Constructal design of a semi-elliptical fin inserted in a lid-driven square cavity with mixed convection

The present study is focused on the geometric optimization, according to Constructal Design, of a semielliptical morphing fin, i.e. a fin that can vary its dimensions, inserted into a lid-driven square cavity under mixed convection. The fluid flow is considered incompressible, two-dimensional, laminar and at the steady state. Conservation equations of mass, momentum and energy are solved numerically by means of the Finite Volume Method. Moreover, buoyancy forces are modeled with Boussinesq approximation. The main purpose here is to maximize the dimensionless heat transfer rate between the heated fin and the surrounding flow for different Reynolds (ReH = 10, 10^2 and 10^3) and Rayleigh (RaH = 10^3, 10^4, 10^5 and 10^6) numbers keeping constant the Prandtl number (Pr = 0.71). The studied domain has two constraints (areas of fin and cavity) and one degree of freedom given by the aspect ratio between the height and length of the fin (H1/L1), which is evaluated in three different surfaces of the cavity and four different area fractions of the fin. Results showed that the optimal configurations presented a gain in the thermal performance on the order of 40% in relation to other geometries. Finally, it is worth to mention that the optimal shapes here discovered are highly influenced by Reynolds and Rayleigh numbers

Fluid flow and heat transfer maximization of elliptic cross- section tubes exposed to forced convection: A numerical approach motivated by Bejan's theory

This work investigates, through Constructal Design, the impact of the spacing between two cylindrical bodies with elliptic cross-section in the maximization of the heat transfer density under external forced convection flow. The horizontal-to-vertical axis ratio of the cross-section is also analyzed. The model is assumed two-dimensional, steady, incompressible, and laminar. The flow arises due to a pressure difference, which is expressed in terms of Bejan number. In addition, for all cases, thermophysical properties are defined by constant Prandtl number (Pr=0.72). The conservation equations of momentum, energy, and mass are solved numerically by means of the Finite Volume Method. Results show that the optimal configurations perform considerably better, increasing the heat transfer density between 50% and 97% when compared to the lower level cases investigated. Additionally, it has been demonstrated that the system tends to adapt its optimal architecture to every flow studied and provides a favorable flow configuration that achieves the objective function, i.e. maximizes the heat transfer in a reduced physical domain: this is fully consistent with the principles of Constructal Law