Constructal design of X-shaped conductive pathways for cooling a heat-generating body

Lorenzini, Giulio; Biserni, Cesare; Rocha, Luíz Alberto Oliveira

doi:10.1016/j.ijheatmasstransfer.2012.11.040

Cited by 86 publications

(36 citation statements)

References 40 publications

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“…The current literature also documents various T-and Y-shaped fin geometries corresponding to the minimum resistance to the heat flow relative to the different boundary conditions and constraints [14][15][16]. Furthermore, the effect of the inverted fins (cavities filled with high-conductivity inserts) on the maximum temperature and heat transfer rate were documented in the literature [17,18]. On the contrary to the fins, the inverted fins decrease the resistance to the heat flow in a conductive medium [19].…”

Section: Introductionmentioning

confidence: 94%

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: 94%

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

Çetin¹,

Çetkin²

2017

IJHT

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“…The design should be free to vary, in accord with the Constructal design method [1]. The current literature details the application of this method to smart structures [1][2][3][4][5][6][7][8][11][12][13] and thermofluid design [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. In a few instances, mechanical strength was used as the design objective [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Vascularization for cooling and reduced thermal stresses

Çetkin

Lorente

Bejan

2015

International Journal of Heat and Mass Transfer

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a b s t r a c tThis paper documents the effect of thermal expansion on a vascularized plate that is heated and loaded mechanically. Vascular cooling channels embedded in a circular plate provide cooling and mechanical strength. The coolant enters the plate from the center and leaves after it cools the plate to an allowable temperature limit. The mechanical strength of the plate decreases because of the embedded cooling channels. However, cooling the plate under an allowable temperature level decreases the thermal stresses. The mechanical strength of the plate which is heated and loaded mechanically at the same time can be increased by inserting cooling channels in it. The mechanical and thermofluid behavior of a vascularized plate was simulated numerically. The cooling channel configurations that provide the smallest peak temperature and von Mises stress are documented. There is one cooling channel configuration that is the best for the given set of boundary conditions and constraints; however, there is no single configuration that is best for all conditions.

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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 of X-shaped conductive pathways for cooling a heat-generating body

Cited by 86 publications

References 40 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

Vascularization for cooling and reduced thermal stresses

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

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