Analysis of natural convection of water via heatline approach in various enclosures involving unit area and identical heat input

In today's world, sustainable development is the need of the hour and proper emphasis should be given to heat transport, thermal mixing and thermal management in the various process. Natural convection studies in various square and non-square enclosures have gained significant attention in the recent past. Therefore, a comparative study based on the heat flow within the different type of square and non-square enclosures is required in order to achieve efficient thermal management. The present study deals with the heat transfer performance of six different enclosures of the same area: square, parallelogrammic, concave, triangular, trapezoidal type 1 and trapezoidal type 2 enclosures with an isothermally (case 1) or non-isothermally (case 2) heated bottom wall in the presence of isothermally cooled side walls and the top wall. A detailed numerical analysis is performed for water (Pr = 7) and Rayleigh numbers (Ra) ranging from 103 to 105. The nonlinear coupled partial differential equation of flow and temperature fields are solved via the Galerkin finite method with penalty parameter. The fluid flow and temperature distributions are visualized via streamlines and isotherms, respectively. The convective heat flow and thermal mixing are efficiently analyzed via the heatlines (mathematically represented as heatfunctions). Heat transfer rates are represented in terms of average Nusselt numbers. Overall thermal mixing is higher in the curved and trapezoidal type 2 enclosure. Highest heat transfer rate is observed in the triangular enclosure.