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 φ 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 φ 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 φ and Pr . Multiple flow/convective circulations are observed at Pr = 0.015 for all φ 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 φ = 75° at Da = 10 –3 . The cavity with inclination angle φ = 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 φ = 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 φ = 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 (Θ cup ) is higher for case 1 compared to case 2, and it is almost invariant with φ for higher Pr ( Pr = 7.2 and 1000) in case 1 at Da = 10 –3 .