Based on the concept of the entransy which characterizes heat transfer ability, a new heat exchanger performance evaluation criterion termed the entransy dissipation number is established. Our analysis shows that the ...Based on the concept of the entransy which characterizes heat transfer ability, a new heat exchanger performance evaluation criterion termed the entransy dissipation number is established. Our analysis shows that the decrease of the entransy dissipation number always increases the heat exchanger effectiveness for fixed heat capacity rate ratio. Therefore, the smaller the entransy dissipation number, the better the heat exchanger performance is. The entransy dissipation number in terms of the number of exchanger heat transfer units or heat capacity rate ratio correctly exhibits the global performance of the counter-, cross-and parallel-flow heat exchangers. In comparison with the heat exchanger performance evaluation criteria based on entropy generation, the entransy dissipation number demon-strates some distinct advantages. Furthermore, the entransy dissipation number reflects the degree of irreversibility caused by flow imbalance.展开更多
The concepts of entransy flux and entransy dissipation in radiative heat transfer were introduced based on the analogy with heat conduction and heat convection processes. Entransy will be partially dissipated during t...The concepts of entransy flux and entransy dissipation in radiative heat transfer were introduced based on the analogy with heat conduction and heat convection processes. Entransy will be partially dissipated during the radiative heat transfer processes due to the irreversibility. The extremum principle of entransy dissipation was developed for optimizing radiative heat transfer processes. This principle states that for a fixed boundary temperature the radiative heat transfer is optimized when the entransy dissipation is maximized, while for a fixed boundary heat flux the radiative heat transfer process is optimized when the entransy dissipation is minimized. Finally, examples for the application of the entransy dissipation extre- mum principle are presented.展开更多
By taking equivalent thermal resistance, which reflects the average heat conduc- tion effect and is defined based on entransy dissipation, as optimization objective, the "volume to point" constructal problem...By taking equivalent thermal resistance, which reflects the average heat conduc- tion effect and is defined based on entransy dissipation, as optimization objective, the "volume to point" constructal problem of how to discharge the heat generated in a fixed volume to a heat sink on the border through relatively high conductive link is re-analyzed and re-optimized in this paper. The constructal shape of the control volume with the best average heat conduction effect is deduced. For the elemental area and the first order construct assembly, when the thermal current density in the high conductive link is linear with the length, the optimized shapes of assemble based on the minimization of entransy dissipation are the same as those based on minimization of maximum temperature difference, and the mean tem- perature difference is 2/3 of the maximum temperature difference. For the second and higher order construct assemblies, the thermal current densities in the high conductive link are not linear with the length, and the optimized shapes of assem- ble based on the minimization of entransy dissipation are different from those based on minimization of maximum temperature difference. For the same parame- ters, the constructs based on minimization of entransy dissipation and the con- structs based on minimization of maximum temperature difference are compared, and the results show that the constructs based on entransy dissipation can de- crease the mean temperature difference better than the constructs based on mini- mization of maximum temperature difference. But with the increase of the number of the order, the mean temperature difference does not always decrease, and there exist some fluctuations. Because the idea of entransy describes the heat transfer ability more suitably, all of the heat conduction constructal problems may be re-optimized based on it.展开更多
In the present work,a principle of equipartition of entransy dissipation(EoED) for heat exchanger design is established,which says that for a heat exchanger design with given heat duty and heat transfer area,the total...In the present work,a principle of equipartition of entransy dissipation(EoED) for heat exchanger design is established,which says that for a heat exchanger design with given heat duty and heat transfer area,the total entransy dissipation rate reaches the minimum when the local entransy dissipation rate is uniformly distributed along the heat exchanger.When the heat transfer coefficient is unfixed,the total entransy dissipation obtained by the EoED principle is less than that obtained by the principle of equipartition of temperature difference(EoTD).Furthermore,the exchanger effectiveness obtained by the EoED principle is larger than that obtained by the EoTD principle.When the heat transfer coefficient is fixed,the EoED principle is equivalent to the EoTD principle.We show that the equipartition of entropy production(EoEP) and EoED principles give rise to difference in entropy generation and entransy dissipation for a heat exchanger optimization design.The discrepancies are caused by distinct features of entropy production minimization and entransy dissipation minimization principles,the former is to optimize the design of heat exchanger by making the lost available work minimum,while the latter is not involved with heat-work conversion.It is found that the entropy generation number is not suitable for evaluating heat exchanger performance,since it directly depends on the inlet and outlet temperatures of working fluids.On the contrary,the entransy dissipation number is not directly related to the inlet and outlet temperatures of working fluids.Therefore,the entransy dissipation number is more suitable for serving as a criterion to evaluate heat exchanger performance.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
The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer.For two cases(body with heat generation and body heated externally)of a solid conducting wall with an o...The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer.For two cases(body with heat generation and body heated externally)of a solid conducting wall with an open cavity,a dimensionless equivalent thermal resistance based on entransy dissipation definition was taken as the optimization objective to optimize the model constructal ge- ometry.Numerical results validated the necessity and feasibility of the presented method.Comparisons of the numerical results based on minimization of dimensionless maximum thermal resistance and minimization of dimensionless equivalent thermal resistance,respectively,showed that there was no obvious difference between the two results when the volume fractionΦoccupied by cavity was small, but the difference between the two results increased with the increases ofΦand the body aspect ratio H/L for any model.The optimal cavities for bodies heated externally were more slender than those for bodies with heat generation.Heat origin had obvious effect on the global performance of heat transfer. The entransy dissipation of body heated externally increased 2―3 times than that of body with heat generation,indicating that the global performance of heat transfer weakened.The method presented herein provides some guidelines for some relevant thermal design problems.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
Based on entransy dissipation, the mean temperature difference of solenoid (electromagnet) with high thermal conductivity material inserted is deduced, which can be taken as the fundament for heat transfer optimizatio...Based on entransy dissipation, the mean temperature difference of solenoid (electromagnet) with high thermal conductivity material inserted is deduced, which can be taken as the fundament for heat transfer optimization using the extremum principle of entransy dissipation. Then, the electromagnet working at steady state (constant magnetic field, constant heat generating rate per unit volume) is optimized for entransy dissipation minimization (i.e. mean temperature difference minimization) with and without volume constraint. Besides, the effect of high thermal conductivity material on the magnetic field is analyzed, and the minimum mean temperature versus volume and magnetic induction characteristic are also studied.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
Based on constructal theory,a construct of a volume that generates heat at every point and is cooled by the coolant in the constant or tapered channel is optimized by minimizing entransy dissipation rate and flow resi...Based on constructal theory,a construct of a volume that generates heat at every point and is cooled by the coolant in the constant or tapered channel is optimized by minimizing entransy dissipation rate and flow resistance.The optimal constructs of the rectangular elements with dimensionless mean thermal resistance minimization as well as the first-,secondand thirdorder assemblies with dimensionless global flow resistance minimizations are obtained respectively.The results show that both the mean temperature difference and the limiting temperature difference of rectangular elements based on EDR (entransy dissipation rate) and MTD (maximum temperature difference) minimizations respectively are almost equal.Comparing heat transfer performances from the two optimization procedures,the dimensionless global flow resistance is decreased more for the former procedure when the assembly’s order is high.It may create great superiority for constructal optimization to combine the entransy dissipation extreme principle with heat convection.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
In this paper, the physical basis and application conditions of the entransy theory are reviewed and discussed. Entransy can be obtained from the analogy between heat and electrical conductions. It is a state value an...In this paper, the physical basis and application conditions of the entransy theory are reviewed and discussed. Entransy can be obtained from the analogy between heat and electrical conductions. It is a state value and the‘‘potential energy'' of heat. From the viewpoint of thermomass, it reflects the thermal energy of the thermomass in an object. Furthermore, it was also related to the microstate number and is a single value function of the microstate number. The concepts of entransy, entransy flux and entransy dissipation can be used to express the least action of heat transfer. The entransy balance equations for heat transfer and thermodynamic processes and their applications to thermal systems are also reviewed. The differences between the entransy theory, constructal theory, entropy generation minimization, exergy analyses method, principle of uniformity of temperature difference field and field synergy(coordination) principle are also discussed. The entransy theory is different from the other discussed theories. The limitations of the entransy theory are also discussed.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
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
The spectral radiative entransy flux and the total radiative entransy flux are defined for the steady radiative heat transfer processes in enclosures composed of non-isothermal or non-grey, opaque, diffuse surfaces. B...The spectral radiative entransy flux and the total radiative entransy flux are defined for the steady radiative heat transfer processes in enclosures composed of non-isothermal or non-grey, opaque, diffuse surfaces. Based on the definitions, the radiative entransy flux balance equation and the radiative entransy dissipation functions are introduced under spectral and total wavelength condition. Furthermore, the minimum principle of radiative entransy loss, the extreme principle of radiative entransy dissipation and the minimum principle of radiative thermal resistance are developed. The minimum prirlciple of radiative en- transy loss shows that the potential and the net radiative heat flux distribution which meet the control equations and the boundary conditions would make the radiative entransy loss minimum if the net radiative heat flux or the potential distribution of the radiative heat transfer system is given. The extreme principle of radiative entransy dissipation indicates that the minimum radiative entransy dissipation leads to the minimum average potential difference for the prescribed total radiative heat exchange and the maximum radiative entransy dissipation leads to the maximum radiative heat exchange for the prescribed average potential difference. Moreover, the minimum principle of radiative thermal resistance tells us that the aforementioned extreme values of radiative entransy dissipation both correspond to the minimum value of radiative thermal resistance. Application examples are given for the extreme principle of spectral radiative entransy dissipation and the minimum principle of spectral radiative thermal resistance, and the principles are proved to be applicable.展开更多
Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation ...Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation and entransy loss evaluation in these optimization problems is analyzed and discussed.The results show that the entransy loss rate reduces to the entransy dissipation rate in heat transfer processes,and that the entransy loss evaluation is effective for heat transfer optimization.However,the maximum heat transfer rate does not correspond to the minimum entropy generation rate with prescribed heat transfer temperature difference,which indicates that the entropy generation minimization is not always appropriate to heat transfer optimization.For heat-work conversion processes,the maximum entransy loss rate and the minimum entropy generation rate both correspond to the maximum output power,and they are both appropriate to the optimization of the heat-work conversion processes discussed in this paper.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
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 tran展开更多
For distribution optimization of the flow rate of cold fluid and heat transfer area in the parallel thermal network of the thermal control system in spacecraft,a physical and mathematical model is set up,analyzed and ...For distribution optimization of the flow rate of cold fluid and heat transfer area in the parallel thermal network of the thermal control system in spacecraft,a physical and mathematical model is set up,analyzed and discussed with the entransy theory.It is found that the optimization objective of this problem and the optimization direction of the extremum entransy dissipation principle are consistent in theory.For a two-branch thermal network system,the distributions of the flow rate of the cold fluid and the heat transfer area are optimized by calculating the extremum entransy dissipation with the Newton method.The influential factors of the optimized distributions are also analyzed and discussed.The results show that the main influence factors are the heat transfer rate of the branches and the total heat transfer area.The total flow rate of the cold fluid has a threshold,beyond which further increasing its value brings very little influence on the optimization results.Moreover,the difference between the extremum entransy dissipation principle and the minimum entropy generation principle is also discussed when they are used to analyze the problem in this paper,and the extremum entransy dissipation principle is found to be more suitable.In addition,the Newton method is mathematically efficient to solve the problem,which could accomplish the optimized distribution in a very short time for a ten-branch thermal network system.展开更多
基金Supported by the National Basic Research Program of China (Grant No. 2007CB206900)
文摘Based on the concept of the entransy which characterizes heat transfer ability, a new heat exchanger performance evaluation criterion termed the entransy dissipation number is established. Our analysis shows that the decrease of the entransy dissipation number always increases the heat exchanger effectiveness for fixed heat capacity rate ratio. Therefore, the smaller the entransy dissipation number, the better the heat exchanger performance is. The entransy dissipation number in terms of the number of exchanger heat transfer units or heat capacity rate ratio correctly exhibits the global performance of the counter-, cross-and parallel-flow heat exchangers. In comparison with the heat exchanger performance evaluation criteria based on entropy generation, the entransy dissipation number demon-strates some distinct advantages. Furthermore, the entransy dissipation number reflects the degree of irreversibility caused by flow imbalance.
基金Supported by the National Basic Research Program of China ("973" Project) (Grant No. 2007CB206901)
文摘The concepts of entransy flux and entransy dissipation in radiative heat transfer were introduced based on the analogy with heat conduction and heat convection processes. Entransy will be partially dissipated during the radiative heat transfer processes due to the irreversibility. The extremum principle of entransy dissipation was developed for optimizing radiative heat transfer processes. This principle states that for a fixed boundary temperature the radiative heat transfer is optimized when the entransy dissipation is maximized, while for a fixed boundary heat flux the radiative heat transfer process is optimized when the entransy dissipation is minimized. Finally, examples for the application of the entransy dissipation extre- mum principle are presented.
基金Supported by the Program for New Century Excellent Talents in University of Chinathe Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘By taking equivalent thermal resistance, which reflects the average heat conduc- tion effect and is defined based on entransy dissipation, as optimization objective, the "volume to point" constructal problem of how to discharge the heat generated in a fixed volume to a heat sink on the border through relatively high conductive link is re-analyzed and re-optimized in this paper. The constructal shape of the control volume with the best average heat conduction effect is deduced. For the elemental area and the first order construct assembly, when the thermal current density in the high conductive link is linear with the length, the optimized shapes of assemble based on the minimization of entransy dissipation are the same as those based on minimization of maximum temperature difference, and the mean tem- perature difference is 2/3 of the maximum temperature difference. For the second and higher order construct assemblies, the thermal current densities in the high conductive link are not linear with the length, and the optimized shapes of assem- ble based on the minimization of entransy dissipation are different from those based on minimization of maximum temperature difference. For the same parame- ters, the constructs based on minimization of entransy dissipation and the con- structs based on minimization of maximum temperature difference are compared, and the results show that the constructs based on entransy dissipation can de- crease the mean temperature difference better than the constructs based on mini- mization of maximum temperature difference. But with the increase of the number of the order, the mean temperature difference does not always decrease, and there exist some fluctuations. Because the idea of entransy describes the heat transfer ability more suitably, all of the heat conduction constructal problems may be re-optimized based on it.
基金supported by the National Basic Research Program of China ("973" Program) (Grant No.2007CB206900)
文摘In the present work,a principle of equipartition of entransy dissipation(EoED) for heat exchanger design is established,which says that for a heat exchanger design with given heat duty and heat transfer area,the total entransy dissipation rate reaches the minimum when the local entransy dissipation rate is uniformly distributed along the heat exchanger.When the heat transfer coefficient is unfixed,the total entransy dissipation obtained by the EoED principle is less than that obtained by the principle of equipartition of temperature difference(EoTD).Furthermore,the exchanger effectiveness obtained by the EoED principle is larger than that obtained by the EoTD principle.When the heat transfer coefficient is fixed,the EoED principle is equivalent to the EoTD principle.We show that the equipartition of entropy production(EoEP) and EoED principles give rise to difference in entropy generation and entransy dissipation for a heat exchanger optimization design.The discrepancies are caused by distinct features of entropy production minimization and entransy dissipation minimization principles,the former is to optimize the design of heat exchanger by making the lost available work minimum,while the latter is not involved with heat-work conversion.It is found that the entropy generation number is not suitable for evaluating heat exchanger performance,since it directly depends on the inlet and outlet temperatures of working fluids.On the contrary,the entransy dissipation number is not directly related to the inlet and outlet temperatures of working fluids.Therefore,the entransy dissipation number is more suitable for serving as a criterion to evaluate heat exchanger performance.
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 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 entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer.For two cases(body with heat generation and body heated externally)of a solid conducting wall with an open cavity,a dimensionless equivalent thermal resistance based on entransy dissipation definition was taken as the optimization objective to optimize the model constructal ge- ometry.Numerical results validated the necessity and feasibility of the presented method.Comparisons of the numerical results based on minimization of dimensionless maximum thermal resistance and minimization of dimensionless equivalent thermal resistance,respectively,showed that there was no obvious difference between the two results when the volume fractionΦoccupied by cavity was small, but the difference between the two results increased with the increases ofΦand the body aspect ratio H/L for any model.The optimal cavities for bodies heated externally were more slender than those for bodies with heat generation.Heat origin had obvious effect on the global performance of heat transfer. The entransy dissipation of body heated externally increased 2―3 times than that of body with heat generation,indicating that the global performance of heat transfer weakened.The method presented herein provides some guidelines for some relevant thermal design problems.
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 Program for New Century Excellent Talents in University of China (Grant No. NCET-04-1006)Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘Based on entransy dissipation, the mean temperature difference of solenoid (electromagnet) with high thermal conductivity material inserted is deduced, which can be taken as the fundament for heat transfer optimization using the extremum principle of entransy dissipation. Then, the electromagnet working at steady state (constant magnetic field, constant heat generating rate per unit volume) is optimized for entransy dissipation minimization (i.e. mean temperature difference minimization) with and without volume constraint. Besides, the effect of high thermal conductivity material on the magnetic field is analyzed, and the minimum mean temperature versus volume and magnetic induction characteristic are also studied.
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Based on constructal theory,a construct of a volume that generates heat at every point and is cooled by the coolant in the constant or tapered channel is optimized by minimizing entransy dissipation rate and flow resistance.The optimal constructs of the rectangular elements with dimensionless mean thermal resistance minimization as well as the first-,secondand thirdorder assemblies with dimensionless global flow resistance minimizations are obtained respectively.The results show that both the mean temperature difference and the limiting temperature difference of rectangular elements based on EDR (entransy dissipation rate) and MTD (maximum temperature difference) minimizations respectively are almost equal.Comparing heat transfer performances from the two optimization procedures,the dimensionless global flow resistance is decreased more for the former procedure when the assembly’s order is high.It may create great superiority for constructal optimization to combine the entransy dissipation extreme principle with heat convection.
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(51376101)
文摘In this paper, the physical basis and application conditions of the entransy theory are reviewed and discussed. Entransy can be obtained from the analogy between heat and electrical conductions. It is a state value and the‘‘potential energy'' of heat. From the viewpoint of thermomass, it reflects the thermal energy of the thermomass in an object. Furthermore, it was also related to the microstate number and is a single value function of the microstate number. The concepts of entransy, entransy flux and entransy dissipation can be used to express the least action of heat transfer. The entransy balance equations for heat transfer and thermodynamic processes and their applications to thermal systems are also reviewed. The differences between the entransy theory, constructal theory, entropy generation minimization, exergy analyses method, principle of uniformity of temperature difference field and field synergy(coordination) principle are also discussed. The entransy theory is different from the other discussed theories. The limitations of the entransy theory are also discussed.
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 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 Tsinghua University Initiative Scientific Research Program
文摘The spectral radiative entransy flux and the total radiative entransy flux are defined for the steady radiative heat transfer processes in enclosures composed of non-isothermal or non-grey, opaque, diffuse surfaces. Based on the definitions, the radiative entransy flux balance equation and the radiative entransy dissipation functions are introduced under spectral and total wavelength condition. Furthermore, the minimum principle of radiative entransy loss, the extreme principle of radiative entransy dissipation and the minimum principle of radiative thermal resistance are developed. The minimum prirlciple of radiative en- transy loss shows that the potential and the net radiative heat flux distribution which meet the control equations and the boundary conditions would make the radiative entransy loss minimum if the net radiative heat flux or the potential distribution of the radiative heat transfer system is given. The extreme principle of radiative entransy dissipation indicates that the minimum radiative entransy dissipation leads to the minimum average potential difference for the prescribed total radiative heat exchange and the maximum radiative entransy dissipation leads to the maximum radiative heat exchange for the prescribed average potential difference. Moreover, the minimum principle of radiative thermal resistance tells us that the aforementioned extreme values of radiative entransy dissipation both correspond to the minimum value of radiative thermal resistance. Application examples are given for the extreme principle of spectral radiative entransy dissipation and the minimum principle of spectral radiative thermal resistance, and the principles are proved to be applicable.
基金supported by the Natural Science Foundation of China(Grant No. 51136001)the Tsinghua University Initiative ScientificResearch Program
文摘Examples of heat transfer and heat-work conversion are optimized with entropy generation and entransy loss,respectively based on the generalized heat transfer law in this paper.The applicability of entropy generation and entransy loss evaluation in these optimization problems is analyzed and discussed.The results show that the entransy loss rate reduces to the entransy dissipation rate in heat transfer processes,and that the entransy loss evaluation is effective for heat transfer optimization.However,the maximum heat transfer rate does not correspond to the minimum entropy generation rate with prescribed heat transfer temperature difference,which indicates that the entropy generation minimization is not always appropriate to heat transfer optimization.For heat-work conversion processes,the maximum entransy loss rate and the minimum entropy generation rate both correspond to the maximum output power,and they are both appropriate to the optimization of the heat-work conversion processes discussed in this paper.
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. 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 tran
基金supported by Tsinghua University Initiative Scientific Research Program
文摘For distribution optimization of the flow rate of cold fluid and heat transfer area in the parallel thermal network of the thermal control system in spacecraft,a physical and mathematical model is set up,analyzed and discussed with the entransy theory.It is found that the optimization objective of this problem and the optimization direction of the extremum entransy dissipation principle are consistent in theory.For a two-branch thermal network system,the distributions of the flow rate of the cold fluid and the heat transfer area are optimized by calculating the extremum entransy dissipation with the Newton method.The influential factors of the optimized distributions are also analyzed and discussed.The results show that the main influence factors are the heat transfer rate of the branches and the total heat transfer area.The total flow rate of the cold fluid has a threshold,beyond which further increasing its value brings very little influence on the optimization results.Moreover,the difference between the extremum entransy dissipation principle and the minimum entropy generation principle is also discussed when they are used to analyze the problem in this paper,and the extremum entransy dissipation principle is found to be more suitable.In addition,the Newton method is mathematically efficient to solve the problem,which could accomplish the optimized distribution in a very short time for a ten-branch thermal network system.
