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 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 ...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
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
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 op...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
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 te...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 th...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
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
Based on constructal theory,the constructs of the leaf-like fins are optimized by taking minimum entransy dissipation rate(for the fixed total thermal current,i.e.,the equivalent thermal resistance) as optimization ob...Based on constructal theory,the constructs of the leaf-like fins are optimized by taking minimum entransy dissipation rate(for the fixed total thermal current,i.e.,the equivalent thermal resistance) as optimization objective.The optimal constructs of the leaf-like fins with minimum dimensionless equivalent thermal resistance are obtained.The results show that there exists an optimal elemental leaf-like fin number,which leads to an optimal global heat conduction performance of the first order leaf-like fin.The Biot number has little effects on the optimal elemental fin number,optimal ratios of length and width of the elemental and first order leaf-like fins;with the increase of the thermal conductivity ratio of the vein and blade,the optimal elemental fin number and optimal ratio of the length and width of the elemental leaf-like fin increase,and the optimal shape of the first order leaf-like fin becomes tubbier.The optimal construct based on entransy dissipation rate minimization is obviously different from that based on maximum temperature difference minimization.The dimensionless equivalent thermal resistance based on entransy dissipation rate minimization is reduced by 11.54% compared to that based on maximum temperature difference minimization,and the global heat conduction performance of the leaf-like fin is effectively improved.For the same volumes of the elemental and first order leaf-like fins,the minimum dimensionless equivalent thermal resistance of the first order of the leaf-like fin is reduced by 30.10% compared to that of the elemental leaf-like fin,and the global heat conduction performance of the first order leaf-like fin is obviously better than that of the elemental leaf-like fin.Essentially,this is because the temperature gradient field of the first order leaf-like fin based on entransy dissipation rate minimization is more homogenous than that of the elemental leaf-like fin.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the leaf-like fin,and can provide some guidelines for the thermal design of the fins from the viewpoint of heat transfer optimization.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 m...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
A model of three-dimensional helm-shaped body composed of a helm-shaped fin and inner heat sources is built in this paper. For the specified volumes of the body, fin and heat source, the constructal optimizations of t...A model of three-dimensional helm-shaped body composed of a helm-shaped fin and inner heat sources is built in this paper. For the specified volumes of the body, fin and heat source, the constructal optimizations of the body with single and multiple inner heat sources are implemented. The entransy-dissipation-rate-based equivalent thermal resistance(ETR) is minimized in the optimizations. It shows that for the helm-shaped body with multiple inner heat sources, there exist an optimal ratio of the heat source distance to the radius of the extended fin and a twice optimal radius ratio of the centre fin to the extended fin which lead to the double minimum dimensionless ETR. Comparing the optimal result of the body with helm-shaped fin with that with annular fin, the radius of the centre fin and the distance between the heat source and the center of the body are decreased, and the ETR is decreased by 9.57%. Essentially, the temperature gradient field of the helm-shaped body is more homogenous, and its global heat transfer performance is improved.展开更多
A three-dimensional disc model with non-uniform heat generating is built.A series of cooling channels are inserted to cool this disc which is strewn in a hierarchical pattern.To reveal thermal and flow characteristics...A three-dimensional disc model with non-uniform heat generating is built.A series of cooling channels are inserted to cool this disc which is strewn in a hierarchical pattern.To reveal thermal and flow characteristics,a composite objective function comprised of the maximum temperature difference(MTD)and pumping power is constructed.The deployment pattern of cooling channels contains two cases,i.e.,the radial-pattern and dendritic-pattern.By capitalizing on constructal design method together with finite element method,the diameter of radial-pattern cooling channels is optimized in the first place.Next,the diameter,angle coefficient and length coefficient of dendritic-pattern cooling channels are three degrees-of-freedom to be stepwise optimized at different heat generating conditions.Furthermore,NSGA-II algorithm is introduced into the multiobjective problem.Upon obtaining its Pareto optimal solution set,Topsis method is invoked to yield the optimal solutions under given weighted coefficients.The heat generation over the entire body and the volume ratio of cooling channels operate as the primary constraints.Based on these premises,constructal design will be stepwise performed by varying three degrees-offreedom.The obtained results state that more heating components or devices should be installed as close to the cooling water inlet as possible.This can further reduce MTD at the same cost of pumping power,thereby improve thermal and flow performance and prolong the lifespan of devices.As optimized with two degrees-of-freedom,the MTD is reduced by 18.6%compared with the counterpart obtained from single degree-of-freedom optimization,while the pumping power is increased by 59.8%.As optimized with three degrees-of-freedom,the MTD is decreased by 6.2%compared with the counterpart from two degrees-of-freedom optimization,while the pumping power is increased by 3.0%.It is manifest that when two sub-objectives form a composite objective,the performance improvement of one sub-objective will inevitably elicit the vitiation of the alternative.展开更多
Steam generator is optimized by applying entransy dissipation extremum principle and constructal theory and adopting analyti-cal method.The obtained results show that the optimal spacing between adjacent tubes,the mas...Steam generator is optimized by applying entransy dissipation extremum principle and constructal theory and adopting analyti-cal method.The obtained results show that the optimal spacing between adjacent tubes,the mass flow rate of gas and the maximum entransy dissipation rate all depend on the dimensionless diameter of one tube,the dimensionless pressure difference number and the dimensionless length of flow channel of gas.Besides the three dimensionless groups,the optimal numbers of riser tubes and downcomer tubes and their summation all depend on the dimensionless height of one tube.The maximum entransy dissipation rate increases as the pressure difference that drives the gas flowing increases,and as the diameter of one tube and the length of flow channel both decrease.The mean heat flux in the heat transfer process of hot gas grows greatly,and the performance of the system is improved.Compared with the optimal construct with heat transfer rate maximization,the optimal construct with entransy dissipation rate maximization can improved the heat transfer effect of the steam generator more.展开更多
Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized,...Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives(EDR minimization and entropy generation rate(EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate(DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network(HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number(EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.展开更多
Based on construtal theory, a nonuniform heat generation problem in a rectangular body is investigated in this paper. Entransy dissipation rate(EDR) is taken as the optimization objective. The optimal body shapes with...Based on construtal theory, a nonuniform heat generation problem in a rectangular body is investigated in this paper. Entransy dissipation rate(EDR) is taken as the optimization objective. The optimal body shapes with constant and variable widths of the high conductivity channel(HCC) are derived. For the rectangular first order assembly(RFOA) with constant cross-section HCC, the shape of the RFOA and width ratio of the HCCs are optimized, and the double minimum EDR is obtained. The heat transfer performance of the RFOA becomes worse when the nonuniform coefficient increases. For the RFOA with variable cross-section HCC, the EDR of the RFOA can be minimized for four times. Compared the optimal construct based on minimum EDR of the RFOA with that based on minimum maximum temperature difference, the shape of the former optimal construct is tubbier, and the average temperature difference is lower. In the practical design of electronic devices, when the thermal safety is ensured, the constructal design scheme of the former optimal construct can be adopted to improve the global heat transfer performance of an electronic device.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 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 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. 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 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(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 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 the leaf-like fins are optimized by taking minimum entransy dissipation rate(for the fixed total thermal current,i.e.,the equivalent thermal resistance) as optimization objective.The optimal constructs of the leaf-like fins with minimum dimensionless equivalent thermal resistance are obtained.The results show that there exists an optimal elemental leaf-like fin number,which leads to an optimal global heat conduction performance of the first order leaf-like fin.The Biot number has little effects on the optimal elemental fin number,optimal ratios of length and width of the elemental and first order leaf-like fins;with the increase of the thermal conductivity ratio of the vein and blade,the optimal elemental fin number and optimal ratio of the length and width of the elemental leaf-like fin increase,and the optimal shape of the first order leaf-like fin becomes tubbier.The optimal construct based on entransy dissipation rate minimization is obviously different from that based on maximum temperature difference minimization.The dimensionless equivalent thermal resistance based on entransy dissipation rate minimization is reduced by 11.54% compared to that based on maximum temperature difference minimization,and the global heat conduction performance of the leaf-like fin is effectively improved.For the same volumes of the elemental and first order leaf-like fins,the minimum dimensionless equivalent thermal resistance of the first order of the leaf-like fin is reduced by 30.10% compared to that of the elemental leaf-like fin,and the global heat conduction performance of the first order leaf-like fin is obviously better than that of the elemental leaf-like fin.Essentially,this is because the temperature gradient field of the first order leaf-like fin based on entransy dissipation rate minimization is more homogenous than that of the elemental leaf-like fin.The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the leaf-like fin,and can provide some guidelines for the thermal design of the fins from the viewpoint of heat transfer optimization.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.51176203 and 51356001)the Natural Science Foundation for Youngsters of Naval University of Engineering(Grant No.HGDQNJJ15007)
文摘A model of three-dimensional helm-shaped body composed of a helm-shaped fin and inner heat sources is built in this paper. For the specified volumes of the body, fin and heat source, the constructal optimizations of the body with single and multiple inner heat sources are implemented. The entransy-dissipation-rate-based equivalent thermal resistance(ETR) is minimized in the optimizations. It shows that for the helm-shaped body with multiple inner heat sources, there exist an optimal ratio of the heat source distance to the radius of the extended fin and a twice optimal radius ratio of the centre fin to the extended fin which lead to the double minimum dimensionless ETR. Comparing the optimal result of the body with helm-shaped fin with that with annular fin, the radius of the centre fin and the distance between the heat source and the center of the body are decreased, and the ETR is decreased by 9.57%. Essentially, the temperature gradient field of the helm-shaped body is more homogenous, and its global heat transfer performance is improved.
基金supported by the National Natural Science Foundation of China(Grant Nos.51779262 and 51579244)the Independent Project of Naval University of Engineering(Grant No.425317Q017)。
文摘A three-dimensional disc model with non-uniform heat generating is built.A series of cooling channels are inserted to cool this disc which is strewn in a hierarchical pattern.To reveal thermal and flow characteristics,a composite objective function comprised of the maximum temperature difference(MTD)and pumping power is constructed.The deployment pattern of cooling channels contains two cases,i.e.,the radial-pattern and dendritic-pattern.By capitalizing on constructal design method together with finite element method,the diameter of radial-pattern cooling channels is optimized in the first place.Next,the diameter,angle coefficient and length coefficient of dendritic-pattern cooling channels are three degrees-of-freedom to be stepwise optimized at different heat generating conditions.Furthermore,NSGA-II algorithm is introduced into the multiobjective problem.Upon obtaining its Pareto optimal solution set,Topsis method is invoked to yield the optimal solutions under given weighted coefficients.The heat generation over the entire body and the volume ratio of cooling channels operate as the primary constraints.Based on these premises,constructal design will be stepwise performed by varying three degrees-offreedom.The obtained results state that more heating components or devices should be installed as close to the cooling water inlet as possible.This can further reduce MTD at the same cost of pumping power,thereby improve thermal and flow performance and prolong the lifespan of devices.As optimized with two degrees-of-freedom,the MTD is reduced by 18.6%compared with the counterpart obtained from single degree-of-freedom optimization,while the pumping power is increased by 59.8%.As optimized with three degrees-of-freedom,the MTD is decreased by 6.2%compared with the counterpart from two degrees-of-freedom optimization,while the pumping power is increased by 3.0%.It is manifest that when two sub-objectives form a composite objective,the performance improvement of one sub-objective will inevitably elicit the vitiation of the alternative.
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Steam generator is optimized by applying entransy dissipation extremum principle and constructal theory and adopting analyti-cal method.The obtained results show that the optimal spacing between adjacent tubes,the mass flow rate of gas and the maximum entransy dissipation rate all depend on the dimensionless diameter of one tube,the dimensionless pressure difference number and the dimensionless length of flow channel of gas.Besides the three dimensionless groups,the optimal numbers of riser tubes and downcomer tubes and their summation all depend on the dimensionless height of one tube.The maximum entransy dissipation rate increases as the pressure difference that drives the gas flowing increases,and as the diameter of one tube and the length of flow channel both decrease.The mean heat flux in the heat transfer process of hot gas grows greatly,and the performance of the system is improved.Compared with the optimal construct with heat transfer rate maximization,the optimal construct with entransy dissipation rate maximization can improved the heat transfer effect of the steam generator more.
基金supported by the National Natural Science Foundation of China(Grant Nos.51506220,51579244)the Natural Science Foundation of Hubei Province(Grant No.2016CFB504)the Independent Project of Naval University of Engineering(Grant No.425317Q017)
文摘Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives(EDR minimization and entropy generation rate(EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate(DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network(HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number(EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51506220, 51579244 and 51356001)
文摘Based on construtal theory, a nonuniform heat generation problem in a rectangular body is investigated in this paper. Entransy dissipation rate(EDR) is taken as the optimization objective. The optimal body shapes with constant and variable widths of the high conductivity channel(HCC) are derived. For the rectangular first order assembly(RFOA) with constant cross-section HCC, the shape of the RFOA and width ratio of the HCCs are optimized, and the double minimum EDR is obtained. The heat transfer performance of the RFOA becomes worse when the nonuniform coefficient increases. For the RFOA with variable cross-section HCC, the EDR of the RFOA can be minimized for four times. Compared the optimal construct based on minimum EDR of the RFOA with that based on minimum maximum temperature difference, the shape of the former optimal construct is tubbier, and the average temperature difference is lower. In the practical design of electronic devices, when the thermal safety is ensured, the constructal design scheme of the former optimal construct can be adopted to improve the global heat transfer performance of an electronic device.
