An extension to the problem of natural convection of a newtonian fluid in a rectangular cavity

The convection in a cavity filled with a newtonian fluid and heated from below has been extended to consider the thermal properties of the walls. The theoretical hyrodynamics of a confined fluid in a cavity has been studied for thermal insulating (TI) or perfect thermal conducting (PTC) walls. Thus, the known 2D problem of the Rayleigh convection has been reworked with thermal boundary conditions incluidng the Biot number (Bi). Previous theoretical results for situations with TI walls, with PTC walls or even combinations of those type of walls were bridged so that a more detailed picture of the hydrodynamics could be obtained. The study was constrained to the onset of convection in steady conditions so that only the Rayleigh number (Ra) was computed. Results shall be presented as plots of the Ra against aspect ratio of the cavity for fixed values of the Bi. Since the TI and PTC extreme cases were bridged by using small Bi steps results were taken as valid. However, the plots of the Ra against the aspect ratio are quite similar to those previously reported with differences in the magnitudes of the Ra which smoothly changes between the two extreme cases. Further discussion on the the heat transport physical mechanism and changes in the number of rolls shall be given.