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Microchannels are important devices to improve the heat exchange in several engineering applications as heat, ventilation and air conditioning, microelectronic cooling, power generation systems and others. The present work performs a numerical study of a microchannel with two trapezoidal blocks subjected to laminar flows, aiming to analyze the influence of the boiling process on the geometric configuration of the microchannel. Constructal Design and Exhaustive Search are used for the geometrical evaluation of the blocks. The Mixture multi-phase model and the Lee phase change model were both employed for the numerical simulation of the boiling process. In this study, the influence of the height and higher width of the first block (H11/L11) over the heat transfer rate and pressure drop for different magnitudes of the ratio between the lower width and higher width (L12/L11) was investigated. It is considered water in monophase cases and water/vapor mixture for multiphase flow. Two different Reynolds numbers (ReH = 0.1 and 10.0) were investigated. Results indicated that, for the present thermal conditions, the consideration of boiling flows were not significant for prediction of optimal configurations. Results also showed that in the cases where the boiling process was enabled, the multi-objective performance was higher than in the cases without boiling, especially for ReH = 0.1.

Significant advancements in developing earth-air heat exchanger models have been detected in the past several decades. It is worth mentioning that this type of device takes advantage of the Earth's constant temperature to cool or heat spaces in buildings so that the identification of its most appropriate geometric configurations to reduce energy consumption is still an actual challenge. In this context, the present paper is focused on the geometric evaluation of several earth-air heat exchangers arrangements according to the Constructal Design method. The performance indicators are the minimization of its soil volume occupation, the minimization of its airflow pressure drop, and the maximization of its thermal potential. Therefore, from a straight duct named Reference Installation, 26 complex geometries have been outlined here using the numerical-analytical investigation. Many ideas emerged from this study: the use of serpentine with low spacing between ducts reduced nearly 39% of the soil volume occupied by the device compared to Reference Installation, showing its applicability in urban regions. In addition, configurations with few curves benefited the decrease of air pressure drop, allowing a performance 30% superior to the most complex shapes. Instead, complex designs can be recommended for thermal potential increase, although the influence of the different configurations over this indicator was not substantial since the maximum improvement achieved between the best and worst shapes proved to be around 6%. Finally, when the three performance indicators are concomitantly considered, several complex geometries reached an overall performance superior to the Reference Installation.

Here we show theoretically that the design of a thermochemical energy storage system for fast response and high thermal power can be predicted in accord with the constructal law of design. In this fundamental configuration, the walls of the elemental cylinder are impregnated with salt, while humid air is blown through the tube. Cases with constant salt volume or constant fluid volume or both are considered. It is shown that the best design in each case meets the equipartition of imperfections principle. The predictions are confirmed by full numerical experiments, allowing to consider various shape ratios and study their impact on the overall performance.

International audience; Here we document the performance of a radiant cooling panel made of flow channels sandwiched between a suspended metal plate and an insulation layer. The flow passages represent the crucial element of the panel. In the present work, the heat transfer and flow characteristics of the panel are investigated. A numerical study is conducted to explore the role played by the flow architectures on the overall performance of the panel in steady state, subjected to radiation and convection heat fluxes from the bottom. A comparison between serpentine and canopy-to-canopy (dendritic) flow channels is presented. In all the cases, the following geometrical constrains apply: fixed plate area and flow volume. From one configuration to the other, the flow is given more freedom to morph in accord with the Constructal approach. We demonstrated that the dendritic architecture allows a significant improvement in the cooling panel performance, with more cooling capacity and less pumping power. In addition, we showed that the morphing of the panel itself toward more compactness is also a way to increase the ratio of cooling capacity/pumping power.

With the growing interest on electric vehicles comes the question of the thermal management of their battery pack. In this work, we propose a thermally efficient solution consisting in inserting between the cells a liquid cooling system based on constructal canopy-to-canopy architectures. In such systems, the cooling fluid is driven from a trunk channel to perpendicular branches that make the tree canopy. An opposite tree collects the liquid in such a way that the two trees match canopy-to-canopy. The configuration of the cooling solution is predicted following the constructal methodology, leading to the choice of the hydraulic diameter ratios. We show that such configurations allow extracting most of the non-uniformly generated heat by the battery cell during the discharging phase, while using a small mass flow rate.

International audience; This paper documents an analytical and numerical study of thermochemical energy storage in an open reactor. The analysis of the pressure losses and temperature distributions allows to predict what the geometrical features of the reactor should be. A numerical model simulating the thermochemical process is then presented and validated. In accord with the Constructal design methodology, the module configuration is morphed following the trends obtained in the analytical part, to head for better overall performances. The results show that the ratio between the heat produced by the chemical reaction within the entire module and the overall pumping power necessary to blow the fluid through the module increases as the imperfections reach equipartition. In terms of module configuration, this means (i) an increase in the number of salt layers and (ii) aspect ratios moving the module volume towards more compactness.

Phase change materials (PCM) may be used as a thermal energy barrier for applications requiring insulation. This project explores the behavior of pure PCM within a two-dimensional rectangular cavity as a thermal barrier using a new thermal barrier efficiency metric. The dimensionless parameters are determined that dictate the efficiency for one-dimensional transport with cyclical heat flux loading on one side and a convective boundary condition on the opposite side. Two limiting conditions for the PCM behavior (No Phase Change and Full Phase Change) are studied analytically, and numerical models show that the predicted thermal barrier efficiency exceeds these limits, suggesting that the limiting conditions provide useful conservative estimates of PCM performance in designing PCM thermal barriers. Results show that both the No Phase Change limit and Full Phase Change efficiencies decrease with increasing Fourier and decreasing Biot numbers. An expression is derived for the CFD-predicted thermal barrier efficiency as a function of No Phase Change and Full Phase Change efficiencies and the Fourier number when Bi = 0.2.

WOS:000384779300059; International audience; This paper illustrates the morphing of flow architecture toward greater performance in a counterflow heat exchanger. The architecture consists of two plenums with a core of counterflow channels between them. Each stream enters one plenum and then flows in a channel that travels the core and crosses the second plenum. The volume of the heat exchanger is fixed while the volume fraction occupied by each plenum is variable. Performance is driven by two objectives, simultaneously: low flow resistance and low thermal resistance. The analytical and numerical results show that the overall flow resistance is the lowest when the core is absent, and each plenum occupies half of the available volume and is oriented in counterflow with the other plenum. In this configuration, the thermal resistance also reaches its lowest value. These conclusions hold for fully developed laminar flow and turbulent flow through the core. The curve for effectiveness vs number of heat transfer units (N-tu) is steeper (when N-tu \textless 1) than the classical curves for counterflow and crossflow. (C) 2016 Elsevier Ltd. All rights reserved.

WOS:000375425800025; International audience

The present work is guided by the Constructal theory to identify the best shapes for the cavity inserted in a cylindrical solid body with a constant heat generation rate. From the assertion that a system must evolve to persist in time, an evolution of the elemental (I-shaped) cavity to a tree-shaped cavity with two branches added to a single branch is proposed. With these modifications, two restrictions (area occupied by the trunk and area occupied by the branches of the cavity) and seven degrees of freedom are used to represent the geometry. The study focused on investigating the effect of the degrees of freedom associated with the cavity branches and the number of cavities. Results show that the optimization of each new degree reduces the maximum excess of temperature. However, the results obtained with a more complex cavity were similar to those obtained by the elemental cavity in reducing the maximum excess temperature. In practical terms, the results are similar. Despite the similarity between the present results and those achieved with a most simple shape. The increase of performance with the increase of degrees of freedom studied here indicates that for complete optimization, the performance of complex shapes can surpass that of the simplest cavity.

WOS:000407742400022; International audience; The architecture of heat exchangers is a classical subject that has been studied extensively in the past. In this paper, we address the fundamental question of what the size of the heat exchanger should be, in addition to what architectural features it should have. The answer to the size question follows from the tradeoff between (1), the useful power lost because of heat transfer and fluid flow and (2), the power destroyed during transportation, manufacturing, and maintenance. Changes in heat exchanger size induce changes in the opposite sign in the power requirements (1), and (2). This fundamental tradeoff regarding size is illustrated by considering one side of a heat exchanger (one flow passage) in laminar flow and in fully rough turbulent flow, with several duct cross sectional shapes and arrays of channels in parallel. The size tradeoff is present in heat exchanger applications across the board, from vehicles to stationary power plants. Published by AIP Publishing.

WOS:000324844800074; International audience; A heat pump that is coupled thermally with the ground extracts heat from the soil in winter, and discharges heat in the summer. The coupling is made through a buried heat exchanger. In this paper we explore the idea of using a single heat exchanger that serves more than one heat pump. Each heat pump draws its mass flow rate from the heat exchanger and, in addition, a background flow rate circulates permanently through the heat exchanger. The places where the heat pumps are connected to the exchanger vary. The objective of the design is to select the configuration of the multi-component system such that the total enthalpy flow rate delivered to the heat pumps is larger and the total pumping power is smaller. The paper documents the effect of geometry (the connections) and the relative sizes (mass flow rates of heat pumps) on the total enthalpy flow rate. The paper shows the parametric domain in which the design with a single heat exchanger is superior in comparison with the classical design where each heat pump is connected to its own heat exchanger. (C) 2013 Elsevier Ltd. All rights reserved.

Volume 8: Heat Transfer and Thermal EngineeringPhoenix, Arizona, USA, November 11–17, 2016Conference Sponsors: ASMEISBN: 978-0-7918-5062-6; International audience; In this paper we report the main advances made by our research group on the heat transfer performance of complex stream architectures embedded in a conducting solid. The immediate application of this review work deals with ground coupled heat pumps. Various configurations are considered: U-shaped with varying spacing between the parallel portions of the U, serpentines with three elbows, and trees with T- and Y-shaped bifurcations. In each case the volume ratio of fluid to soil is fixed. We determine the critical geometric features that allow the heat transfer density of the stream-solid configuration to be the highest that it can be. In the case of U-tubes and serpentines, the best spacing between parallel portions is discovered, whereas the vascular designs morph into bifurcations and angles of connection that provide progressively greater heat transfer rate per unit volume. Next we move to more complex underground structures, connecting several heat pumps to the same fluid loop. We conclude by comparing the merits of the two options.

WOS:000384779300072; International audience; This paper documents a numerical study of time-dependent melting dominated by natural convection in a cylinder filled with a phase change material. In accord with constructal design, the search is for effective heat-flow architectures. The volume-constrained improvement of the designs for heat flow begins with assuming the simplest structure, where a single line serves as heat source. Next, the heat source is endowed with freedom to change its shape as it grows. The objective of the numerical simulations is to discover the geometric features that lead to the fastest melting process. The results show that the heat transfer rate density increases as the complexity and number of degrees of freedom of the structure are increased. Furthermore, the angles between heat invasion lines have a minor effect on the global performance compared to other degrees of freedom: number of branching levels, stem length, and branch lengths. The effect of natural convection in the melt zone is documented. (C) 2016 Elsevier Ltd. All rights reserved.

WOS:000379583900017; International audience; Here, we show that during their half-century history, helicopters have been evolving into geometrically similar architectures with surprisingly sharp correlations between dimensions, performance, and body size. For example, proportionalities emerge between body size, engine size, and the fuel load. Furthermore, the engine efficiency increases with the engine size, and the propeller radius is roughly the same as the length scale of the whole body. These trends are in accord with the constructal law, which accounts for the engine efficiency trend and the proportionality between "motor" size and body size in animals and vehicles. These body-size effects are qualitatively the same as those uncovered earlier for the evolution of aircraft. The present study adds to this theoretical body of research the evolutionary design of all technologies [A. Bejan, The Physics of Life: The Evolution of Everything (St. Martin's Press, New York, 2016)]. Published by AIP Publishing.

Here we show that the heat transfer between a pipe assembly and the soil during the annual temperature cycle of a heat pump depends on the configuration of the flow system. We rely on constructal design to find the flow architecture (spacings, shapes) such that the heat transfer between the assembly and the ground is increased. The flow configuration changes freely, and its design is evolutionary. The better shapes change gradually from slender to square as the volume fraction occupied by the flow assembly increases. The heat transfer performance increases as the depth of the structure decreases, but the depth has a negligible effect on the shape of the structure. The results also show that the heat transfer performance increases as the configuration of the ground volume and the buried structure evolves to the most slender shape possible.

In this paper we explore the use of vascular design that provides cooling and mechanical strength at the same time. We illustrate the concept with a circular plate vascularized with embedded channels. The cooling fluid enters to the plate from the center or from the rim, and leaves after it cools the plate down to an allowable temperature level. The vascular cooling channels also affect the mechanical strength of the plate. We simulated numerically the thermofluid and mechanical behavior for three different structures; radial, dendrites with one pairing level and dendrites with two pairing levels. We found that for a given set of conditions (applied pressure difference, coolant inlet position, and number of the cooling channels) there is one configuration that is best; however, there is no single configuration that is best for all conditions.

This study shows that the main features of a steam generator can be determined based on the method of constructal design. The generator is endowed with freedom to morph, and then is optimized by putting the right components in the right places. The number of steam tubes is sufficiently large, so that the steam generator may be modeled as continuous. The total volume of the assembly and the volume of the steam tubes are fixed. The geometry is free to vary in the search for maximum heat transfer density. The steam flow in the tubes is modeled in two ways: single-phase and two-phase fully developed turbulent flow. Results of the analysis are: the location of the flow reversal (i.e. the demarcation between the tubes of the downcomer and those of the riser), the optimal spacing between adjacent tubes, and the number of tubes for the downcomer and the riser. Copyright © 2010 John Wiley & Sons, Ltd.

This paper shows how the configuration of a heat exchanger with fixed size controls the global performance. The cold-side fluid is driven by natural convection in vertical round tubes connected via two plenums. The hot-side fluid flows perpendicularly to the vertical tubes, and heats them by forced convection. The flow is laminar on both sides. The search for the flow configuration is pursued from a configuration with two tubes to three and four tubes. When the configuration has two tubes, the best design is with tubes with nearly the same diameter. When there are three tubes, it is possible to optimize the tube spacings as well. The constructal design represents a departure from the traditional approach, which consists of many tubes with the same diameter and spacing.

Here we show that there is a complete analogy between the configuring of heat and fluid flow and the configuring of the “flow of stresses”. The common principle is the avoidance of flow strangulations. This endows the flow systems (fluid, heat, stresses) with high density: for example, strongest for a fixed volume, or lightest for a fixed load. Examples treated in detail are “ducts” for the flow of stresses (slender bars in tension of compression), bifurcated bars shaped as Y and V, and slender and tapered plates (adhesive joints, tendons, ligaments), which are shown to be analogous to convection boundary layers. The design value of the “flow of stresses” concept is emphasized: to facilitate the flow of stresses (and the flow of fluid and heat) is to generate the configuration of the flow system, in accord with the constructal law.

In this paper we consider the fundamental problem of how to heat a stream to a specified exit temperature such that the overall fuel consumption is minimal. As illustration, we consider metal slabs that move at constant speed through a very slender enclosure with fixed total volume and arbitrary (nonuniform) distribution of cross-sectional area (heat transfer contact area). The heating is provided by a large number of heaters, which are distributed arbitrarily along the enclosure. The combustion gases flow in the x direction, which is oriented against the direction of the metal stream. The heat transfer is by convection. We show that minimal heat consumption is achieved when the heaters and the heat transfer contact area are distributed nonuniformly. The density of heaters per unit length must decrease as x−0.8 toward the entrance of the metal stream, and the heat transfer contact area must increase in proportion with x. These features suggest that the metal must move not as a single stream but as a tree-shaped flow. The metal enters in several parallel streams, which serve as tributaries to larger streams, leading to a single stream that exits at the specified temperature.

In this study, we describe the constructal-theory search for the geometry of a solar chimney. The objective is to increase the power production over the area occupied by the plant. The ratio height/radius, maximum mass flow rate and maximum power under the constraints of a fixed area and volume are determined. We find that the power generated per unit of land area is proportional to the length scale of the power plant. The analysis is validated by a detailed mathematical model. Pressure losses are reported in terms of the dimensionless length scale of the system, and are illustrated graphically. They indicate that the pressure drop at the collector inlet and at the transition section between the collector and chimney are negligible, and the friction loss in the collector can be neglected when the svelteness (Sv) of the entire flow architecture is greater than approximately 6.

This paper is a proposal to embed tree-shaped vasculatures in a wall designed such that the wall withstands without excessive hot spots the intense heating that impinges 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 coolant may flow in either direction, center–perimeter, or perimeter–center, although here only the center–perimeter flow direction is illustrated. Numerical simulations of conjugate heat and fluid flow in three directions show that it is possible to determine all the optimal geometric features of vasculatures with up to three levels of bifurcation (n = 3). The global performance is evaluated in terms of the overall thermal resistance, pressure difference, flow resistance and pumping power. The improvements in global performance diminish as the number of bifurcation levels increases. No flow architecture is universally superior. The dendritic designs are superior at the low and high ends of the pressure difference range. The radial designs are superior at intermediate pressure difference numbers.

Here we report the heat and fluid flow characteristics of counterflow heat exchangers with tree-shaped line-to-line flow channels. The flow structures of the hot and cold sides are sequences of point-to-line trees that alternate with upside-down trees. The paper shows under what conditions the tree vascularization offers greater heat flow access than corresponding conventional designs with parallel single-scale channels. The analytical part is based on assuming fully developed laminar flow in every channel and negligible longitudinal conduction in the solid. The numerical part consists of simulations of three-dimensional convection coupled with conduction in the solid. It is shown that tree vascularization offers greater heat flow access (smaller global thermal resistance) than parallel channels when the number of pairing levels increases and the available pumping power or pressure drop is specified. When the solid thermal conductivity increases, the heat transfer effectiveness decreases because of the effect of longitudinal heat conduction. The nonuniformity in fluid outlet temperature becomes more pronounced when the number of pairing levels increases and the pumping power (or pressure drop number) increases. The nonuniformity in outlet fluid temperature decreases when the solid thermal conductivity increases.

Here we develop vasculatures for smart materials with volumetric cooling capability under time-varying conditions. The objective is for the vascularized composite to survive without coolant flow such that its peak temperature does not overshoot the maximum allowable level. The transient performance of four vasculatures is reported: grids (G) and radial channels (R), and two flow directions, inlet in the center (I) and outlet in the center (O). Designs with outlet in the center offer short response times when the Be number is smaller than 10 9 . Configurations with outlet in the center offer short heat removal times and small hot volume fractions.

Vascular structures are contemplated for cooling the skins and leading surfaces of future high speed aircraft. This paper evaluates the proposal to cool with a flow architecture shaped as trees (dendritic) a parallelepipedic body that is heated uniformly. The coolant enters the body through one face and exits through the opposite face. The vasculature connects the two faces, and consists of trees that alternate with upside down trees. The fields for fluid flow and heat transfer are determined numerically in three dimensions. The effect of local pressure losses at bends, junctions and entrances is documented. Designs with tree-shaped architectures having up to four levels of bifurcation are evaluated for fluid flow and heat transfer performance, and are compared with the performance of a design with a single sheet of fluid sweeping the upper surface of the body. The fluid flow conductance of the tree designs increases when the number of bifurcation levels increases. The thermal performance of tree designs can be improved by endowing the tree design with more freedom such that the bifurcations generate asymmetric daughter channels. The tree designs outperform the fluid sheet design dramatically: the global thermal resistance of the tree designs is roughly one tenth of the global thermal resistance of the fluid sheet design.

This paper shows that the architecture of a steam generator for a power plant can be deduced on the basis of the constructal law. According to constructal theory, the flow architecture emerges in time such that it provides progressively greater access to its currents. The circulation of water is driven by buoyancy in one large tube (the downcomer) and many parallel smaller tubes (the riser). The total flow volume is fixed. Two flow models are used: single phase liquid in the downcomer and riser, and liquid–vapor mixture in the riser tubes. Features that result from constructal design are: the tube diameters, the number of riser tubes, the water circulation rate, the rate of steam production, and how the flow architecture should change when the operating pressure and the size of the flow system change.

Vascularized materials are a new generation of smart-material concepts that offer novel volumetric functionalities such as self-cooling, self-healing, renewal, cleansing, and “designed” transport properties (permeability, effective thermal conductivity). In this paper, we evaluate the volumetric cooling performance of slabs with embedded flow architectures consisting of grids (G) and radial channels (R). Both flow directions are considered: inlet (I) and outlet (O) in the center of the slab. In total, four configurations (GI, RI, GO, RO) compete for high performance in three directions: (i) low peak of overheating, or low global thermal resistance, (ii) small volume fractions (σ) occupied by high temperatures, and (iii) small pumping power. The results show that grids have lower global flow resistance than radial designs while local junction losses are important. The designs with inlet in the center are attractive in having lower global flow resistance than those with outlet in the center. When objective (i) is considered, designs with outlet in the center are recommended, and the gains in performance are significant if junction losses are negligible and Reynolds numbers are small. For objective (ii), RO is attractive if Sv is greater than 10 or Be is smaller than 109. When the three objectives (i)–(iii) are considered at the same time, the configurations with the outlet in the center (GO, RO) are superior when the flow system operates at low pumping power, and that GI and RI are attractive at high pumping power.

This paper is a proposal to vascularize a solid wall with transverse tree-shaped channels with fluid flow from side to side. The purpose of the fluid flow is to intercept in counterflow the solid heat conduction caused by an intense heat flux that lands on the exit plane of the wall. Tree architectures with 1–4 levels of bifurcation are simulated numerically, as a conjugate (convection and conduction) heat flow phenomenon in three dimensions. The effect of local pressure losses at junctions and entrances is included. The numerical work covers the Reynolds number range 10–550, svelteness number range 2.2–11.5, wall porosity range 0.01–0.1, and pressure drop number range 3 × 105–1010. The objective of the tree flow is to keep down the peaks of hot spot temperatures and the fraction of the volume occupied by high temperatures while using minimum pumping power. It is shown that the tree design is very effective, and that there is an optimal number of bifurcation levels for a specified porosity and pressure drop number. Tree designs are more effective than designs with parallel channels when the pressure drop number and the porosity are sufficiently large.

According to constructal theory, the “generation of flow configuration” is a universal phenomenon in physics. This phenomenon is covered by the constructal law: “For a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it.” This paper shows how the constructal law can be used to (1) predict and explain features of “design” in nature, and (2) design effective strategies and configurations for engineering. Many natural flow designs rely on two flow mechanisms: channels with relatively low resistivity, interwoven with diffusion across the interstices. The “design” is the balance between the two mechanisms. The flow from line to line (or plane to plane) through a sufficiently fine porous medium encounters less resistance than the flow through parallel channels when it is configured as trees that alternate with upside down trees: from this follows the prediction that natural porous media (e.g., hill slope) should be multiscale (bidisperse) and non-uniformly distributed. A porous medium contaminated with ionic species is decontaminated the fastest when the ionic flow is configured as two flow mechanisms in balance: “channeling” driven by potential differences between optimally positioned electrodes, and diffusion driven by concentration differences across the interstices between the channels.

This paper proposes to apply constructal theory to the optimization of ionic transfer by electrokinetics through porous media. By using an external electrical source (potential difference, or current), the ions from the pore solution of a saturated porous medium can be transferred (channelled) in an accelerated fashion, while the direction of their transport can be controlled by the electrodes position and polarity. The constructal law of maximization of flow access is used to optimize the electrokinetic process in two ways: (i) in time and (ii) in space. In (i), the ionic transport is shown to be driven by a diffusive mechanism before convection due to electrical effects which dominate the transfer. Constructal theory explains how the combination of the two mechanisms corresponds to an optimization of transport in time. In an application to ionic decontamination, the optimal location of the electrodes is determined from the constructal law by setting the diffusive ionic flow rate equal to the ionic flow rate due to electrical effects.

WOS:000368434600025; International audience; Transfers through porous materials where the driving force is a concentration difference or a pressure difference are useful characteristics of a pore network arrangement. Two schools of thought are prevalent in this area-first, macroscopic characteristics are not too difficult to obtain experimentally and parameters like diffusion coefficients or permeability serve as input data for models describing transfers through porous media. Such parameters are helpful in describing the transfers but they are of no value for predicting transfers because they are very poorly related to pore network topology. Secondly, theoretical descriptions at the level of the material microstructure fail to represent the actual material, even when they are coupled with up-to-date visualization techniques (e.g. three-dimensional tomography). This work documents a tentative link between the pore network geometry and the diffusion coefficient, a macroscopic parameter. We apply the constructal law of design to determine the most probable pore path configurations that minimize the diffusion transfer resistance and determine the macroscopic diffusion coefficient. The predicted diffusion coefficients are compared to experimental results from aqueous and gaseous diffusion paths through two porous materials.

WOS:000362130700067; International audience; Rotating electric machines generate heat volumetrically, and are cooled by forced convection aided by the self-pumping effect. In this paper we focus on the fundamental relationship between the internal flow architecture of the gas cooled winding and its thermal performance, which is represented by the nearly uniform distribution of peak temperature throughout the winding volume. We show that the cooling passages can be sized such that the volumetric cooling is most effective. From this finding follows the number of passages and their distribution through the heat generating volume. The principle is developed analytically, and it is then validated based on numerical simulations of the cooling architecture. The paper also reports the thermodynamics basis of the self-pumping effect, and its natural occurrence as free convection in general, which includes atmospheric circulation. (C) 2015 Elsevier Ltd. All rights reserved.

WOS:000365361400027; International audience; Here we develop analytically the formulas for effective permeability in several configurations using the closed-form description of tree networks designed to provide flow access. The objective was to find the relation between the permeability and porosity of tree-shaped fissures. We found the effect of the fracture size on the permeability for fixed number of bifurcation and the results showed that the permeability of the fracture network increased rapidly with the size of the fracture. Next, we found a relation between the Reservoir Quality Index (RQI) and the porosity of the fracture. The results in this paper have been validated by comparison with experimental and numerical results. We show that the permeability formulas do not vary much from one tree design to the next, suggesting that similar formulas may apply to naturally fissured porous media with unknown precise details, which occur in natural reservoirs. (C) 2015 Elsevier Ltd. All rights reserved.

WOS:000361163800020; International audience; This paper documents the joint performance of heat pumps that are served by a common loop buried in the ground, and which operate simultaneously: one heat pump absorbs heat from the buried loop whereas the other one rejects heat. A background flow is circulated in the underground loop even when the two heat pumps are not operating. The objective is to determine the performance and the manner in which it is affected by the way in which the two heat pumps are connected to the loop. The performance measures are the heat transfer rates into and out of the heat pumps, and the total pumping power required by the assembly. The paper documents the individual performance of the heat pumps, and their relative performance, which is the ratio of heating absorbed by one pump to the heating rejected by the other pump. (C) 2015 Elsevier Masson SAS. All rights reserved.

WOS:000359166000013; International audience; The diffusion coefficient of tritium in its liquid form through cementitious materials is an indicator of durability in the domain of nuclear waste disposal. Because the cement-based materials designed for the waste storage have very high confinement properties, diffusion tests tend to last several months if not years in some cases. Therefore, basing the determination of the tritium diffusion coefficient on the experimental data measured during non steady state is tempting. The aim of this work is to demonstrate that the determination during the transient regime of the effective diffusion coefficient and the material porosity leads to non-negligible underestimation of these quantities. Moreover, it appears that, when using a numerical model for the determination, their validity can only be judged on the basis of more than one criterion, whether those criteria are obtained from the experimental data or from a numerical model. (C) 2015 Elsevier Ltd. All rights reserved.

WOS:000352315700044; International audience; Condensers are flow architectures needed to provide high rates of condensation (or cooling) per unit volume, in enclosures with fixed volume. Their design has not changed from configurations consisting of the banks of horizontal tubes. In this paper, we outline a free path to evolving the design by exploring new features of flow configuration: flattened tubes, multiple tube sizes, arrays of flattened tubes, vertical tubes with turbulent film flow, forced convection condensation instead of gravity driven condensation, and the optimal length of a horizontal tube, i.e., the number of tubes in a column aligned with vapor cross flow. We show that the condensation density can be increased sizably by varying freely and without bias the morphology of the flow system: the shapes and arrangement of the cooled surfaces on which condensation occurs. The evolution of technology is described in terms of the special time direction of the useful (purposeful) changes in the configuration (shapes, arrangements) of surfaces on which flow/condensation occurs. This explains what "evolution" means. It is an important step for physics, not just technology.

This paper is a fundamental study of the effect of junction losses on the optimized geometry of tree-shaped flows. Several classes of flows are investigated systematically in a T-shaped construct with fixed internal and external size: laminar with non-negligible entrance and junction losses, and turbulent in tubes with smooth and rough walls. It is shown that in all cases junction losses have a sizeable effect on optimized geometry when Sv2

This paper reports the development of optimal vascularization for supplying self-healing smart materials with liquid that fills and seals the cracks that may occur throughout their volume. The vascularization consists of two-dimensional grids of interconnected orthogonal channels with two hydraulic diameters (D1, D2). The smallest square loop is designed to match the size (d) of the smallest crack. The network is sealed with respect to the outside and is filled with pressurized liquid. In this work, the crack site is modelled as a small spherical volume of diameter d. When a crack is formed, fluid flows from neighbouring channels to the crack site. This volume-to-point flow is optimized using two formulations: (1) incompressible liquid from steady constant-strength sources located in every node of the grid and from sources located equidistantly on the perimeter of the vascularized body of length scale L and (2) slightly compressible liquid from an initially pressurized grid discharging in time-dependent fashion into one crack site. The flow in every channel is laminar and fully developed. The objectives are (a) to minimize the global resistance to the flow from the grid to the crack site and (b) to minimize the time of discharge from the pressurized grid to the crack site. It is shown that methods (a) and (b) yield similar results. There is an optimal ratio of channel diameters D2/D1 < 1, and it decreases as the grid fineness (L/d) increases. The global flow resistance of the grid with optimized ratio of diameters is approximately half of the resistance of the corresponding grid with one channel size (D1 = D2). The optimized ratio of diameters and the minimized global resistance depend on how the grid intersects the crack site: this effect is minor and stresses the robustness of the vascularized design.

This paper details the generation of multi-scale flow structure in a package with heat sources. The model is based on abandoning two common assumptions (1) the assumption that there are many channels (components) in the package, which is traditionally made to exploit simplifications due to symmetry, and (2) the assumption that the heat-generating components have negligible thickness. Numerical simulations document the flow stagnation and separation generated by blunt heat sources, and the effect of these flow phenomena on the optimized internal flow structure. The effect of asymmetric thermal boundary conditions on the optimal spacing between heat-generating plates is significant. If the package has some channels with symmetric boundary conditions, and some with asymmetric boundary conditions, then the optimal structure has multiple spacings. The effect of freedom on design performance is documented by optimizing competing configurations that have different numbers of degrees of freedom.

SUMMARY This is a review of recent progress on constructal design made in two directions: multi-scale flow structures, and multi-objective design. The first direction is associated with the maximization of heat transfer rate density in a fixed volume in the limit of decreasing length scales, where boundary layers touch, and optimized channels are no longer slender. In the first example of this type, spacings are optimized based on the intersection of asymptotes method. In the second, the heat transfer density is further increased by placing progressively smaller plates in the entrances of the channels formed by the first generation of plates. In the third example, the placement of discrete heat sources on a vertical wall with natural and forced convection is optimized. The second direction is the discovery of architectures that result from two competing objectives, for example, mechanical strength and thermal insulation. It is shown that the internal configuration of a cavernous brick wall can be deduced from the clash between the two objectives. The same concept can be used to optimize the shape and structure of support beams that must be strong and, at the same time, must resist sudden attack by intense heating. Copyright # 2005 John Wiley & Sons, Ltd.

In this paper constructal theory is applied to the fundamental problem of how to arrange discrete heat sources on a wall cooled by forced convection. The global objective is to maximize the conductance between the discrete heated wall and the fluid. This is equivalent to minimizing the temperature of the hot spot on the wall, when the heat generation rate is specified. The mechanism by which the global objective is achieved is the generation of flow configuration, in this case the distribution of discrete heat sources. Two different analytical approaches are used: (i) large number of small heat sources, and (ii) small number of heat sources with finite length, which are mounted on a flat wall. Both analyses show that the heat sources should be placed nonuniformly on the wall, with the smallest distance between them near the tip of the boundary layer. If the Reynolds number is high enough, then the heat sources should be mounted flush against each near the entrance to the channel. The analytical results are validated by a numerical study of discrete heat sources that are distributed nonuniformly inside a channel formed by parallel plates. 2004 Elsevier Ltd. All rights reserved.

In this article we show numerically that the entire flow geometry of a vertical diverging or converging channel with laminar natural convection can be optimized for maximal heat transfer rate density (total heat transfer rate per unit of flow system volume). The geometry is free to change in three ways: (1) the spacing between the walls, (2) the distribution of heating along the walls, and (3) the angle between the two walls. Numerical simulations cover the Rayleigh number range 105 ≤ RaH ≤ 107, where H is the channel height. Nonuniform wall heating is modeled as an isothermal patch of varying height H 0 (≤H) on each wall, which is placed either at the bottom (entrance) end of the channel, or at the top (exit) end. The results confirm that the use of upper unheated sections enhances the chimney effect and the heat transfer. The new aspect is that the heat transfer rate density decreases because the unheated sections increase the total volume. It is shown that for maximal heat transfer rate density it is b...

This paper is an application of the constructal method to the discovery of the optimal distribution of discrete heat sources cooled by laminar natural convection. The global objective is to maximize the global conductance between the wall and the fluid, or to minimize the hot-spot temperatures when the total heat generation rate and global system dimensions are specified. Two scenarios are investigated: (i) a large number of small heat sources mounted on a vertical wall facing a fluid reservoir, and (ii) a small number of finite-size heat sources mounted on the inside of the side wall of a two-dimensional enclosure. It is shown that the optimal distribution is not uniform (the sources are not equidistant), and that as the Rayleigh number increases the heat sources placed near the tip of a boundary layer should have zero spacings. In both (i) and (ii), the optimal configuration of the wall with discrete sources is generated by the pursuit of maximal global performance subject to global constraints. � 2003 Elsevier Ltd. All rights reserved.

In this paper we develop the optimal tree-shaped flow paths for cooling a disc-shaped body by convection. Heat is generated uniformly over the disc area. The coolant enters through the center of the disc, and exits through ports positioned equidistantly along the perimeter. The unknown is the flow architecture. The constraints are the disc size and the total volume occupied by the ducts. It is assumed that the ducts are narrow enough so that the flow is hydrodynamically and thermally fully developed. The ultimate goal is to determine flow architectures that reach simultaneously two objectives: (i) minimal global fluid flow resistance (or pumping power), and (ii) minimal global thermal resistance. When the architecture is optimized for (i), the result is a dendritic structure in which every geometric feature is uniquely determined. The corresponding thermal resistance decreases as the total mass flow rate and the pumping power increase. When the objective is (ii), the optimal architecture has radial ducts, not dendrites. The corresponding fluid-flow resistance increases as the flow rate increases and the global thermal resistance decreases. Put together, these geometric results show that methods (i) and (ii) lead to nearly the same combined performance (thermal and fluid). Examined more closely, the dendrites produced by method (i) perform progressively better as the length scales become smaller. Optimized increasing complexity is the route to high thermal and fluid-flow performance in the limit of decreasing scales.