Luiz Alberto Oliveira Rocha

Constructal Design of Complex Assembly of Fins

Constructal design is a method that conducts the designer toward flow (e.g., heat flux) architectures that have greater global performance. This numerical work uses this method to seek for the best geometry of a complex assembly of fins, i.e., an assembly where there is a cavity between the two branches of the T-Y-assembly of fins and two additional extended surfaces. The global thermal resistance of the assembly is minimized four times by geometric optimization subject to the following constraints: the total volume, the volume of fin material, the volume of the cavity, and the volume of the two additional extended surfaces. Larger amount of fin material improves the performance of the assembly of fins. The three times optimized global thermal resistance of the complex assembly of fins performs 32% better than the best T-Y-configuration under the same thermal and geometric conditions. The three times minimized global thermal resistance of the complex assembly of fins was correlated by power laws as a function of its corresponding optimal configurations.

Constructal Design of Convective Y-Shaped Cavities by Means of Genetic Algorithm

In the present work constructal design is employed to optimize the geometry of a convective, Y-shaped cavity that intrudes into a solid conducting wall. The main purpose is to investigate the influence of the dimensionless heat transfer parameter a over the optimal geometries of the cavity, i.e., the ones that minimize the maximum excess of temperature (or reduce the thermal resistance of the solid domain). The search for the best geometry has been performed with the help of a genetic algorithm (GA). For square solids (H/L = 1.0) the results obtained with an exhaustive search (which is based on solution of all possible geometries) were adopted to validate the GA method, while for H/L ≠ 1.0 GA is used to find the best geometry for all degrees of freedom investigated here: H/L, t1/t0, L1/L0, and α (four times optimized). The results demonstrate that there is no universal optimal shape that minimizes the thermal field for all values of a investigated. Moreover, the temperature distribution along the solid domain becomes more homogeneous with an increase of a, until a limit where the configuration of “optimal distribution of imperfections” is achieved and the shape tends to remain fixed. Finally, it has been highlighted that the GA method proved to be very effective in the search for the best shapes with the number of required simulations much lower (8 times for the most difficult situation) than that necessary for exhaustive search.

Constructal Law and the Unifying Principle of Design

Preface: Constructal law, design in nature, and complexity Chapter 1. The Constructal Design of Humanity on the Globe, A. Bejan and S. Lorente Chapter 2. Towards a Quantitative Unifying Theory of Natural Design of Flow Systems: Emergence and Evolution, A. F. Miguel Chapter 3. Leaf Shapes and Venation Patterns, A. H. Reis Chapter 4. Drainage Basins Evolution with Non-Erodible Regions, M. R. Errera and C. A. Marin Chapter 5. Software Evolution and the Constructal Law, S. Perin Chapter 6. Constructal Design of High Conductivity Inserts, J. A. Souza and J. C. Ordonez Chapter 7. Constructal Design of T-shaped Water Distribution Networks, P. Bieupoude, Y. Azoumach and P. Neveu Chapter 8. The Constructal Theory of Electrokinetic Transport through a Porous System, S. Lorente Chapter 9. Constructal Theory Applied to Vascular Countercurrent Networks, Weizhong Dai Chapter 10. Constructal Design of Animate and Inanimate Systems: an Answer to Consumerism? J. V. C. Vargas Chapter 11. Constructal Design of Rectangular conjugate Cooling Channels, T. Bello- Ochende, O. T. Olakoyejo, and J. P. Meyer Chapter 12. The Flow of Stresses: Constructal Design of Perforated Plates Subjected to Tension or Buckling, L. A. Isoldi, M. V. Real, A. L. G. Correia, J. Vaz, E. D. dos Santos and L. A. O. Rocha Chapter 13. Equipartition of Joulean Heat in Thermoelectric Generators, A. K. Pramanick Chapter 14. Constructal Design of Refrigeration Devices, H. Zhang, X. Liu, R. Xiong and S. Zhu Chapter 15. Constructal Design of Vortex Tubes, E. D. dos Santos, C. H. Marques, G. Stanescu, L. A. Isoldi and L. A. O. Rocha Chapter 16. Constructal Design of Wave Energy Converters, E. D. dos Santos, B. N. Machado, N. Lopes, J. A. Souza, P. R. F. Teixeira, M. N. Gomes, L. A. Isoldi and L. A. O. Rocha Chapter 17. Constructal Design of Thermal Systems, L. A. O. Rocha, E. D. dos Santos, D. C. Cunha, F. L. Garcia, G. Lorenzini, C. Biserni, M. Letzow, J. A. V. Costa, J. A. Souza and L. A. Isoldi Index

Geometric Optimization of Periodic Flow and Heat Transfer in a Volume Cooled by Parallel Tubes

tween an entire heat-generating volume and a pulsating stream of coolant that bathes the volume. The coolant flows through an array of round and equidistant tubes. Two laminar flow configurations are considered: stop-and-go flow, where the reservoir of coolant is on one side of the volume, and back-and-forth flow, where the volume is sandwiched between two reservoirs of coolant. The total heat transfer rate between the volume and the coolant is determined numerically for many geometric configurations in the pressure drop number range 10 2 1. The optimal tube radius and the maximum volumetric heat transfer rate are determined numerically. The numerical optimization results are later predicted based on scale analysis by matching the longitudinal and transversal time scales of the temperature field in each tube, for each pulsation stroke. The predicted scales lead to power-law formulas that correlate the results and summarize the optimal geometry. The optimal tube size is nearly the same in stop-and-go flow and back-andforth flow, and is independent of the pulsation frequency. @DOI: 10.1115/1.1337654#

Numerical Study of the Effect of the Relative Depth on the Overtopping Wave Energy Converters According to Constructal Design

The conversion of wave energy in electrical one has been increasingly studied. One example of wave energy converter (WEC) is the overtopping device. Its main operational principle consists of a ramp which guides the incoming waves into a reservoir raised slightly above the sea level. The accumulated water in the reservoir flows through a low head turbine generating electricity. In this sense, it is performed a numerical study concerned with the geometric optimization of an overtopping WEC for various relative depths: d/λ = 0.3, 0.5 and 0.62, by means of Constructal Design. The main purpose is to evaluate the effect of the relative depth on the design of the ramp geometry (ratio between the ramp height and its length: H1/L1) as well as, investigate the shape which leads to the highest amount of water that insides the reservoir. In the present simulations, the conservation equations of mass, momentum and one equation for the transport of volumetric fraction are solved with the finite volume method (FVM). To tackle with water-air mixture, the multiphase model Volume of Fluid (VOF) is used. Results showed that the optimal shape, (H1/L1)o, has a strong dependence of the relative depth, i.e., there is no universal shape that leads to the best performance of an overtopping device for several wave conditions.

Convective analysis of constructal T-shaped fins

In this work the optimization of T-shaped fins is considered. The potentiality of the Constructal theory applied to heat transfer process in obtaining optimal T-shaped profiles is demonstrated. The range of validity of unidirectional conduction model used through the optimization performed relies on the Biot number criterion, which in some cases appears to be an approximation too weak especially when higher heat transfer coefficients due to the characteristics of the flux and of external surface are involved. After a general overview about elemental profiles and how their geometry has developed in recent years, an original method for obtaining a reasonable assess of the heat transfer coefficient is presented. The aim of the authors is to give a new perspective in optimization process that must guide to optimal results taking into account the real contribution of the whole set of factors and variables involved, with special regards to the contribution of the convective heat transfer.

Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces

The purpose here is to investigate, by means of the constructal principle, the influence of the convective heat transfer flux at the cavity surfaces over the optimal geometry of a T-shaped cavity that intrudes into a solid conducting wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The convective heat flux is imposed as a boundary condition of the cavity surfaces and the geometric optimization is achieved for several values of parameter a = (2hA1/2/k)1/2. The structure of the T-shaped cavity has four degrees of freedom: L0/L1 (ratio between the lengths of the stem and bifurcated branches), H1/L1 (ratio between the thickness and length of the bifurcated branches), H0/L0 (ratio between the thickness and length of the stem), and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (φ). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for fixed values of H/L = 1.0 and φ = 0.1. Even for the first and second levels of optimization, (L1/L0)○○ and (H0/L0)○, the results revealed that there is no universal shape that optimizes the cavity geometry for every imposed value of a. The T-shaped cavity geometry adapts to the variation of the convective heat flux imposed at the cavity surfaces, i.e., the system flows and morphs with the imposed conditions so that its currents flow more and more easily. The three times optimal shape for lower ratios of a is achieved when the cavity has a higher penetration into the solid domain and for a thinner stem. As the magnitude of a increases, the bifurcated branch displaces toward the center of the solid domain and the number of highest temperature points also increases, i.e., the distribution of temperature field is improved according to the constructal principle of optimal distribution of imperfections.

Distributed energy tapestry for heating the landscape

Here we show that the production and use of heating on an area must be distributed in clusters organized such that the losses associated with centers of production are balanced by the losses associated with distribution lines. The energy needs increase in time because the population density and the individual need increase. We consider only the increase in the individual need in time. We illustrate the “distributed energy systems” concept with the production and distribution of hot water on an area. Four classes of designs are analyzed and compared: (0) individual, i.e., one water heater for one user, (r) radial, i.e., N users supplied via radial pipes from a central heater, (2) dendritic network constructed by pairing N users around a central heating, and (4) dendritic network constructed by quadrupling the elemental areas occupied by the users. We show that there is an optimal cluster size (N) as a tradeoff between central losses and distributed losses. We also discover that several distinct (abrupt) de...

Vascular design for reducing hot spots and stresses

This paper is a proposal to embed tree-shaped vasculatures in a wall designed such that the wall withstands without excessive hot spots and peak stresses the intense heating and pressure that impinge on it. The vasculature is a quilt of square-shaped panels, each panel having a tree vasculature that connects the center with the perimeter. The vascular designs for volumetric cooling can be complemented by the shaping and distributing of channels for maximum strength and thermal performance at the same time. Numerical simulations of heat flow and thermal stresses in three directions show that it is possible to determine the optimal geometric features of configurations with radial channels and trees with radial and one level of bifurcations. The global performance is evaluated in terms of the overall thermal resistance and peak von Mises stresses. The dendritic design is superior under the studied thermal condition.

Constructal Design of Y-Shaped Conductive Pathways for Cooling a Heat-Generating Body

This paper applies constructal design to obtain numerically the configuration that facilitates the access of the heat that flows through Y-shaped pathways of a high-conductivity material embedded within a square-shaped heat-generating medium of low-conductivity to cooling this finite-size volume. The objective is to minimize the maximal excess of temperature of the whole system, i.e., the hot spots, independent of where they are located. The total volume and the volume of the material of high thermal conductivity are fixed. Results show that there is no universal optimal geometry for the Y-shaped pathways for every value of high conductivity investigated here. For small values of high thermal conductivity material the best shape presented a well defined format of Y. However, for larger values of high thermal conductivity the best geometry tends to a V-shaped (i.e., the length of stem is suppressed and the bifurcated branches penetrates deeply the heat-generating body towards the superior corners). A comparison between the Y-shaped pathway configuration with a simpler I-shaped blade and with X-shaped configuration was also performed. For constant values of area fraction occupied with a high-conductivity material and the ratio between the high thermal conductivity material and low conductivity of the heat-generating body (φ = 0.1 and = 100) the Y-shaped pathways performed 46% and 13% better when compared to I-shaped and X-shaped pathway configuration, respectively. The best thermal performance is obtained when the highest temperatures (hot spots) are better distributed in the temperature field, i.e., according to the constructal principle of optimal distribution of imperfections.