Desing construtal aplicado à convecção de calor em cavidades com obstáculos

Abstract

From the perspective of the constructal design, this work investigated the convection process in a lid-driven cavity with an isothermal block (BI) inside, with the aim of maximizing the dimensionless heat transfer rate (𝑞∗) on the walls of the block. Keeping the BI vertically centred (𝑦0∗ = 0,5) in the cavity, the degrees of freedom (GL) considered for the system were the cavity and BI aspect ratios (𝐴𝑅 and 𝐴𝑅0, respectively), combined with the dimensionless horizontal position of the BI inside the cavity (𝑥0∗ ). In addition to these parameters, the size of the isothermal block – symbolized by  – was also considered a key parameter of the system. For this purpose, four different sizes were considered to the BI ( = 1/4, 1/8, 1/16 and 1/32), making it possible to analyze their effects on the flow and convective heat transfer inside the system. By varying these parameters, a total of 280 different designs were generated and tested for the system, which were evaluated in the dominant forced, mixed, and natural convection scenarios, resulting in 840 analyzed 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. All the equations were solved computationally through numerical simulations carried out in ANSYS FLUENT 2023 R1, which uses the finite volume method (MVF). Among the 280 different designs created and tested for the system, the one that proved to be the most effective in promoting 𝑞∗ was characterized by 𝐴𝑅 = 0.35 (horizontal cavity) and 𝐴0 = 1 (square). Through this design, giving to the BI its largest size ( = 1/4), the maximum value of 𝑞∗ (31,19) was achieved with the BI subtly shifted to the right (𝑥0 ∗ = 0,6) in the forced convection scenario. In general, this system configuration stood out in promoting 𝑞∗ due to having a larger lid, which moves a greater amount of fluid, thus increasing the momentum of the flow. In addition, the horizontal shape of the cavity narrows its upper gap, bringing the top wall of the BI closer to the sliding lid and thus reducing the thickness of the thermal boundary layer that forms there, which benefits heat transfer.