Heatline Analysis for Natural Convection within Porous Rhombic Cavities with Isothermal/Nonisothermal Hot Bottom Wall

Analysis has been carried out for energy distribution and thermal mixing in steady laminar natural convective flow through the porous rhombic cavities with inclination angle ? for various applications such as geothermal, grain storage, electronic cooling, etc. A generalized non-Darcy model without the Forchheimer inertia term is used to predict the flow in porous media. The effect of the Darcy number (Da) and the role of ? on the energy distribution and thermal mixing within porous rhombic cavities with isothermal (case 1) and nonisothermal (case 2) hot bottom walls are illustrated via " heatlines". Heat transfer is found to be primarily conduction dominant at Da = 10 -5 even at a higher Rayleigh number (Ra = 10 6). The onset of convection occurs at Da = 10 -4, and the distorted heatlines from the hot bottom wall take a longer path to reach the cold side walls of the cavity. Larger heat transfer and thermal mixing occurs for Da = 10 -3 at Ra = 10 6 irrespective of ? and Pr. Multiple flow/convective circulations are observed at Pr = 0.015 for all ? values at Da = 10 -3. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity at Pr = 0.7, 7.2, and 1000 for ? = 75� at Da = 10 -3. The cavity with inclination angle ? = 30� enhances the convective heat transfer from the hot wall to the cold wall, and the heat transfer to the right cold wall is a maximum for ? = 75�, as depicted by "heatlines" irrespective of Pr at Da = 10 -3. Average Nusselt number studies based on heatfunction gradients also show that the cavity with ? = 30� gives a maximum heat-transfer rate from the bottom to the left wall irrespective of Pr in case 1 at Da = 10 -3. The cup mixing temperature (? cup) is higher for case 1 compared to case 2, and it is almost invariant with ? for higher Pr (Pr = 7.2 and 1000) in case 1 at Da = 10 -3. � 2011 American Chemical Society.