Based on constructal theory and entransy theory,a generalized constructal optimization of a solidification heat transfer process of slab continuous casting for a specified total water flow rate in the secondary coolin...Based on constructal theory and entransy theory,a generalized constructal optimization of a solidification heat transfer process of slab continuous casting for a specified total water flow rate in the secondary cooling zone was carried out.A complex function was taken as the optimization objective to perform the casting.The complex function was composed of the functions of the entransy dissipation and surface temperature gradient of the slab.The optimal water distribution at the sections of the secondary cooling zone were obtained.The effects of the total water flow rate in the secondary cooling zone,casting speed,superheat and water distribution on the generalized constructal optimizations of the secondary cooling process were analyzed.The results show that on comparing the optimization results obtained based on the optimal water distributions of the 8 sections in the secondary cooling zone with those based on the initial ones,the complex function and the functions of the entransy dissipation and surface temperature gradient after optimization decreased by 43.25%,5.90%and 80.60%,respectively.The quality and energy storage of the slab had obviously improved in this case.The complex function,composed of the functions of the entransy dissipation and surface temperature gradient of the slab,was a compromise between the internal and surface temperature gradients of the slab.Essentially,it is also the compromise between energy storage and quality of the slab.The"generalized constructal optimization"based on the minimum complex function can provide an optimal alternative scheme from the point of view of improving energy storage and quality for the parameter design and dynamic operation of the solidification heat transfer process of slab continuous casting.展开更多
A strip laminar cooling process is investigated in this paper. Entransy theory and generalized constructal optimization are introduced into the optimization. Total water flow amount(WFA) in the laminar cooling zone(LC...A strip laminar cooling process is investigated in this paper. Entransy theory and generalized constructal optimization are introduced into the optimization. Total water flow amount(WFA) in the laminar cooling zone(LCZ) and complex function are taken as the constraint and optimization objective, respectively. The entransy dissipation(ED) and maximum temperature different(MTD) of the strip are simultaneously considered in the complex function. WFA distributions of the headers in the LCZ are optimized. The effects of the total WFA, strip thickness and cooling water temperature on the optimal results are analyzed.The optimal cooling scheme is the eleventh cooling mode for the considered total 257 cooling schemes, and the complex function,ED and MTD of the strip are decreased by 11.59%, 5.59% and 17.58% compared with the initial cooling scheme, respectively.The total WFA and strip thickness have the obvious influences on the optimal cooing scheme, but the cooling water temperature has no influence in the parameter analysis range of this paper. The "generalized optimal construct" derived by minimum complex function shows a compromise between the energy retention and quality of the strip.展开更多
The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer.For a heat transfer model of a rectangular solid wall with an open T-shaped cavity,a dimensionless equi...The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer.For a heat transfer model of a rectangular solid wall with an open T-shaped cavity,a dimensionless equivalent thermal resistance based on entransy dissipation is taken as optimization objective,and constructal optimization for the model is carried out when the system volume,the cavity volume and the volume of rectangle occupied by T-shaped cavity are fixed.Numerical results indicate that the optimal geometry construct of cavity can be schemed out based on entransy dissipation extremum principle.The formulation of dimensionless global(maximum)thermal resistance presented in a literature is modified;some new rules which are different from those reported in the literature are obtained based on the minimization of the modified objective.Comparisons of the numerical results show that the optimal system constructs deduced respectively from the two thermal resistance objectives are very different.The optimization by taking equivalent thermal resistance minimization as objective can more effectively reduce mean temperature difference of heat transfer than the optimization by taking maximum thermal resistance minimization as objective,so that the performance of heat transfer for the total system can be improved.The more freedom the cavity has,the better the total system performance is.The correlations of the equivalent thermal resistance and the maximum thermal resistance of the system and three geometric degrees of freedom are found by using function fitting.展开更多
The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization.Firstly,the emergence and development process of both the mass entransy and its dissipalion ex...The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization.Firstly,the emergence and development process of both the mass entransy and its dissipalion extremum principle are reviewed.Secondly,the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for opti-mizing the mass transfer processes of one-way isothermal mass transfer,two-way isothermal equimolar mass transfer,and iso-thermal throttling and isothermal crystallization are summarized.Thirdly,the combination of the mass entransy dissipation ex-tremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized.The scientific features of the mass entransy dissipation extremam principle are emphasized.展开更多
Using constructal entransy dissipation rate minimization method based on discrete variable cross-section conducting path,constructal optimizations of elemental area with variable cross-section conducting path are perf...Using constructal entransy dissipation rate minimization method based on discrete variable cross-section conducting path,constructal optimizations of elemental area with variable cross-section conducting path are performed,and the results are compared with the optimization results of elemental area with the constant cross-section conducting path.The comparison shows that the minimum mean temperature difference based on elemental area with variable cross-section conducting path increases and approaches a constant as the assembly's order increases,but the minimum mean temperature difference based on elemental area with constant cross-section conducting path decreases and approaches a constant as the assembly's order increases.The difference between them is caused by the different dimensionless mean temperature difference of the first order assembly.A universal constructal optimization method by self similar organization to improve heat transfer ability and its corresponding rule are proposed.With the constructal optimization method by self similar organization based on entransy dissipation rate minimization objective,the mean temperature difference approaches a constant as the assembly's order increases.展开更多
The constructal optimizations of T-shaped fin with two-dimensional heat transfer model are carried out by finite element method and taking the minimization of equivalent thermal resistance based on entransy dissipatio...The constructal optimizations of T-shaped fin with two-dimensional heat transfer model are carried out by finite element method and taking the minimization of equivalent thermal resistance based on entransy dissipation and the minimization of maximum thermal resistance as optimization objectives, respectively. The effects of the global parameter a (integrating the coefficient of convective heat transfer, the overall area occupied by fin and its thermal conductivity) and the volume fraction ? of fin on the minimums of equivalent thermal resistance and maximum thermal resistance as well as their corresponding optimal configurations are analyzed. The comparison of the results based on the above two optimization objectives is conducted. The results show that the optimal structures based on the two optimization objectives are obviously different from each other. Compared with the optimization result by taking the minimization of maximum thermal resistance as the objective, the optimization result by taking the equivalent thermal resistance minimization as the objective can reduce the average temperature difference in the fin obviously. The increases of a and ? can all improve the working status of local hot spot and the global heat transfer performance of the system. But the improvement effects of the increases of a and ? on the minimization of equivalent thermal resistance are different from those on the minimization of maximum thermal resistance. For either objective, the effect of a is different from that of ?. The T-shaped fin with minimum equivalent thermal resistance is much taller than that with minimum maximum thermal resistance; for either optimization objective, the stem of fin is thicker than the branches of fin, and the stem thickness is relatively close to branch thickness when the minimization of equivalent thermal resistance is taken as the optimization objective. The T-shaped fin with flat stem and slender branches can benefit the reduction of the maximum thermal resistance.展开更多
In this paper,constructal optimization of the twice Y-shaped assemblies of fins with six freedom degrees(characteristic parameters of geometry)is performed by employing finite element method and taking dimensionless m...In this paper,constructal optimization of the twice Y-shaped assemblies of fins with six freedom degrees(characteristic parameters of geometry)is performed by employing finite element method and taking dimensionless maximum thermal resistance as a performance index,and the heat transfer performance of the twice Y-shaped assemblies of fins under various conditions with different freedom degrees are analyzed.The results show that the twice assemblies can improve the heat transfer performance of Y-shaped fin remarkably,and the minimum maximum thermal resistance of the twice Y-shaped assemblies of fins decreases by 36.37%compared with that of once Y-shaped assembly of fins.It is also proved again that the larger the number of freedom degrees for evolving is,the more perfect the system performance is.The effects of different characteristic parameters of geometry on the performance of the twice Y-shaped assemblies of fins are different,one should pay different attention to these parameters in practical engineering designs.The effects of two angles on the maximum thermal resistance are larger,but the optima of the two angles are robust.The effects of two height ratios on the maximum thermal resistance are more remarkable than those of two thickness ratios.展开更多
Based on constructal theory,the constructs of three"volume-point"heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are opti...Based on constructal theory,the constructs of three"volume-point"heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three"volume-point"heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on"volume-point"heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.展开更多
For a vertical insulating wall,a product function of heat flow and strength with power weight is introduced as the complex optimization objective to compromise between insulating performance and mechanical performance...For a vertical insulating wall,a product function of heat flow and strength with power weight is introduced as the complex optimization objective to compromise between insulating performance and mechanical performance.Under the global constraints of fixed external dimensions and safety requirements,the constructal optimization of the wall is carried out by taking the complex function maximization as the objective.It is shown that the maximum of the complex-objective function and its corresponding optimal internal structure design under a certain environmental condition can be obtained by allowing the internal structure of the wall to vary(evolve)freely.The validity,effectivity and applicability of the complex function are proved by the results and the power weight parameter in the range from 0.4 to 4 can compromise between the requirements of insulating and strength simultaneously and preferably.The constructal optimization with coequal attention to heat flow and strength and the corresponding results are discussed in detail.The optimal structure design and the corresponding performance analyses under various environmental conditions of application are presented.When the change of environment is greater and the total Rayleigh number is bigger,the insulating wall with large number of cavities should be employed.When the total Rayleigh number is small,the better performance can be obtained by reasonably employing the insulating wall with small number of cavities.The complex function has better selfadaptability,and the results in the recent literature are special cases of this paper.展开更多
This paper investigates the MED(Minimum Entransy Dissipation)optimization of heat transfer processes with the generalized heat transfer law q∝(A(T^(n))m.For the fixed amount of heat transfer,the optimal temperature p...This paper investigates the MED(Minimum Entransy Dissipation)optimization of heat transfer processes with the generalized heat transfer law q∝(A(T^(n))m.For the fixed amount of heat transfer,the optimal temperature paths for the MED are obtained The results show that the strategy of the MED with generalized convective law q∝(△T)^m is that the temperature difference keeps constant,which is in accordance with the famous temperature-difference-field uniformity principle,while the strategy of the MED with linear phenomenological law q∝A(T^-1)is that the temperature ratio keeps constant.For special cases with Dulong-Petit law q∝(△T)^1.25 and an imaginary complex law q∝(△(T^4))^1.25,numerical examples are provided and further compared with the strategies of the MEG(Minimum Entropy Generation),CHF(Constant Heat Flux)and CRT(Constant Reservoir Temperature)operations.Besides,influences of the change of the heat transfer amount on the optimization results with various heat resistance models are discussed in detail.展开更多
Analogizing with the heat conduction process,the entransy dissipation extremum principle for thermal insulation process can be described as:for a fixed boundary heat flux(heat loss)with certain constraints,the thermal...Analogizing with the heat conduction process,the entransy dissipation extremum principle for thermal insulation process can be described as:for a fixed boundary heat flux(heat loss)with certain constraints,the thermal insulation process is optimized when the entransy dissipation is maximized(maximum average temperature difference),while for a fixed boundary temperature,the thermal insulation process is optimized when the entransy dissipation is minimized(minimum average heat loss rate).Based on the constructal theory,the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective.The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained.The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate,the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers;the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers,and can help to improve their global thermal insulation performances.The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems,which will help to extend the application range of the entransy dissipation extremum principle.展开更多
Based on constructal theory and entransy theory,the optimal designs of constant-and variable-cross-sectional cylindrical heat sources are carried out by taking dimensionless equivalent resistance minimization as optim...Based on constructal theory and entransy theory,the optimal designs of constant-and variable-cross-sectional cylindrical heat sources are carried out by taking dimensionless equivalent resistance minimization as optimization objective.The effects of the cylindrical height,the cylindrical shape and the ratio of thermal conductivity of the fin to that of the heat source are analyzed.The results show that when the volume of the heat source is fixed,there exists an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius which leads to the minimum dimensionless equivalent thermal resistance.With the increase in the height of the cylindrical heat source and the ratio of thermal conductivity,the minimum dimensionless equivalent thermal resistance decreases gradually.For the heat source model with inverted variable-cross-sectional cylinder,there exist an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius and an optimal radius ratio of the smaller and bigger circles of the cylindrical fin which lead to a double minimum dimensionless equivalent thermal resistance.Therefore,the heat transfer performance of the cylindrical heat source is improved by adopting the cylindrical model with variable-cross-section.The optimal constructs of the cylindrical heat source based on the minimizations of dimensionless maximum thermal resistance and dimensionless equivalent thermal resistance are different.When the thermal security is ensured,the optimal construct of the cylindrical heat source based on minimum equivalent thermal resistance can provide a new alternative scheme for the practical design of heat source.The results obtained herein enrich the work of constructal theory and entransy theory in the optimal design field of the heat sources,and they can provide some guidelines for the designs of practical heat source systems.展开更多
The mass entransy describes the mass-diffusion ability of the solution system, and the mass-diffusion process with the finite concentration difference always leads to the mass-entransy dissipation. This paper studies ...The mass entransy describes the mass-diffusion ability of the solution system, and the mass-diffusion process with the finite concentration difference always leads to the mass-entransy dissipation. This paper studies the equimolar reverse constant-temperature mass-diffusion process with Fick's law( g∝Δ(c)). The optimal concentration paths for the MED(Minimum Entransy Dissipation) are derived and compared with those for the MEG(Minimum Entropy Generation) and CCR(Constant Concentration Ratio) operations. It is indicated that the strategy of the MED is equivalent to that of the CCD(Constant Concentration Difference) of the same component; whether the MED or the MEG is selected as the optimization objective, the strategy of the CCD is much better than that of the CCR.展开更多
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 proces...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.展开更多
The emergence and development of constructal theory,which has been a new discipline branch to research sorts of structures in nature and engineering,are reviewed.The core of the constructal theory is that various shap...The emergence and development of constructal theory,which has been a new discipline branch to research sorts of structures in nature and engineering,are reviewed.The core of the constructal theory is that various shapes and structures of the matters in nature are generated from the tendency to obtain optimal performance.Constructal theory and its application are summarized,from disciplines such as heat,mechanism,fluid flow,electricity,magnetism and chemistry,to life and non-life systems in nature.展开更多
The entransy and entransy dissipation extremum principle proposed have opened up a new direction for the heat transfer optimi-zation.The emergence and development of entransy theory are reviewed.Entransy theory and it...The entransy and entransy dissipation extremum principle proposed have opened up a new direction for the heat transfer optimi-zation.The emergence and development of entransy theory are reviewed.Entransy theory and its applications are summarized from several aspects,such as heat conduction,heat convective,heat radiation,heat exchanger design and mass transfer,etc.The emphases are focused on four aspects,i.e.,the comparison between entropy generation rate and entransy dissipation rate,the combination of entransy dissipation extreme principle with finite time thermodynamics,the combination of entransy dissipation extreme principle with the heat conduction constructal theory,and the combination of entransy dissipation extreme principle with the heat convective constructal theory.The scientific features of entransy theory are emphasized.展开更多
The liquid-solid phase change process of a simple one-dimensional slab is studied in this paper.By taking entransy dissipation minimization as optimization objective,the optimal external reservoir temperature profiles...The liquid-solid phase change process of a simple one-dimensional slab is studied in this paper.By taking entransy dissipation minimization as optimization objective,the optimal external reservoir temperature profiles are derived by using optimal control theory under the condition of a fixed freezing or melting time.The entransy dissipation corresponding to the optimal heat exchange strategies of minimum entransy dissipation is 8/9 of that corresponding to constant reservoir temperature operations,which is independent of all system parameters.The obtained results for entransy dissipation minimization are also compared with those obtained for the optimal heat exchange strategies of minimum entropy generation and constant reservoir temperature operations by numerical examples.The obtained results can provide some theoretical guidelines for the choice of optimal cooling or heating strategy in practical liquid-solid phase change processes.展开更多
This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives,respectively,by combining the met...This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives,respectively,by combining the methods of theoretical analysis and numerical calculation.The eight types of heat sinks are uniform height rectangular fin heat sink,non-uniform height rectangular fin heat sink,inline cylindrical pin-fin heat sink(ICPHS),plate single-row pin fin heat sink(PSRPHS),plate inline pin fin heat sink(PIPHS),plate staggered pin fin heat sink(PSPHS),single-layered microchannel heat sink(SLMCHS)with rectangular cross sections and double-layered microchannel heat sink(DLMCHS)with rectangular cross sections,respectively.And the ten performance indexes are heat transfer rate maximization,maximum thermal resistance minimization,minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate(equivalent thermal resistance for short),field synergy number maximization,entropy generation rate minimization,operation cost minimization,thermo-economic function value minimization,pressure drop minimization,enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization,respectively.The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other.The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition.The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed.The results obtained herein have some important theoretical significances and application values,and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications.展开更多
Umbrella-shaped assembly of cylindrical fins is optimized by adopting analytical method and taking dimensionless mean thermal resistance (MTR) as performance index. The optimal construct of umbrella-shaped assembly is...Umbrella-shaped assembly of cylindrical fins is optimized by adopting analytical method and taking dimensionless mean thermal resistance (MTR) as performance index. The optimal construct of umbrella-shaped assembly is obtained. The results show that the heat conductance performance of the assembly becomes ever worse with ever greater number of elemental cylindrical fins,the umbrella-shaped assembly reduces to cylindrical fin in some values of design parameters,and the diameters’ dependence on design parameters is weak for the optimized assembly. An equivalent thermal resistance defined based on entransy dissipation rate (EDR) reflects an average heat transfer effect of the assembly. The constructal design corresponding to the minimum EDR (or MTR) should be adopted for designing an assembly of fins in engineering at the limit safe condition.展开更多
Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory.Three types of 3-D circular disc heat sink models,i.e.without collection micr...Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory.Three types of 3-D circular disc heat sink models,i.e.without collection microchannels,with center collection microchannels,and with edge collection microchannels,are established respectively.Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels,that of circular disc heat sink with center collection microchannels is the minimum,so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages.Furthermore,the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes.With the mass flow rate increasing,both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease.With the heat flux increasing,the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged.With the same mass flow rate and heat flux,the larger the microchannel branch number,the smaller the maximum thermal resistance.While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.展开更多
基金supported by the National Key Basic Research and Devel-opment Program of China("973"Project)(Grant No.2012CB720405)the National Natural Science Foundation of China(Grant Nos.51176203 and 51206184)the Natural Science Foundation of Hubei Province(Grant No.2012FFB06905)
文摘Based on constructal theory and entransy theory,a generalized constructal optimization of a solidification heat transfer process of slab continuous casting for a specified total water flow rate in the secondary cooling zone was carried out.A complex function was taken as the optimization objective to perform the casting.The complex function was composed of the functions of the entransy dissipation and surface temperature gradient of the slab.The optimal water distribution at the sections of the secondary cooling zone were obtained.The effects of the total water flow rate in the secondary cooling zone,casting speed,superheat and water distribution on the generalized constructal optimizations of the secondary cooling process were analyzed.The results show that on comparing the optimization results obtained based on the optimal water distributions of the 8 sections in the secondary cooling zone with those based on the initial ones,the complex function and the functions of the entransy dissipation and surface temperature gradient after optimization decreased by 43.25%,5.90%and 80.60%,respectively.The quality and energy storage of the slab had obviously improved in this case.The complex function,composed of the functions of the entransy dissipation and surface temperature gradient of the slab,was a compromise between the internal and surface temperature gradients of the slab.Essentially,it is also the compromise between energy storage and quality of the slab.The"generalized constructal optimization"based on the minimum complex function can provide an optimal alternative scheme from the point of view of improving energy storage and quality for the parameter design and dynamic operation of the solidification heat transfer process of slab continuous casting.
基金supported by the National Basic Research Program of China ("973" Project) (Grant No. 2012CB720405)the National Natural Science Foundation of China (Grant Nos. 51506220 & 51356001)
文摘A strip laminar cooling process is investigated in this paper. Entransy theory and generalized constructal optimization are introduced into the optimization. Total water flow amount(WFA) in the laminar cooling zone(LCZ) and complex function are taken as the constraint and optimization objective, respectively. The entransy dissipation(ED) and maximum temperature different(MTD) of the strip are simultaneously considered in the complex function. WFA distributions of the headers in the LCZ are optimized. The effects of the total WFA, strip thickness and cooling water temperature on the optimal results are analyzed.The optimal cooling scheme is the eleventh cooling mode for the considered total 257 cooling schemes, and the complex function,ED and MTD of the strip are decreased by 11.59%, 5.59% and 17.58% compared with the initial cooling scheme, respectively.The total WFA and strip thickness have the obvious influences on the optimal cooing scheme, but the cooling water temperature has no influence in the parameter analysis range of this paper. The "generalized optimal construct" derived by minimum complex function shows a compromise between the energy retention and quality of the strip.
基金Supported by the Program for New Century Excellent Talents in Universities of China(Grant No.20041006)Foundation for the Authors of National Excellent Doctoral Dissertation of China(Grant No.200136)
文摘The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer.For a heat transfer model of a rectangular solid wall with an open T-shaped cavity,a dimensionless equivalent thermal resistance based on entransy dissipation is taken as optimization objective,and constructal optimization for the model is carried out when the system volume,the cavity volume and the volume of rectangle occupied by T-shaped cavity are fixed.Numerical results indicate that the optimal geometry construct of cavity can be schemed out based on entransy dissipation extremum principle.The formulation of dimensionless global(maximum)thermal resistance presented in a literature is modified;some new rules which are different from those reported in the literature are obtained based on the minimization of the modified objective.Comparisons of the numerical results show that the optimal system constructs deduced respectively from the two thermal resistance objectives are very different.The optimization by taking equivalent thermal resistance minimization as objective can more effectively reduce mean temperature difference of heat transfer than the optimization by taking maximum thermal resistance minimization as objective,so that the performance of heat transfer for the total system can be improved.The more freedom the cavity has,the better the total system performance is.The correlations of the equivalent thermal resistance and the maximum thermal resistance of the system and three geometric degrees of freedom are found by using function fitting.
基金supported by the National Natural Science Foundation China(Grant Nos.51176203 and 10905093)
文摘The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization.Firstly,the emergence and development process of both the mass entransy and its dissipalion extremum principle are reviewed.Secondly,the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for opti-mizing the mass transfer processes of one-way isothermal mass transfer,two-way isothermal equimolar mass transfer,and iso-thermal throttling and isothermal crystallization are summarized.Thirdly,the combination of the mass entransy dissipation ex-tremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized.The scientific features of the mass entransy dissipation extremam principle are emphasized.
基金supported by Program for New Century Excellent Talents in Universities of China and the Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.200136)
文摘Using constructal entransy dissipation rate minimization method based on discrete variable cross-section conducting path,constructal optimizations of elemental area with variable cross-section conducting path are performed,and the results are compared with the optimization results of elemental area with the constant cross-section conducting path.The comparison shows that the minimum mean temperature difference based on elemental area with variable cross-section conducting path increases and approaches a constant as the assembly's order increases,but the minimum mean temperature difference based on elemental area with constant cross-section conducting path decreases and approaches a constant as the assembly's order increases.The difference between them is caused by the different dimensionless mean temperature difference of the first order assembly.A universal constructal optimization method by self similar organization to improve heat transfer ability and its corresponding rule are proposed.With the constructal optimization method by self similar organization based on entransy dissipation rate minimization objective,the mean temperature difference approaches a constant as the assembly's order increases.
基金supported by the National Natural Science Foundation of China (Grant No. 10905093)the Program for New Century Excellent Talents in University of China (Grant No. NCET-04-1006)+1 种基金the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)the Natural Science Foundation for Youngsters of Naval University of Engineering (Grant No. HGDQNJJ10017)
文摘The constructal optimizations of T-shaped fin with two-dimensional heat transfer model are carried out by finite element method and taking the minimization of equivalent thermal resistance based on entransy dissipation and the minimization of maximum thermal resistance as optimization objectives, respectively. The effects of the global parameter a (integrating the coefficient of convective heat transfer, the overall area occupied by fin and its thermal conductivity) and the volume fraction ? of fin on the minimums of equivalent thermal resistance and maximum thermal resistance as well as their corresponding optimal configurations are analyzed. The comparison of the results based on the above two optimization objectives is conducted. The results show that the optimal structures based on the two optimization objectives are obviously different from each other. Compared with the optimization result by taking the minimization of maximum thermal resistance as the objective, the optimization result by taking the equivalent thermal resistance minimization as the objective can reduce the average temperature difference in the fin obviously. The increases of a and ? can all improve the working status of local hot spot and the global heat transfer performance of the system. But the improvement effects of the increases of a and ? on the minimization of equivalent thermal resistance are different from those on the minimization of maximum thermal resistance. For either objective, the effect of a is different from that of ?. The T-shaped fin with minimum equivalent thermal resistance is much taller than that with minimum maximum thermal resistance; for either optimization objective, the stem of fin is thicker than the branches of fin, and the stem thickness is relatively close to branch thickness when the minimization of equivalent thermal resistance is taken as the optimization objective. The T-shaped fin with flat stem and slender branches can benefit the reduction of the maximum thermal resistance.
基金supported by the National Natural Science Foundation of China(Grant No.10905093)the Program for New Century Excellent Talents in University of China(Grant No.NCET-04-1006)the Foun-dation for the Author of National Excellent Doctoral Dissertation of China(Grant No.200136)
文摘In this paper,constructal optimization of the twice Y-shaped assemblies of fins with six freedom degrees(characteristic parameters of geometry)is performed by employing finite element method and taking dimensionless maximum thermal resistance as a performance index,and the heat transfer performance of the twice Y-shaped assemblies of fins under various conditions with different freedom degrees are analyzed.The results show that the twice assemblies can improve the heat transfer performance of Y-shaped fin remarkably,and the minimum maximum thermal resistance of the twice Y-shaped assemblies of fins decreases by 36.37%compared with that of once Y-shaped assembly of fins.It is also proved again that the larger the number of freedom degrees for evolving is,the more perfect the system performance is.The effects of different characteristic parameters of geometry on the performance of the twice Y-shaped assemblies of fins are different,one should pay different attention to these parameters in practical engineering designs.The effects of two angles on the maximum thermal resistance are larger,but the optima of the two angles are robust.The effects of two height ratios on the maximum thermal resistance are more remarkable than those of two thickness ratios.
基金supported by the National Natural Science Foundation of China(Grant No.51176203)the Natural Science Foundation of Naval University of Engineering(Grant No.HGDYDJJ10011)the Natural Science Foundation for Youngsters of Naval University of Engineering(Grant No.HGDQNJJ10017)
文摘Based on constructal theory,the constructs of three"volume-point"heat conduction models with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale are optimized by taking minimum entransy dissipation rate as optimization objective.The optimal constructs of the three"volume-point"heat conduction models with minimum dimensionless equivalent thermal resistance are obtained.The results show that the optimal constructs of the three-dimensional cylindrical assembly based on the minimizations of dimensionless equivalent thermal resistance and dimensionless maximum thermal resistance are different,which is obviously different from the comparison between those of the corresponding two-dimensional rectangular assembly based on the minimizations of these two objectives.The optimal constructs based on rectangular and triangular elements on microscale and nanoscale when the size effect takes effect are obviously different from those when the size effect does not take effect.Because the thermal current density in the high conductivity channel of the rectangular and triangular second order assemblies are not linear with the length,the optimal constructs of these assemblies based on the minimization of entransy dissipation rate are different from those based on the minimization of maximum temperature difference.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the construct.The studies on"volume-point"heat conduction constructal problems at three-dimensional conditions and microscale and nanoscale by taking minimum entransy dissipation rate as optimization objective extend the application range of the entransy dissipation extremum principle.
基金supported by the National Natural Science Foundation of China(Grant No.10905093)the Program for New Century Excellent Talents in University of China(Grant No.NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.200136)
文摘For a vertical insulating wall,a product function of heat flow and strength with power weight is introduced as the complex optimization objective to compromise between insulating performance and mechanical performance.Under the global constraints of fixed external dimensions and safety requirements,the constructal optimization of the wall is carried out by taking the complex function maximization as the objective.It is shown that the maximum of the complex-objective function and its corresponding optimal internal structure design under a certain environmental condition can be obtained by allowing the internal structure of the wall to vary(evolve)freely.The validity,effectivity and applicability of the complex function are proved by the results and the power weight parameter in the range from 0.4 to 4 can compromise between the requirements of insulating and strength simultaneously and preferably.The constructal optimization with coequal attention to heat flow and strength and the corresponding results are discussed in detail.The optimal structure design and the corresponding performance analyses under various environmental conditions of application are presented.When the change of environment is greater and the total Rayleigh number is bigger,the insulating wall with large number of cavities should be employed.When the total Rayleigh number is small,the better performance can be obtained by reasonably employing the insulating wall with small number of cavities.The complex function has better selfadaptability,and the results in the recent literature are special cases of this paper.
基金supported by the National Natural Science Foundation of China(Grant Nos.51576207,51356001&51579244)
文摘This paper investigates the MED(Minimum Entransy Dissipation)optimization of heat transfer processes with the generalized heat transfer law q∝(A(T^(n))m.For the fixed amount of heat transfer,the optimal temperature paths for the MED are obtained The results show that the strategy of the MED with generalized convective law q∝(△T)^m is that the temperature difference keeps constant,which is in accordance with the famous temperature-difference-field uniformity principle,while the strategy of the MED with linear phenomenological law q∝A(T^-1)is that the temperature ratio keeps constant.For special cases with Dulong-Petit law q∝(△T)^1.25 and an imaginary complex law q∝(△(T^4))^1.25,numerical examples are provided and further compared with the strategies of the MEG(Minimum Entropy Generation),CHF(Constant Heat Flux)and CRT(Constant Reservoir Temperature)operations.Besides,influences of the change of the heat transfer amount on the optimization results with various heat resistance models are discussed in detail.
基金supported by the National Key Basic Research and Development Program of China(‘973’Program)(Grant No.2012CB720405)the National Natural Science Foundation of China(Grant No.51176203)the Natural Science Foundation for Youngsters of Naval University of Engineering(Grant No.HGDQNJJ11008)
文摘Analogizing with the heat conduction process,the entransy dissipation extremum principle for thermal insulation process can be described as:for a fixed boundary heat flux(heat loss)with certain constraints,the thermal insulation process is optimized when the entransy dissipation is maximized(maximum average temperature difference),while for a fixed boundary temperature,the thermal insulation process is optimized when the entransy dissipation is minimized(minimum average heat loss rate).Based on the constructal theory,the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective.The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained.The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate,the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers;the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers,and can help to improve their global thermal insulation performances.The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems,which will help to extend the application range of the entransy dissipation extremum principle.
基金supported by the National Natural Science Foundation of China(Grant Nos.5120618451176203&51356001)
文摘Based on constructal theory and entransy theory,the optimal designs of constant-and variable-cross-sectional cylindrical heat sources are carried out by taking dimensionless equivalent resistance minimization as optimization objective.The effects of the cylindrical height,the cylindrical shape and the ratio of thermal conductivity of the fin to that of the heat source are analyzed.The results show that when the volume of the heat source is fixed,there exists an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius which leads to the minimum dimensionless equivalent thermal resistance.With the increase in the height of the cylindrical heat source and the ratio of thermal conductivity,the minimum dimensionless equivalent thermal resistance decreases gradually.For the heat source model with inverted variable-cross-sectional cylinder,there exist an optimal ratio of the center-to-centre distance of the fin and the heat source to the cylinder radius and an optimal radius ratio of the smaller and bigger circles of the cylindrical fin which lead to a double minimum dimensionless equivalent thermal resistance.Therefore,the heat transfer performance of the cylindrical heat source is improved by adopting the cylindrical model with variable-cross-section.The optimal constructs of the cylindrical heat source based on the minimizations of dimensionless maximum thermal resistance and dimensionless equivalent thermal resistance are different.When the thermal security is ensured,the optimal construct of the cylindrical heat source based on minimum equivalent thermal resistance can provide a new alternative scheme for the practical design of heat source.The results obtained herein enrich the work of constructal theory and entransy theory in the optimal design field of the heat sources,and they can provide some guidelines for the designs of practical heat source systems.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51576207 & 51356001)
文摘The mass entransy describes the mass-diffusion ability of the solution system, and the mass-diffusion process with the finite concentration difference always leads to the mass-entransy dissipation. This paper studies the equimolar reverse constant-temperature mass-diffusion process with Fick's law( g∝Δ(c)). The optimal concentration paths for the MED(Minimum Entransy Dissipation) are derived and compared with those for the MEG(Minimum Entropy Generation) and CCR(Constant Concentration Ratio) operations. It is indicated that the strategy of the MED is equivalent to that of the CCD(Constant Concentration Difference) of the same component; whether the MED or the MEG is selected as the optimization objective, the strategy of the CCD is much better than that of the CCR.
基金supported by the National Natural Science Foundation of China(Grant Nos.51506220&51579244)the National Key Basic Research and Development Program of China(Grant No.2012CB720405)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.51176203)the Natural Science Foundation of Naval University of Engineering(Grant No.HGDYDJJ10011)
文摘The emergence and development of constructal theory,which has been a new discipline branch to research sorts of structures in nature and engineering,are reviewed.The core of the constructal theory is that various shapes and structures of the matters in nature are generated from the tendency to obtain optimal performance.Constructal theory and its application are summarized,from disciplines such as heat,mechanism,fluid flow,electricity,magnetism and chemistry,to life and non-life systems in nature.
基金supported by the National Natural Science Foundation of China(51176203,10905093)
文摘The entransy and entransy dissipation extremum principle proposed have opened up a new direction for the heat transfer optimi-zation.The emergence and development of entransy theory are reviewed.Entransy theory and its applications are summarized from several aspects,such as heat conduction,heat convective,heat radiation,heat exchanger design and mass transfer,etc.The emphases are focused on four aspects,i.e.,the comparison between entropy generation rate and entransy dissipation rate,the combination of entransy dissipation extreme principle with finite time thermodynamics,the combination of entransy dissipation extreme principle with the heat conduction constructal theory,and the combination of entransy dissipation extreme principle with the heat convective constructal theory.The scientific features of entransy theory are emphasized.
基金supported by the Program for New Century Excellent Talents in Universities of China(Grant No 20041006)the Foundation for the Authors of National Excellent Doctoral Dissertation of China(Grant No 200136)
文摘The liquid-solid phase change process of a simple one-dimensional slab is studied in this paper.By taking entransy dissipation minimization as optimization objective,the optimal external reservoir temperature profiles are derived by using optimal control theory under the condition of a fixed freezing or melting time.The entransy dissipation corresponding to the optimal heat exchange strategies of minimum entransy dissipation is 8/9 of that corresponding to constant reservoir temperature operations,which is independent of all system parameters.The obtained results for entransy dissipation minimization are also compared with those obtained for the optimal heat exchange strategies of minimum entropy generation and constant reservoir temperature operations by numerical examples.The obtained results can provide some theoretical guidelines for the choice of optimal cooling or heating strategy in practical liquid-solid phase change processes.
基金supported by the National Natural Science Foundation of China(Grant Nos.51779262,51506220 and 51579244)。
文摘This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives,respectively,by combining the methods of theoretical analysis and numerical calculation.The eight types of heat sinks are uniform height rectangular fin heat sink,non-uniform height rectangular fin heat sink,inline cylindrical pin-fin heat sink(ICPHS),plate single-row pin fin heat sink(PSRPHS),plate inline pin fin heat sink(PIPHS),plate staggered pin fin heat sink(PSPHS),single-layered microchannel heat sink(SLMCHS)with rectangular cross sections and double-layered microchannel heat sink(DLMCHS)with rectangular cross sections,respectively.And the ten performance indexes are heat transfer rate maximization,maximum thermal resistance minimization,minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate(equivalent thermal resistance for short),field synergy number maximization,entropy generation rate minimization,operation cost minimization,thermo-economic function value minimization,pressure drop minimization,enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization,respectively.The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other.The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition.The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed.The results obtained herein have some important theoretical significances and application values,and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications.
基金supported by the National Natural Science Foundation of China (Grant No.10905093)the Program for New Century Excellent Talents in University of China (Grant No.NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No.200136)
文摘Umbrella-shaped assembly of cylindrical fins is optimized by adopting analytical method and taking dimensionless mean thermal resistance (MTR) as performance index. The optimal construct of umbrella-shaped assembly is obtained. The results show that the heat conductance performance of the assembly becomes ever worse with ever greater number of elemental cylindrical fins,the umbrella-shaped assembly reduces to cylindrical fin in some values of design parameters,and the diameters’ dependence on design parameters is weak for the optimized assembly. An equivalent thermal resistance defined based on entransy dissipation rate (EDR) reflects an average heat transfer effect of the assembly. The constructal design corresponding to the minimum EDR (or MTR) should be adopted for designing an assembly of fins in engineering at the limit safe condition.
基金supported by the National Natural Science Foundation of China(Grant Nos.51979278,51579244 and 51506220)。
文摘Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory.Three types of 3-D circular disc heat sink models,i.e.without collection microchannels,with center collection microchannels,and with edge collection microchannels,are established respectively.Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels,that of circular disc heat sink with center collection microchannels is the minimum,so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages.Furthermore,the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes.With the mass flow rate increasing,both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease.With the heat flux increasing,the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged.With the same mass flow rate and heat flux,the larger the microchannel branch number,the smaller the maximum thermal resistance.While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.
