Buoyancy driven flow within an inclined elliptic enclosure

Buoyancy driven flow and associated heat convection in an elliptical enclosure has been investigated. The enclosure which is the space between two horizontal concentric confocal elliptic tubes is heated through its inner tube surface which is maintained at either uniform temperature or uniform heat flux. The induced buoyancy driven flow and the associated heat convection are predicted at different enclosure orientations. The full governing equations in terms of vorticity, stream function and temperature are solved numerically using Fourier Spectral Method. Beside Rayleigh and Prandtl numbers the heat convection process in the enclosure depends on the geometry of the enclosure and the angle of inclination with respect to gravity vector. The geometry of the enclosure is represented in terms of major axes ratio and axis ratio of inner tube. The study considered a moderate range of Rayleigh numbers between 5 × 103 and 1 × 105 while Prandtl number is fixed at 0.7. The inner tube axis ratio is considered between 0 and 1 while the ratio between the two major axes is considered up to 3. The angle of inclination of the minor axes with respect to gravity vector is varied from 0 to 90°. The results for local and average Nusselt numbers as well as temperature distribution are obtained and discussed together with the details of both flow and thermal fields. For isothermal heating conditions, the study has shown an optimum value for major axes ratio that minimizes the rate of heat transfer in the enclosure. While in case of heating at uniform heat flux the study revealed existence of major axes ratio at which the mean temperature of the inner wall is maximum. Another aspect of this paper is the prediction of global flow circulation around the inner tube in case of asymmetrical orientation of the enclosure with respect to the gravity vector.