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Constructal Theory Developments in China During the Past Decade
Abstract
This paper reviews the applications and extensions of constructal theory for engineering problems in China. From the original meaning of the word " Constructal " provided by Prof. Bejan at Duke University, its Chinese translation was named as " " , which not only implied the meanings of both the internal structures and external shapes of things, but also expressed the configuration process from small to large, which opposites to the fractal (" " in Chinese) theory. The constructal law was simply stated as: The structures of matters come from their optimal performances. Multidisciplinary , multi-objective and multi-scale constructal optimizations for heat conduction and thermal insulation processes, fluid flow processes, convective heat transfer processes of fins, heat sources, cavities, cooling channels, vascular networks and heat exchangers, mass transfer processes of porous mediums, heat and mass transfer processes of solid-gas reactors and solid oxide fuel cells, iron and steel production processes as well as generalized transfer processes have been performed since 2006. New research objects, model improvements, optimization objectives, boundary conditions, constraint conditions and transfer extensions have been considered in the optimizations. Various new results and findings have been obtained, and more guidelines have been provided for the designs of various transfer processes and systems. It shows that the applications of constructal theory are still being extended in China, which has huge impacts on the developments of various fields, such as industry, agriculture, natural science, etc..
... The heat dissipation problem is one of bottlenecks of their developments, and heat transfer enhancement [1][2][3] is one of the methods to solve this problem. Bejan [4] introduced constructal theory [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] into the heat conduction problem of a rectangular electrical device, and optimized the HCC distribution and the external shape to reduce the maximum temperature difference (MTD) of the electrical device. This was the first practice of the heat transfer enchantment for heat dissipation problem based on constructal theory. ...
Constructal optimizations of the elemental and first order “+” shaped high conductivity channels (HCCs) in the square bodies are carried out based on entransy dissipation rate (EDR) minimization. The optimal shapes of the HCCs and minimum EDRs of the bodies are derived. The results show that there exist optimal geometrical parameters of the first order “+” shaped HCC which lead to triple minimum dimensionless EDR of the body. The optimal shape of the first order “+” shaped HCC derived by EDR minimization makes the global heat conduction performance (GHCP) of the square body improve, and the temperature gradient more homogeneous. The optimal design scheme of the “+” shaped HCC with minimum EDR can be adopted in the heat dissipation problem of the electronic device to improve its GHCP.
... After deep analyses for the formation of the city avenues, Bejan found the constructal law and proposed constructal theory [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. Many scholars performed a lot of deep researches based on constructal theory, and constructal optimization for the iron and steel manufacturing process [53][54][55][56][57][58][59][60][61][62][63][64][65] is one of important applications. ...
Constructal theory is introduced into the molten steel yield maximization of a converter in this paper. For the specific total cost of materials, generalized constructal optimization of a converter steel-making process is performed. The optimal cost distribution of materials is obtained, and is also called as “generalized optimal construct”. The effects of the hot metal composition contents, hot metal temperature, slag basicity and ratio of the waste steel price to the sinter ore price on the optimization results are analyzed. The results show that the molten steel yield after optimization is increased by 5.48% compared with that before optimization when sinter ore and waste steel are taken as the coolants, and the molten steel yield is increased by 6.84% when only the sinter ore is taken as the coolant. It means that taking sinter ore as coolant can improve the economic performance of the converter steelmaking process. Decreasing the contents of the silicon, phosphorus and manganese in the hot metal can increase the molten steel yield. The change of slag basicity affects the molten steel yield a little.
Treelike structures abound in natural as well as man-made transport systems, which have fascinated multidisciplinary researchers to study the transport phenomena and properties and understand the transport mechanisms of treelike structures for decades. The fluid flow and heat transfer in treelike networks have received an increasing attention over the past decade as the highly efficient transport processes observed in natural treelike structures can provide useful hints for optimal solutions to many engineering and industrial problems. This review paper attempts to present the background and research progress made in recent years on the transport phenomenon in treelike networks as well as technological applications of treelike structures. The subtopics included are optimization of branching structures, scaling laws of treelike networks, and transport properties for laminar flow, turbulent flow, heat conduction, and heat convection in treelike networks. Analytical expressions for the effective transport properties have been derived based on deterministic treelike networks, and the effect of branching parameters on the transport properties of treelike networks has also been discussed. Furthermore, numerical simulation results for treelike microchannel networks are presented as well. The proposed transport properties may be beneficial to understand the transport mechanisms of branching structures and promote the applications of treelike networks in engineering and industry.
Open flow network is a weighted directed graph with source and sink to depict flux distributions in the steady state of an open flow system. Energetic food webs, global trade networks, input-output networks and clickstreams, are open flow network models of energy flows, goods flows, money flows, and collective attention flows respectively. Based on the Markov chain techniques, a set of quantities, such as influx, total through-flow, dissipation flow, first-passage flow distances, and first-passage flows can be defined to characterize flows and interactions between nodes. Under this framework, some universal patterns have been found in open flow networks, such as allometric scaling law, generalized Kleiber law, dissipation law, and gravity law, etc. We suppose constructal law cannot only be applied to flow systems with explicit spatial structures like rivers, vascular networks, animal movements, but also can be applied to open flow networks without explicit spatial structures such as energetic food webs, input-output networks, and clickstreams of attention flows. We try to formulate constructal law in the open flow network framework and test it by the real data.
The objective of this numerical study is to investigate the best geometric configuration that maximises heat transfer from the heated base by allowing both the length of the solid substrate and the microchannel heat sink freedom to morph. The thermal performance of the microchannel is based on the minimised peak temperature on the heated surface which gives a global minimised thermal resistance. The optimisation of the geometric parameters of the heat sink and solid substrate is carried out using a computational fluid dynamics code with a goal-driven optimisation algorithm. Results of the effect of Bejan number on the minimised peak temperature and minimised thermal resistance for solid substrate with varying axial lengths of 1 to 10 mm but fixed volume of 0.9 mm3 is presented. Results of optimal channel aspect ratio, solid volume fraction and channel hydraulic diameter of the microchannel were also presented.
In this paper, convective heat transfer processes of nanofluids flowing through tree-shaped network flowing channels with prescribed heat flux on channel wall are investigated. The entropy generation rate equations of nanofluids flowing through the tree-shaped network channels are deduced; the interaction between volume fractions of nanoparticles and entropy generation rate is investigated. For H-shaped tree network flowing channels, the recurrence formulas of total entropy generation rate and the order number of flowing channels are deduced, and the numerical examples are presented. A new dimensionless number is proposed to describe the entropy generation properties of nanofluids. Analytical solutions of entropy generation rate distribution of any order of H-shaped construct of flowing channel using nanofluids are obtained.
A comprehensive assessment of the methodologies of thermodynamic optimization, exergy analysis and thermoeconomics, and their application to the design of efficient and environmentally sound energy systems. The chapters are organized in a sequence that begins with pure thermodynamics and progresses towards the blending of thermodynamics with other disciplines, such as heat transfer and cost accounting. Three methods of analysis stand out: entropy generation minimization, exergy (or availability) analysis, and thermoeconomics.
The book reviews current directions in a field that is both extremely important and intellectually alive. Additionally, new directions for research on thermodynamics and optimization are revealed.
An optimization model for iron-making system covering sinter matching process to blast furnace process is established, in which the energy consumption, CO2 emission and cost minimizations are taken as optimization objectives. Some key constraints are considered according to practical production experience in the modelling. The combination of linear programming (LP) and nonlinear programming (NLP) methods is applied. The optimal sinter matching scheme under given conditions and the optimization results for different objectives are obtained. Effects of sinter grade and basicity on all the optimal objectives and coke ratio in blast furnace process are analyzed, respectively. The results obtained indicate that compared with the initial values, the energy consumption/CO2 emission of iron-making system decreases by 2.03% for objectives of energy consumption/CO2 emission minimizations and 1.89% for the objective of cost minimization, the cost decreases by 17.88% and 18.13%, respectively. All the three criteria decrease with the increasing lump usage, coal powder injection, blast temperature, and decreasing coke ratio for the iron-making system.
An iron and steel production whole process (ISPWP) with coking, sintering, iron-making, steel-making, continuous casting and steel-rolling procedures is considered in the paper. A complex function (CF) composed of steel yield (SY), useful energy (UE) and maximum temperature difference (MTD) is chosen as the optimization objective. The chemical compositions of the sinter ore, hot metal and iron slag, raw material dosages, process temperatures, cooling water flow rates and total cost of the raw materials, fuels and power investments of the ISPWP in one year are taken as the constraints, respectively. Constructal optimization of the ISPWP is conducted with the help of constructal theory and finite time thermodynamic (FTT) theory. The maximum CF of the ISPWP, optimal cost distributions among the procedures (generalized optimal construct) and optimal parameters in the thermodynamic cycles are obtained. Some parameters, such as equivalent diameter of the sinter particle, sinter layer porosity and casting speed, on the optimization results of the ISPWP are analyzed. The results show that compared with the initial scheme, the CF, SY and UE after optimization are increased by 27.63%, 2.70% and 32.91%, and the MTDs of the slab and strip are decreased by 3.84% and 11.56%, respectively. Therefore, the generalized optimal construct of the ISPWP makes a slight increment of the SY, evident increment of the UE, slight decrement of the slab MTD and big decrement of the strip MTD, which realizes an evident performance improvement of the ISPWP. New design guidelines for the ISPWP are provided after optimizations, which enriches the generalized thermodynamic optimization theory for ISPWP.
This review covers two aspects of “evolution” in thermodynamics. First, with the constructal law, thermodynamics is becoming the domain of physics that accounts for the phenomenon of evolution in nature, in general. Second, thermodynamics (and science generally) is the evolving add-on that empowers humans to predict the future and move more easily on earth, farther and longer in time. The part of nature that thermodynamics represents is this: nothing moves by itself unless it is driven by power, which is then destroyed (dissipated) during movement. Nothing evolves unless it flows and has the freedom to change its architecture such that it provides greater and easier access to the available space. Thermodynamics is the modern science of heat and work and their usefulness, which comes from converting the work (power) into movement (life) in flow architectures that evolve over time to facilitate movement.
Waste energy recovery and utilization presents a crucial opportunity in primary energy reduction and energy efficiency improvement for the global iron and steel industry. However, lack of comprehensive and practical methodology, the exact quantity of waste energy is often poorly quantified. This paper develops an innovative techno-economic model to quantify this opportunity that links theoretical, technical, and economic potential with the characteristics of waste energy resources and waste recycling technologies. Various forms of waste energy, such as sensible heat, pressure energy, and chemical energy, were examined. In addition, four scenarios were established to evaluate future energy saving potential and energy consumption reduction under the synergistic effect of technology promotion and structure adjustment. Findings show that the proportion of practical potential is less than 20% when considering the technical implementation rate for the average industry value. The selected 35 energy-saving technologies contribute to 3.08 GJ/t crude steel of cumulative energy savings, and technology implementation plays a significant role in energy consumption reduction. A sensitivity analysis indicates that energy price and discount rate are the most sensitive factors.
Inequality " is a common observation about us, as members of society. In this article, we unify physics with economics by showing that the distribution of wealth is related proportionally to the movement of all the streams of a live society. The hierarchical distribution of wealth on the earth happens naturally. Hierarchy is unavoidable, with staying power, and difficult to efface. We illustrate this with two architectures, river basins and the movement of freight. The physical flow architecture that emerges is hierarchical on the surface of the earth and in everything that flows inside the live human bodies, the movement of humans and their belongings, and the engines that drive the movement. The nonuniform distribution of wealth becomes more accentuated as the economy becomes more developed, i.e., as its flow architecture becomes more complex for the purpose of covering smaller and smaller interstices of the overall (fixed) territory. It takes a relatively modest complexity for the nonuniformity in the distribution of wealth to be evident. This theory also predicts the Lorenz-type distribution of income inequality, which was adopted empirically for a century. Published by AIP Publishing. [http://dx.
This paper reviews the constructal optimizations of two classes of extended bodies, i.e. cavity and fin, two classes of vascular networks, i.e. H-shaped vascular channels and line-line vascular channels and the multidisciplinary and multi-objective constructal optimization of vertical insulating walls performed in the Naval University of Engineering by combining entropy generation minimization and entransy theory with constructal theory. The results obtained herein have some important theoretical significances and application values.
This paper reviews the multidisciplinary , multi-objective and multi-scale constructal optimizations for heat conduction and thermal insulation processes, fluid flow processes, convective heat transfer processes of fins, vascular networks and heat exchangers, mass transfer processes of porous mediums as well as heat and mass transfer processes of solid-gas reactors and solid oxide fuel cells performed in the Naval University of Engineering. The optimal constructs of various transfer processes with different optimization objectives are obtained. The generalized constructal optimization idea, the generalized potential difference and generalized flux extremum principle as well as the generalized dissipation extremum principle are proposed. A model of generalized transfer process based on various transfer processes is built, a unified method to solve the constructal problems for various transfer processes is proposed, and the optimal construct of the model is obtained.
A helm-shaped fin (HSF) with single and multiple internal heat sources (IHSs) are investigated. Based on constructal theory, the volumes of the HSF and IHS are set as the constraints. The dimensionless maximum thermal resistance (DMTR) of the model is selected as the optimization objective, and its optimal construct is obtained. The results show that for the HSF with single IHS, the dimensionless thickness should be avoided in the constructal design of the model to improve its heat transfer performance (HTP). For the HSF with multiple IHSs, the DMTR has its double minimum, and it can be further decreased by increasing the IHS’s number and convective heat transfer parameter , respectively. The DMTR of the optimal construct with is decreased by 15.35% than that with . The DMTR of the model with HSF and nonuniform heat generation is decreased by 6.57% compared with that with circular-shaped fin. Moreover, the optimal constructs of the models with uniform and nonuniform heat generations are different, and a more uniform heat generation of the IHS leads to a better HTP of the model with HSF. The results obtained in this paper can provide some theoretical guidelines for the fin designs of real thermal systems.
This paper summarizes the important results regarding the improvement in the thermophysical properties of nanofluids. The influence of important parameters like particle's (loading, material, size, and shape), base fluid type, temperature, additives and pH value has been considered. There are many conflicting reports on the influence of parameters on thermophysical properties and the literature in this field is widespread, so this article would be beneficial for investigators to have a precise screening of a broad range of studies in this field. Further literature review of the applications of nanofluids with a particular focus on the advantages of using nanofluids in solar collectors and as coolants in automotive heat exchangers. The authors hope that this review can help in the translation of nanofluid technology from the lab scale research to industrial applications in solar collectors and automotive sector. At last, the paper identifies the opportunities for future research.
This paper proposes a growth simulation approach to optimize the internal cooling geometries in heat conduction system. The idea is inspired by the well-known constructal theory which generates the heat conducting paths by a sequence of optimization and organization steps. Firstly, numerical experiments are implemented to confirm the potential of leaf veins as concept generators for conducting path design. Then, a computational framework is built to simulate the adaptive growth of conductive cooling channels. To make the channels being able to grow freely in the domain, a new method called ‘conductivity spreading approach (CSA)’ is developed to transform nodal temperatures of growing channels into those of the underlying ground structure. With such transformation, growth dependences on the initial ground structure, like the nodes connections and locations, are eliminated and cooling channels can therefore grow towards an arbitrary direction to form an optimum layout solution. To illustrate the growth simulation in a directive and descriptive manner, a fundamental ‘volume-to-point’ problem is considered, in which the high conductivity material grows starting from the heat sink, extends spreading the whole region, and forms at convergence a configuration of tree-like network. The proposed constructal optimization method promises to be an “intelligent” CAD approach for various conductive cooling design applications.
Why is size so important? Why are " economies of scale " a universal feature of all flow systems, animate, inanimate, and human made? The empirical evidence is clear: the bigger are more efficient carriers (per unit) than the smaller. This natural tendency is observed across the board, from animal design to technology, logistics, and economics. In this paper, we rely on physics (thermodynamics) to determine the relation between the efficiency and size. Here, the objective is to predict a natural phenomenon, which is universal. It is not to model a particular type of device. The objective is to demonstrate based on physics that the efficiencies of diverse power plants should increase with size. The analysis is performed in two ways. First is the tradeoff between the " external " irreversibilities due to the temperature differences that exist above and below the temperature range occupied by the circuit executed by the working fluid. Second is the allocation of the fluid flow irreversibility between the hot and cold portions of the fluid flow circuit. The implications of this report in economics and design science (scaling up, scaling down) and the necessity of multi-scale design with hierarchy are discussed. Published by AIP Publishing.
Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.
This study documents geometrical optimization of inserts with high-emissivity applied for cooling a disc-shaped body with heat generation based on constructal theory. The high-emissivity inserts used for cooling purposes are located in radial direction in three structures: radial structure, radial structure with one level of discontinued pairing and radial structure with two levels of discontinued pairing. An analytical method is proposed for calculating the maximum temperature of the disc which is verified by the numerical results of a commercial program. The aim of design and optimization is obtaining the best configuration so that thermal resistance is minimized. The degrees of freedom are the radius of pairing the aspect of inserts? thickness. Results show that the percentage of area which is allocated to high-emissivity inserts has the most significant effect on thermal resistant. Secondly, the factor that affects the maximum temperature of the disc is number of inserts in center of the disc. In other word, increasing the high-emissivity area and number of inserts lead to reduction of the thermal resistance. Moreover, by evaluating the results, it is apprehended that by adding pairing to the structure even in same number of inserts the thermal resistance reduced significantly.
The triangular assemblies of a “volume-point” heat conduction model at micro and nanoscales are investigated by using constructal theory. The optimizations of the triangular assemblies are carried out by taking minimization of maximum thermal resistance as optimization objective. The optimal constructs of the triangular assemblies with size effect are obtained, which is evidently different from those without size effect. The results show that with the increase in the internal complexity of the construct, the heat transfer performance of the construct does not always decrease, and different optimal internal design structures should be adopted according to different parameters. The “volume-point” heat conduction constructal optimization based on maximum thermal resistance minimization with triangular element can effectively reduce the maximum temperature limitation of the triangular assembly, and enhance its system safety. The optimization results obtained based on triangular element will provide some significant guidelines for the structural designs of micro-electronic devices.
Here we show that bodies of the same size suspended uniformly in space constitute a system (a “suspension”) in a state of uniform volumetric tension because of mass-to-mass forces of attraction. The system “snaps” hierarchically, and evolves faster to a state of reduced tension when the bodies coalesce spontaneously nonuniformly, i.e., hierarchically, into few large and many small bodies suspended in the same space. Hierarchy, not uniformity, is the design that emerges, and it is in accord with the constructal law. The implications of this principle of physics in natural organization and evolution are discussed.
Physics is concise, simple, unambiguous, and constantly improving. Yet, confusion reigns in the field especially with respect to complexity and the second law of thermodynamics. In this paper, we step back and take a look at these notions—their meaning and definition—on the background provided by nature and thermodynamics. We review the central concepts and words that underpin the physics of evolutionary design today: information, knowledge, evolution, change, arrow of time, pattern, organization, drawings, complexity, fractal dimension, object, icon, model, empiricism, theory, disorder, second law, the “any” system in thermodynamics, morphing freely, and the constructal law. We show, for example, that information is not knowledge, fractal dimension is not a measure of complexity, and pattern is not a live flow architecture. Drawings, as physical means to facilitate the flow of knowledge, are subject to the natural tendency toward design evolution. Complexity, organization, and evolution in nature are most powerful and useful when pursued as a discipline, with precise terms, rules, and principles.
Based on the rectangular element and variable cross-section conducting path, the high effective-conduction channel distribution was re-optimized without premises that the last-order construct must be optimal and the high effective-conduction material is uniformly distributed in every element. The optimization results show that the optimal distribution of the area of high effective-conduction material in each element along the conducting path is nonuniformly. The optimal distribution of high effective-conduction material is deduced, and the maximum thermal resistance is reduced effectively. Further theoretical analysis reveals that increasing the number of elements is not always reducing the maximum thermal resistance remarkably, and the optimal aspect ratio of the rectangular area is close to 2.
The iron and steel industry is one of major sectors in term of energy consumption and CO2 emission in China. In this paper, we evaluate the reduction potential of CO2 emissions in China׳s iron and steel sector, based on the co-integration method and scenario design. We find that there is a long-term relationship between carbon intensity and its affecting factors, such as energy substitution, labor productivity, technology, and energy price. Monte Carlo simulation is further used for risk analysis. The results show that under BAU (business as usual) situation, the carbon intensity of China׳s iron and steel sector will be 0.3693 t CO2/100 CNY by 2020. However, the reduction potential of CO2 emissions in 2020 will be 541.75 million tons and 856.68 million tons under the moderate carbon-reducing scenario and the advanced carbon-reducing scenario, respectively. Based on the results of the elasticities obtained in the long-term equilibrium equation, some policy recommendations for CO2 emissions reduction in China׳s iron and steel industry are suggested.
Based on constructal theory, the "volume-point" heat conduction constructal optimization with triangular element at micro and nanoscales is carried out by taking minimum dimensionless maximum thermal resistance as optimization objective and releasing the constraint that the new-order assembly should be assembled by the optimized last-order assembly. The optimal construct of the "volume-point" heat conduction model under the effect of size effect is obtained. The results show that the optimal constructs with size effect and without size effect are obviously different. The heat transfer performance of the new-order assembly obtained by last-order assembly optimization constructal design method is not always the optimal one; compared with the global optimization constructal design method with the last-order assembly optimization constructal design method, the temperature limitation of the triangular assembly can be effectively reduced by using the global optimization constructal design method, and its heat transfer performance can be obviously improved.
On the premise to ensure the stability of energy supply and the normal production safety, using mathematical programming method, the dynamic mathematical optimization model was set up based on the optimal allocation of the surplus gas between the buffer users and production scheduling of the steam between the production equipments. The accuracy of power network production output is effectively improved by this optimization model, which can make full use of secondary energy and residual heat and energy, and achieve the rationalization of the outsourcing and the optimization of electricity production structure, hence effectively reduce the diffuse gas and steam, save energy, and also reduce the production cost of enterprises.