Computational Analysis of Natural Convection in Inclined Rectangular Enclosures of Different Aspect Ratios

Abstract

Numerical investigations are conducted for free convective flow of a fluid with or without internal heat generation in rectangular enclosures of different aspect ratios and at various angles of inclination. Two principal parameters for this problem are the external Rayleigh number, RaE, which represents the effect due to the differential heating of the sidewalls and the internal Rayleigh number, RaI, which represents the strength of the internal heat generation. Results are obtained for a fixed external Rayleigh number, RaE = 2×105 with internal Rayleigh number, RaI = 0 (without internal heat generation) and also with RaI = 2×105 (with internal heat generation). Flow patterns and isotherms do not show any significant difference between the cases with and without internal heat generation other than slight shift and changes in stream function and isotherm values as long as the internal Rayleigh number RaI is less than or equal to the external Rayleigh number RaE. Local heat flux ratios along the hot and the cold wall decrease monotonically in the flow direction for a major downstream portion. At certain inclinations the local heat flux ratios increase initially and then decrease. The variation of average heat flux ratio is similar for cases with and without internal heat source situation but the corresponding amount of heat transfer is higher through the hot wall and lower through the cold wall with internal heat generation. On the other hand, the convection strength increases as the enclosure shape changes from slender through square to shallow at any particular inclination but does not vary significantly with inclination at a particular aspect ratio.