering interest. This is due to its many applications, such as in cavity walls, double-pane windows and solarcollectors. Excellent reviews of the past experimental and numerical re- search work reporting on the flow patterns and heat transfer rates in rectangular enclosures are available and will not be discussed here [l-3]. Real thermal systems can deviate significantly from the simple rectangular cavity model of Fig. l(a). For example, in building applications the model should include the association of two cavities communicating laterally through a doorway, window, corridor or over an incomplete dividing partition [4]. Natural con- vection in the air layerof a double-pane windowis coupled with the internal naturalconvection in the room and external convection and could deviate from models such as the one shown in Fig. l(a). Further, data obtained from the basic cavity model are not strictly applicable to the solar collector cavitywhere the internal convection is coupled with external con- vection at the glazing [5]. These and the possible insu- lating effectof partitions are some of the reasons which recently encouraged researchers to turn their attention to the study of convectionin complex enclosures and, in particular, to enclosures with par- tial and complete partitions at the end walls. The effect of partial partitions normalto the end walls on fluid flow and heat transfer in enclosures was investigated in refs. [6-141. In the case of a completely partitioned enclosure the convection in the two result- ing cavities is coupled, Fig. l(b). Reports on this geometry are scarce and are only in general qualitative agreement, with disagreement in the actual numerical values which calls for further clarification, Anderson and Bejan [15] reported that N equidistant thin alu- miniumpartitions in a water-filled enclosure having AR = l/3 at Ra = log-10” reduced the overall heat transfer rate by a factor (N+ 1))“.6’ (i.e. by a factor 0.65 for N = 1). Nishimura et al. [ 161 performed both an experimental and a numerical investigation. In theirexperiments the partitions weremade of thin copper plates, the working fluid was water, the enclos- ure aspect ratio was 4 and 10 and the Rayleigh number rangedfrom lo6 to 109; they found a heattrans- fer reduction factor of 0.42 for a singlepartition. From theirnumerical simulations (AR = 4, Pr = 6, lo4 < Ra < 10’) the authors reported a reduction by a factor (N+ 1) ’ (i.e. a factor 0.5 for N = 1). 2. MATHEMATICAL FORMULATION AND NUMERICAL METHODS Figure 1 is a schematic of the basic, or non-par- titioned, enclosure (identified with the subscript ‘b’) and of the partitioned enclosure (identified with the 1645