Visualization of heat transport due to natural convection for hot materials confined within two entrapped porous triangular cavities via heatline concept

Abstract

This paper analyzes the detailed heat transfer within two entrapped porous triangular cavities involving cold inclined walls and hot horizontal walls. A penalty finite element analysis with bi-quadratic elements is performed to investigate the results in terms of isotherms, streamlines and heatlines and local and average Nusselt numbers. The parameters for this study are Darcy number, Da ( 10 - 5 – 10 - 3 ) , Prandtl number, Pr ( 0.015 – 1000 ) and Rayleigh number ( 10 3 – 5 × 10 5 ) . It has been found that at small Darcy number ( Da = 10 - 5 ) , heat transfer is primarily conduction dominant and heatlines are found to be orthogonal to the isotherms. The presence of multiple circulations in streamlines and heatlines are observed within the lower triangle at small Prandtl number Pr = 0.015 with high Darcy number ( Da = 10 - 3 ) whereas only single pair of circulations are observed for higher Prandtl numbers. The convective cells in heatlines gradually become enhanced as Pr increases from 0.015 to 1000. In contrast, variation of Prandtl number gives negligible change in heating pattern within the upper triangle and intensity of streamlines and heatlines are less irrespective of Prandtl number. Heat transfer rates are estimated in terms of local ( Nu l , Nu h ) and average Nusselt numbers ( Nu l ¯ , Nu h ¯ ) . Heat transfer rates are also explained based on heatlines. Local Nusselt numbers with spatial distribution exhibit monotonic trend irrespective of Da and Pr for the upper triangle whereas wavy distribution of local Nusselt number occur for the lower triangle. For Da = 10 - 3 , average Nusselt numbers ( Nu h ¯ and Nu l ¯ ) increase exponentially with Ra at higher Rayleigh numbers. But, overall lower heat transfer rates are observed for the upper triangle. Finally, it is concluded that lower triangle has always has higher heat recovery capacity compared to upper triangle. To achieve efficient heat transfer, fluids with high Prandtl numbers are recommended for the lower triangle whereas any fluid with any Prandtl number may be acceptable for the upper triangle.