Numerical study of heat transfer by laminar and turbulent natural convection in tall cavities of fac ¸ade elements J. Xama ´n b,2 , G. A ´ lvarez a,1 , L. Lira a,b , C. Estrada c, * a CENIDET-SNIT-SEP, Mechanical Engineering Department, Prol. Av. Palmira s/n. Col. Palmira, Cuernavaca, Morelos CP 62490, Me ´xico b CENAM, Thermophysical Properties Laboratory, Km. 4.5 carret. a los Cue `s, El Marque ´s, Quere ´taro, Me ´xico c CIE-UNAM, Centro Cultural Xochicalco s/n. Temixco, Morelos CP 62580, Me ´xico Received 28 July 2004; received in revised form 7 October 2004; accepted 1 November 2004 Abstract Laminar and turbulent natural convection flow in a two-dimensional tall rectangular cavity heated from the vertical side has been investigated numerically for aspect ratios of 20, 40 and 80. The finite volume method was used to solve the conservation equations of mass, momentum and energy for Rayleigh numbers from 10 2 to 10 8 , the flow was considered either laminar or turbulent. For turbulent flow, four different turbulence models ke were compared along with their experimental results for a cavity with an aspect ratio of 30, it was found that the better approach was with the one reported by Ince and Launder turbulent model [N. Ince, B. Launder, On the computation of buoyancy- driven turbulent flows in rectangular enclosures, Int. J. Heat Fluid Flow 10 (1989) 110–117]. The average Nusselt numbers as a function of Rayleigh numbers for the aspect ratios range of 20–80 were calculated and compared with five convective Nusselt number correlations reported from the literature. Convective Nusselt number correlations for laminar flow in the range of 10 2  Ra  10 6 and for turbulent flow in the range of 10 4  Ra  10 8 were presented. This study will help to have more accurate heat transfer parameters for applications such as fac ¸ade elements, insulating units, double-skin fac ¸ades, etc. # 2004 Elsevier B.V. All rights reserved. Keywords: Tall Cavity; Natural convection; k–e model; MFVF 1. Introduction Natural convection in cavities has been broadly studied due to many applications in engineering, such as windows with double glass, solar collectors, conservation of energy in buildings, cooling electronic devices. All of them show the importance of the processes of heat transfer. Presently, the literature review mentions that the energy consumption reduction for heating and cooling loads in buildings is an extremely important task. Thus, theoretical and experi- mental studies are financially supported in many countries of Europe for passive solar heating and cooling of buildings. Passive cooling plays an important role in providing a thermally suitable environment for human comfort by natural ventilation. The multi-functional ventilated fac ¸ades (MFVF) are applied to bioclimatic building design. The MFVFs are passive systems formed by an assembly of modules with two panes of different materials (opaque or semitransparent) separated by an air channel that is used to collect or evacuate solar radiation absorbed by the fac ¸ade. The MFVFs are useful because the heat evacuated by the channel not only reduces energy consumption, but also decreases the temperature of fac ¸ade indoors walls. Airflow in the channel can be due to natural convection or forced convection, using indoor or outdoor air. Recently, technical solutions on the MFVF are widely studied and applied to bioclimatic building design. Soria et al. [1] designed MFVF, Todorovic and Cvjetkovic [2] studied the double building envelopes and Gratia and De Herde [3] showed the optimal operation of a south double-skin fac ¸ade. There are different www.elsevier.com/locate/enbuild Energy and Buildings 37 (2005) 787–794 * Corresponding author. E-mail addresses: jxaman@cenam.mx (J. Xama ´n), gaby@cenidet.edu.mx (G. A ´ lvarez), llira@cenidet.edu.mx (L. Lira), cestrada@cie.unam.mx (C. Estrada). 1 Tel.: +777 3 12 7613; fax: +777 3 12 7613. 2 Tel.: +442 2 11 05 00; fax: +442 2 11 05 48. 0378-7788/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2004.11.001