R. Damle, J. Cadafalch, R. Consul, and A. Oliva

Centre TecnOlogic de Transferencia de Calor (CTTC)
Lab. de Termotecnia i Energetica
Universitat Politecnica de Catalunya (UPC)
labtie@labtie. mmt. upc. es, www. cttc. upc. edu

Finite volume numerical computations have been carried out in order to study the free convective heat transfer in differentially heated inclined air cavities. The air cavity inclination was varied from 0 =0 degrees ( heated from below) to 0 =90 degrees(heated from side) for aspect ratios of 10 to 300. Both two-dimensional and three-dimensional solutions have been obtained and compared with the literature.

Introduction

Natural convection in inclined differentially heated cavities is a subject of major interest and has been widely studied by many authors. Comprehensive review of both experimental and theoretical studies have been given by Ayyaswamy[6], and Hart[7]. Experiments on inclined cavities have been reported by Inaba [3]. Catton, Ayyaswamy and Clever[8] used a Galerkin method to investigate natural convection in inclined rectangular region, and there results show a pronounced aspect ratio dependency on the Nusselt number. The experimental cor­relation for natural convection in rectangular cavities by Hollands[1] gives Nusselt number for large aspect ratios for angles of inclination between 30 and 60 degrees.

Long inclined differentially heated cavities are frequently encountered in solar applications. Often these rectangular cavities have high aspect ratio with the length varying from 0.5m to 3m, finite depth varying from 0.5m to 2m or even larger and thicknesses from 10mm to 50 mm. The temperatures could range from ambient to about 300°C in such applications. More­over they are oriented at different angles of inclination to the horizontal. The heat transfer by natural convection then depends on parameters like the aspect ratio, inclination, temper­ature differences etc. A correlation of Nusselt number for all situations mentioned above for such rectangular cavities is not available currently and would be desirable.

The authors are carrying out numerical studies in order to develop a general correlation for convective heat transfer which would be applicable to most of the situations encountered in solar applications. For obtaining such a correlation, finite volume technique is being em­ployed to model the heat transfer and fluid flow in differentially heated inclined rectangular cavities. Different meshes, numerical schemes and convergence criteria are being worked out to find most appropriate numerical model, the solution to which would lead to a Nusselt number correlation over a wider range. The work presented here is a part of the numerical studies that have been conducted and the models that have been worked out. The solutions undergo a verification process with the post processing tool based on the Richardson ex­trapolation theory and on the grid convergence index (GCI) that estimates their uncertainty due to discretization[4][5].