L. A. O. Rocha

Geometric Optimization of C-Shaped Cavities According to Bejan's Theory: General Review and Comparative Study

The aim of this paper is to consider, by means of the numerical investigation, the geometric optimization of a cavity that intrudes into a solid with internal heat generation. The objective is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The cavity is rectangular, with fixed volume and variable aspect ratio. The cavity shape is optimized for two sets of boundary conditions: isothermal cavity and cavity cooled by convection heat transfer. The optimal cavity is the one that penetrates almost completely the conducting wall and proved to be practically independent of the boundary thermal conditions, for the external ratio of the solid wall smaller than 2. As for the convective cavity, it is worthy to know that for values of H/L greater than 2, the best shape is no longer the one that penetrates completely into the solid wall, but the one that presents the largest cavity aspect ratio H0/L0. Finally, when compared with the optimal cavity ratio calculated for the isothermal C-shaped square cavity, the cavities cooled by convection highlight almost the same optimal shape for values of the dimensionless group λ ≤ 0.01. Both cavities, isothermal and cooled by convection, also present similar optimal shapes for ϕ0 0.7. However, in the range 0.3 ≤ ϕ0 ≤ 0.7, the ratio (H0/L0)opt calculated for the cavities cooled by convection is greater than the one presented by isothermal cavities. This difference is approximately 17% when λ = 0.1 and ϕ0 = 0.7, and 20% for λ = 1 and ϕ0 = 0.5.

Constructal Design Applied to a Channel with Triangular Fins Submitted to Forced Convection

The purpose of this work is to present a numerical study of a two-dimensional channel with two triangular fins submitted to a laminar flow with forced convection heat transfer, evaluating the geometry of the first fin through the Constructal Design method. The main objectives are to maximize the heat transfer rate and minimize the pressure difference between the inlet and outlet flow of the channel for different dimensions of the first channel fin, considering the same Reynolds (ReH = 100) and Prandtl numbers (Pr = 0.71). The problem is subjected to three constraints given by the channel area, fin area and maximum occupancy area of each fin. The system has three degrees of freedom. The first is given by the ratio between height and length of the channel, which is kept fixed, H/L = 0.0625. The other two are the ratio between height and width of the upstream fin base (H3/L3) positioned on the lower surface of the channel, and the ratio between height and width of the downstream fin (H4/L4) positioned on the upper surface of the channel, which is also kept fixed, H4/L4 = 1.11. The problem is simulated for three different values of the fraction area of upstream fin (φ1 = 0.1, 0.2 and 0.3). For the numerical approach of the problem, the conservation equations of mass, momentum and energy are solved using the finite volume method (MVF). The results showed that a ratio of φ1 = 0.2 is the one that best meets the proposed multi-objective. It was also observed that φ1 = 0.1 led to a better fluid dynamics performance with a ratio between the best and the worst performance for fluid dynamics case of 25.2 times. For φ1 = 0.3, the best thermal performance is achieved, where the optimal case has a performance 65.75% higher than that reached for the worst case.

The Assembly of the Fins and the Shape of the Body

This chapter intends to address these questions, studying different shapes of bodies and simultaneously optimizing both the assembly of fins and the body.

Tree-Shaped Cavities

This chapter illustrates how to discover the shape of open cavities that intrude into a solid conducting wall. The cavity can also be seen as a “negative fin” or “inverted fin,” because its shape would be generated if a fin were to be inserted into the body and its volume removed from the solid body. Open cavities can also be understood as the region between adjacent fins.

Tree-Shaped Flow Networks Fundamentals

The size of the offspring vessels and airways in circulatory and respiratory trees can be predicted by theory. We first review the relationship connecting a parent tube to daughter tubes based on the application of optimization principles, such as minimizing energy expenditure, minimizing the total flow resistance.

Constructal Design of the Assembly of Fins

Performance is the measure of how the system achieves its aims. This chapter and the next apply the constructal law (see Chap. 2) to the design of high-performance man-made systems. The so-called constructal design is a method that guides the designer toward flow configurations (architectures) that provide maximum global performance. On the other side, among the engineering problems, the field of heat transfer has demonstrated for many years how the principle of generating flow geometry works. The oldest and clearest illustrations are the optimization of solid wall features known as extended surfaces or fins (Chen 2012).

Tree-Shaped Flow Networks in Nature and Engineered Systems

Our world is made up of things that have shapes. The apparently endless diversity of shapes can be ranked and compared. Similar patterns and forms in natural systems abound, from the honeycomb configuration in living tissue and cell aggregates to the tree-shape configuration in lightning, neurons, plant roots and branches, blood distribution systems, and river basins. Tree architecture is ubiquitous, both in small- and large-scale systems, in systems that have nothing in common apart from the purpose of allowing something to flow.

Tree-Shaped High Thermal Conductivity Pathways

Constructal design has also been applied successfully to the cooling of electronics through conductive heat transfer on different thermal tree constructs (Ledesma et al. in J Appl Phys 82(1):89–100, 1997; Almogbel and Bejan in Int J Heat Mass Transf 42:3739–3756, 1999; Alebrahim and Bejan in Int J Heat Mass Transf 42:3585–3597, 1999; Almogbel and Bejan in Int J Heat Mass Transf 43:4285–4297, 2000; Rocha et al. in Int J Heat Mass Transf 45(8):1643–1652, 2002; Ghodoossi and Egrican in Energy Convers Manage 45:811–828, 2004; da Silva et al. in Int J Heat Mass Transf 47:4257–4263, 2004; Rocha et al. in Int J Heat Mass Transf 49:2626–2635, 2006; Kuddusi and Denton in Energy Convers Manage 48:1089–1105, 2007).

Transport and Deposition of Particles in Airway Trees

Atmospheric exposure to ambient particulate matter may affect pulmonary function, resulting in adverse health effects. Aerosol particles are also widely used in treatment of obstructive airway diseases, such as asthma. This chapter is completely devoted to particle transport through airways. It covers the physical characteristics of particles, the deposition mechanisms, and physiological factors (breathing patterns) with relevance to particle deposition in the respiratory tree.

On the Design of Two EAHE Assemblies with Four Ducts

This article applies the constructal design method to analyze how to improve the thermal performance of earth-air heat exchangers (EAHE) composed by four ducts. The paper evaluates two types of arrangements for which the centers of the ducts take the shape of rectangles and diamonds. Under volumetric constraints, the vertical Sv and horizontal Sh spacings between the ducts are left free to vary. The objective is to maximize the magnitude of the EAHE instantaneous thermal potential P which is an average of the differences between the temperatures at the ducts outlets and inlets at any instant of time. The temperature fields are computed through numerical simulations, adopting a verified and validated three-dimensional model. Among the results, this work shows how the design can raise by 11% the annual thermal efficiency of the EAHE.