Non-gray radiative convective conductive modeling of a double glass window with a cavity filled with a mixture of absorbing gases Kamal A.R. Ismail * , Carlos Salinas S. Department of Thermal and Fluids Engineering – FEM – UNICAMP, P.O. Box 6122, CEP 13083-970, Campinas (SP), Brazil Received 22 July 2005; received in revised form 20 January 2006 Available online 11 May 2006 Abstract Coupled radiation and natural convection heat transfer occurs in vertical enclosures with walls at different temperatures filled with gas media. In glass window thermal insulation applications in hot climates, infrared absorbing gases appear as an alternative to improve their thermal performance. The thermal modeling of glass windows filled with non-gray absorbing gases is somewhat difficult due to the spec- tral variation of the absorption coefficients of the gases and the phenomena of natural convection. In this work, the cumulative wave- number (CW) model is used to treat the spectral properties of mixtures of absorbing gases and the radiative transport equation is solved using CW model and the discrete ordinates method. Due to the range of temperature variation, the mixture of gases is considered as homogeneous. The absorption coefficients were obtained from the database HITRAN. First, the natural convection in a cavity with high aspect ratio is modeled using a CFD code and the local and global Nusselt numbers are computed and compared with available empirical correlations. Also, the flow pattern for different Rayleigh numbers is analyzed. Then, the heat transfer in the gas domain is approximated by a radiative conductive model with specified heat flux at boundaries which is equivalent to convective transport at the walls surround- ings. The energy equation in its two-dimensional form is solved by the finite volume technique. Three types of gas mixtures, highly absorbing, medium and transparent are investigated, to determinate their effectiveness in reducing heat gain by the gas ambient. Reflec- tive glasses are also considered. The numerical method to solve radiative heat transport equation in gray and non-gray participant media was validated previously. The temperatures distributions in the gas and the glass domain are computed and the thermal performance of the gas mixtures is evaluated and discussed. Also, comparison with pure radiative conductive model is shown. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Numerical modeling; Cumulative wavenumber model; Radiation conduction convection; Glazing; Non-gray gases 1. Introduction Convection heat transfer in gas layers within rectangular cavities appears in many engineering applications and hence a great deal of investigations were dedicated to better understanding of the problem [1–4]. Many experimental results and correlations can be found in Wright [2]. In tropical climates of the southern hemisphere the prin- cipal advantage of a thermal glass window is to avoid heat transfer to the internal ambient and consequently reduce the cooling load requirements to maintain thermal com- fort. In the interior of a building, direct sunlight is the source of significant visibility and directs up to 800 W/m 2 of radiation through windows into the building interior. The use of selective films allows changes in both solar and infrared transmittance, reflectance and absorptance of glass windows. The films can be designed to absorb or reflect according to the wavelength of the incident radia- tion and generally can be incorporated with glass window filling gases. Other techniques employ low conductivity gases such as Argon and Helium instead of air as a filling gas in double glass windows. Double glass windows filled with infrared absorbing gases, ventilated double glass win- dows, and glass windows employing combination of these 0017-9310/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2006.01.051 * Corresponding author. Tel.: +55 19 37883214; fax: +55 19 37883213. E-mail addresses: kamal@fem.unicamp.br (K.A.R. Ismail), csalinas _99@ yahoo.com (C. Salinas S.). www.elsevier.com/locate/ijhmt International Journal of Heat and Mass Transfer 49 (2006) 2972–2983