Heat flow visualization analysis on natural convection in rhombic enclosures with isothermal hot side or bottom wall

The heat flow visualization method based on heatfunction has been adopted to analyze natural convection via differential heating (case 1) and Rayleigh-Benard convection (case 2) in fluid filled (Prandtl number, Pr=0.015-1000) rhombic enclosures with various inclination angles, φ, using the Galerkin finite element method for the range of Rayleigh number, Ra=103-105. An accurate prediction of the flow structure and heat distribution in such configurations is of great importance due to various engineering applications such as solar energy systems, cooling of electronic devices, combustion, etc. The strength of fluid and heat flow increases with φ and Ra due to an enhanced convection effect and the maximum magnitude of streamfunction (ψmax) and heatfunction (Πmax) is observed at φ=90° in both cases. Conduction based static fluid solutions are also found at φ=90° associated with convection based dynamic fluid solutions in case 2 for all Pr. Heating strategies are compared via heatlines and also based on local (Nu) and average Nusselt numbers (Nu¯). It is also shown that φ=30° shows higher Nu¯ in case 2 compared to case 1, whereas φ=90° shows higher Nu¯ in case 1 compared to case 2 for all Pr. There exists a critical rhombic angle (φ=50°) such that differential heating may be the profound heating situation at φ≥50° for materials involving Pr=1000. Also, the rhombic cavity may be an alternative geometrical design in convective thermal processing of fluids with vertical thermal gradient (case 2) as it establishes only convection based dynamic solutions for all possible angles (φ<90°).