INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2000; 34: 585–607 Numerical heat transfer in a cavity with a solar control coating deposited to a vertical semitransparent wall G. Alvarez a, * ,1 and C. A. Estrada b,2 a CENIDET-DGIT-SEP, AP 5 -164, Cuernaaca, Morelos, Mexico b Centro de Inestigaciones en Energı ´a —UNAM, AP 34, Temixco, Morelos, Mexico SUMMARY A transient two-dimensional computational model of combined natural convection, conduction, and radiation in a cavity with an aspect ratio of one, containing air as a laminar and non-participating fluid, is presented. The cavity has two opaque adiabatic horizontal walls, one opaque isothermal vertical wall, and an opposite semitransparent wall, which consists of a 6-mm glass sheet with a solar control coating of SnS–Cu x S facing the cavity. The semitransparent wall also exchanges heat by convection and radiation from its external surface to the surroundings and allows solar radiation pass through into the interior of the cavity. The momentum and energy equations in the transient state were solved by finite differences using the alternating direction implicit (ADI) technique. The transient conduction equation and the radiative energy flux boundary conditions are coupled to these equations. The results in this paper are limited to the following conditions: 10 4 Gr 10 6 , an isothermal vertical cold wall of 21°C, outside air temperatures in the range 30°C T 0 40°C and incident solar radiation of AM2 (750 Wm -2 ) normal to the semitransparent wall. The model allows calculation of the redistribution of the absorbed component of solar radiation to the inside and outside of the cavity. The influences of the time step and mesh size were considered. Using arguments of energy balance in the cavity, it was found that the percentage difference was less than 4 per cent, showing a possible total numerical error less than this number. For Gr =10 6 a wave appeared in the upper side of the cavity, suggesting the influence of the boundary walls over the air flow inside the cavity. A Nusselt number correlation as a function of the Rayleigh number is presented. Copyright © 2000 John Wiley & Sons, Ltd. KEY WORDS: cavities; natural convection; radiation; solar control coating 1. INTRODUCTION Over the last two decades, new technologies have been proposed and developed to control the thermal gains through the large windowpanes of tall buildings to reduce their energy * Correspondence to: Mechanical Engineering Department, CENIDET-DGIT-SEP, AP 5-164, Cuernavaca, Morelos CP 62050, Mexico. 1 E-mail: cenidet2@infosel.net.mx 2 E-mail: gace@infosel.net.mx Copyright © 2000 John Wiley & Sons, Ltd. Receied February 1999 Reised May 1999