Geometric optimization of a rectangular isothermal block inside a lid-driven cavity by means of constructal design

The present work applies the Constructal Design method to analyze the performance of a rectangular isothermal block (IB) - inside an adiabatic lid-driven cavity with an isothermal lid - submitted to mixed convection heat transfer with unstable stratification. The effect of IB configuration on heat transfer performance is investigated via numerical simulation of heat and flow dynamics. The modeling for numerical simulations involves steady, laminar, and incompressible flow in a two-dimensional domain filled with a Newtonian fluid (air). Equations of mass, momentum, and energy balance are solved using numerical simulations based on the finite volume method (FVM). The main purpose of employing the Constructal Design method is to maximize the dimensionless heat transfer rate (q⁎) between the IB and the surrounding fluid. The constraint are the cavity area and the IB/cavity area fraction (ϕ = 1/4, 1/8, 1/16, and 1/32), while the IB aspect ratio and its horizontal position are the degrees of freedom (DOF). The behavior of the system is investigated for different operational conditions given by the Richardson Number (Ri = 0.1, 1.0, and 10), for fixed Grashof (GrA = 105) and Prandtl (Pr = 0.71) numbers. Considering all possible combinations of the analyzed parameters, 162 different geometric configurations were tested (54 for each Ri). The results indicate that higher heat transfer rates are associated with the largest aspect ratio tested for each IB-cavity area fraction. For ϕ = 1/16 and Ri = 0.1 – when the IB assumes a tall shape – q⁎ is 143.2% greater than the square shape. Considering all cases, the highest q⁎ is related to the flow dominated by forced convection (Ri = 0.1) and the IB placed to the right, where the IB-cavity area fraction and the IB aspect ratio are 1/4 and 3.0, respectively.