Analysis of the Design of Cavities with Isothermal Blocks under Mixed Convection

Using the constructal design method (CDM), this study aimed to evaluate how the convective heat transfer in a lid‑driven cavity, with an isothermal block (IB) inside, is affected by the cavity aspect ratio (AR). In addition to the impact of AR on the convection process, the effects of the size block – represented by Φ – and its dimensionless horizontal position (x0*) inside the cavity were also explored. Sixty-two designs were evaluated under different Richardson numbers (Ri) representing forced, mixed, and natural convection mechanisms, resulting in 186 cases. The convective flow inside the cavity was considered Newtonian, two-dimensional, laminar, incompressible, and steady‑state. The mathematical model consisted of the conservation equations of mass, momentum (in x and y directions), and energy. The differential equations that comprise the mathematical model were solved computationally through numerical simulations using the finite volume method. Based on the results obtained, it was observed that to increase the convective heat transfer inside the cavity, the most recommended option is to use lower AR values corresponding to a horizontally elongated cavity shape. Among all the different designs tested for the system, the one that proved to be the most suitable for promoting the convective heat transfer, measured by the dimensionless heat transfer rate (q*) on the IB walls, was defined by AR = 0.35 and Φ = ¼. It was through this design, with the IB horizontally positioned in its center (x0* = 0.5), that the highest value of q* (31.08) was obtained in the dominant forced convection scenario (Ri = 0.1).