Constructal design applied to the optimization of complex geometries: T-Y-shaped cavities with two additional lateral intrusions cooled by convection

Lorenzini, Giulio; Garcia, Ferran; Santos, Elizaldo Domingues dos; Biserni, Cesare; Rocha, Luíz Alberto Oliveira

doi:10.1016/j.ijheatmasstransfer.2011.10.057

Cited by 40 publications

(19 citation statements)

References 14 publications

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“…Lorenzini and Rocha documented the T-and Y-shaped cavity geometries optimized according to the constructal law [24]. Later, Lorenzini et al documented the optimized complex geometries of T-Y-shaped cavities with lateral intrusions cooled by convection [25]. Lorenzini et al uncovers what should be the length scales of the rectangular cavity inserted into a heat generating cylindrical body in order to achieve minimum excess temperature [26].…”

Section: Introductionmentioning

confidence: 99%

The effect of cavities and T-shaped assembly of fins on overall thermal resistances

Çetin¹,

Çetkin²

2017

IJHT

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In this study, authors show that maximum excess temperature on a heat generating cylindrical solid domain can be minimized with numerically optimized rectangular cavities and T-shaped fins. The effect of the cavities and the fins on overall thermal resistances were compared while their volume fraction in a unit volume element is fixed. Furthermore, the designs correspond to the minimum thermal resistance were uncovered for two types of flows; parallel and cross-flow. The governing equations of the heat transfer and the fluid flow were solved simultaneously in order to show the effects of design on the flow characteristics and the thermal performance. Two-dimensional solution domain was used to uncover the thermal performance in cross-flow case because the flow direction is perpendicular to the heat transfer surface area of the heat generating domain. However, three-dimensional domain was used in parallel flow case because the fluid flows along the outer surface of the heat generating domain. For the cross-flow case, the results show that T-shaped assembly of fins with longer stem and shorter tributaries correspond to the lower peak temperature. In addition, the results also show that there is an optimal cavity shape that minimizes the peak temperature. This optimal shape becomes thinner when the number of the cavities increase. In parallel flow case, fins with thicker and shorter stem and longer tributaries correspond to the minimum excess temperature. In addition, the longer and thinner cavities increase the thermal performance in parallel flow case.

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Section: Introductionmentioning

confidence: 99%

The effect of cavities and T-shaped assembly of fins on overall thermal resistances

Çetin¹,

Çetkin²

2017

IJHT

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“…A partir dessa constatação, diversos estudos vêm sendo realizados avaliando diferentes formas geométricas para cavidade de dissipação de calor com Design Construtal a fim de encontrar arranjos ótimos para aumentar a troca térmica dentro das restrições impostas. Podemos citar os trabalhos em cavidade em forma de 'C' [20,21], 'T' [22], 'H' [23] e até mesmo formas mistas como 'T-Y' [24].…”

Section: Introductionunclassified

Otimização construtal de uma cavidade multi-bifurcada para dissipação de calor

2017

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O propósito do trabalho é analisar a influência dos parâmetros geométricos sobre a dissipação de calor de um perfil bidimensional com uma cavidade multi-bifurcada mantendo a área da cavidade constante. A simulação numérica foi realizada através da solução da equação da difusão do calor com MEF. Foi calculado o campo de distribuição de temperaturas no regime permanente e com geração de calor interna fixa e foi assumido que a transferência de calor no sólido ocorreu por condução. A geometria da cavidade foi gerada por um sistema de funções iteradas e um algoritmo foi implementado para testar diferentes ângulos de bifurcação, tamanho de cada braço de ramificação e número de iterações para geração da geometria. Entre as cavidades testadas foi possível determinar uma geometria ótima que serve de recomendação teórica para construção de possíveis perfis para troca de calor.Palavras-chave: MEF, dissipação de calor, design construtal.The purpose of this work is to analyze the influence of geometric parameters on the heat dissipation of a two-dimensional profile with a multi-bifurcated cavity keeping the cavity area constant. The numerical simulation was performed through the solution of the heat diffusion equation with MEF. The temperature distribution field was calculated in the steady state and with fixed internal heat generation and it was assumed that heat transfer to the solid occurred by conduction. The cavity geometry was generated by a system of iterated functions and an algorithm was implemented to test different bifurcation angles, size of each branching arm and number of iterations for geometry generation. Among the wells tested, it was possible to determine an optimum geometry that serves as a theoretical recommendation for the construction of possible profiles for heat exchange.Keywords: FEM, heat dissipation, constructal design. INTRODUÇÃOFractais tem sido usados em diversas áreas de engenharia e o potencial dessa teoria começa a ser importante em diversas aplicações industriais reais [1]. O uso da teoria dos fractais abrange aplicações na área de física [2,3], engenharia química [4,5], finanças [6,5], tráfego de internet [7], processamento de imagens [8,9], dinâmica dos fluidos [10,11], ciência ambiental [12,13], análise de superfícies [14] dentre outros. O motivo dessa gama de aplicações da teoria fractal se deve particularmente a sua característica de descrever a auto-similaridade em diferentes escalas que é uma aproximação do que ocorre na natureza [15,16]. Com uma formulação mais prática, existe também a Teoria Construtal que procura explicar deterministicamente o surgimento de formas na natureza a partir da ideia de um sistema de fluxo que altera sua forma para facilitar o acesso das correntes que fluem através dele. Dentro da Teoria Construtal é definido por Adrian Bejan o método Design Construtal como o uso da Lei Construtal como uma ferramenta na procura de melhores configurações e também melhores estratégias para resolução de um determinado problema que depende de geometria [17].Um problema freque...

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“…However, current literature only discusses how this high-conductivity material should be distributed in a uniformly heated domain. [11][12][13][14][15] Here, we uncover how the high-conductivity material should be placed when the heat generation is non-uniform. Here, we use constructal theory in order to uncover how the shape of the highconductivity inserts should be in order to minimize maximum temperature in a non-uniformly heated domain.…”

Section: Introductionmentioning

confidence: 99%

The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain

Çetkin

Oliani

2015

Journal of Applied Physics

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Here, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L 0 , where L 0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change. V C 2015 AIP Publishing LLC.

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Constructal design applied to the optimization of complex geometries: T-Y-shaped cavities with two additional lateral intrusions cooled by convection

Cited by 40 publications

References 14 publications

The effect of cavities and T-shaped assembly of fins on overall thermal resistances

The effect of cavities and T-shaped assembly of fins on overall thermal resistances

Otimização construtal de uma cavidade multi-bifurcada para dissipação de calor

The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain

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