Heatline based thermal management for natural convection in porous rhombic enclosures with isothermal hot side or bottom wall

An accurate prediction of the flow structure and heat distribution in rhombic configurations are of greater importance due to its significant engineering i.e. cooling of electronics devices as well as natural applications i.e. geothermal extraction. Heatline method is used to analyze natural convection in porous rhombic enclosures with various inclination angles, φ for differential (case 1) and Rayleigh–Benard heating situations (case 2). Increase in φ(φ = 90°) results in pure conduction dominant heat transfer with stagnant fluid condition for φ = 90° at Da = 10−5 and a slight perturbation of φ at higher Da (Da ⩾ 4 × 10−5) leads to convection based dynamic solution for φ = 90° in case 2 irrespective of Pr. At Da = 10−3, strength of fluid and heat flow increase with φ due to enhanced convection effect and φ = 90° shows maximum magnitude of streamfunction (ψmax) and heatfunction (Πmax) values in both cases except convection based solution at φ = 90° for Pr = 7.2. Both cases are compared based on local (Nu) and average Nusselt numbers ( Nu ¯ ) and those are adequately explained based on heatlines. Also, Nu ¯ increases with Da in both cases except convection based solution at φ = 90° for Pr = 7.2. Overall, Nu ¯ is higher for case 2 at φ ⩽ 45° whereas case 1 shows larger Nu ¯ for φ ⩾ 45° irrespective of Pr at Da = 10−3. Hence, φ = 45° is the critical rhombic angle which demarcates the heating strategies of case 1 and case 2 to achieve higher heat transfer rates ( Nu ¯ ) in various applications.