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
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
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
Based on constructal theory,"disc-to-point" heat conduction is optimized by minimizing the entransy dissipation rate whereby a critical point is determined that distributes the high-conductivity material acc...Based on constructal theory,"disc-to-point" heat conduction is optimized by minimizing the entransy dissipation rate whereby a critical point is determined that distributes the high-conductivity material according to optimized radial or branch patterns.The results show that the critical point is determined by the product of the thermal conductivity ratio of the two materials and the volume fraction of the high-conductivity material allocated to the entire volume.The notion of optimal heat transfer performance can be attributed to the disc based on the entransy dissipation extremum principle.Comparing the results based on EDR minimization (entransy dissipation rate minimization) with those based on MTD minimization (maximum temperature difference minimization),one finds that the performance derived from the two optimization procedures are different.When the product of the thermal conductivity ratio and volume fraction is 30,the critical point of the former procedure is that for which the nondimensional radius of the disc equals 1.75,while that of the latter procedure is that for which this radius of the disc equals 2.18.Comparing heat transfer performances from the two procedures,the mean heat transfer temperature difference is decreased more for the former procedure thereby receiving an improved performance quota.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
The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For a heat transfer model of a rectangular solid wall with an open T-shaped cavity, a dimensionless eq...The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For a heat transfer model of a rectangular solid wall with an open T-shaped cavity, a dimensionless equivalent thermal resistance based on entransy dissipation is taken as optimization objective, and constructal optimization for the model is carried out when the system volume, the cavity volume and the volume of rectangle occupied by T-shaped cavity are fixed. Numerical results indicate that the optimal geometry construct of cavity can be schemed out based on entransy dissipation extremum principle. The formulation of dimensionless global (maximum) thermal resistance presented in a literature is modified; some new rules which are different from those reported in the literature are obtained based on the minimization of the modified objective. Comparisons of the numerical results show that the optimal system constructs deduced respectively from the two thermal resistance objectives are very different. The optimization by taking equivalent thermal resistance minimization as objective can more effectively reduce mean temperature difference of heat transfer than the optimization by taking maximum thermal resistance minimization as objective, so that the performance of heat transfer for the total system can be improved. The more freedom the cavity has, the better the total system performance is. The correlations of the equivalent thermal resistance and the maximum thermal resistance of the system and three geometric degrees of freedom are found by using function fitting.展开更多
The analysis of the “tree-like network” construct method has been repeated. The high effective conduction channel distribution has been optimized again, without the premise that the new order assembly construct must...The analysis of the “tree-like network” construct method has been repeated. The high effective conduction channel distribution has been optimized again, without the premise that the new order assembly construct must be assembled by the optimized last order construct. It is proved that the “tree-like network” construct method is faultiness. A more optimal construct is obtained,; when the thermal conductivity; the proportion of the two heat conduction materials are constant, the limit of the minimum heat resistance is derived. All these conclusions can be used to guide the engineering application.展开更多
For a vertical insulating wall,a product function of heat flow and strength with power weight is introduced as the complex optimization objective to compromise between insulating performance and mechanical performance...For a vertical insulating wall,a product function of heat flow and strength with power weight is introduced as the complex optimization objective to compromise between insulating performance and mechanical performance.Under the global constraints of fixed external dimensions and safety requirements,the constructal optimization of the wall is carried out by taking the complex function maximization as the objective.It is shown that the maximum of the complex-objective function and its corresponding optimal internal structure design under a certain environmental condition can be obtained by allowing the internal structure of the wall to vary(evolve)freely.The validity,effectivity and applicability of the complex function are proved by the results and the power weight parameter in the range from 0.4 to 4 can compromise between the requirements of insulating and strength simultaneously and preferably.The constructal optimization with coequal attention to heat flow and strength and the corresponding results are discussed in detail.The optimal structure design and the corresponding performance analyses under various environmental conditions of application are presented.When the change of environment is greater and the total Rayleigh number is bigger,the insulating wall with large number of cavities should be employed.When the total Rayleigh number is small,the better performance can be obtained by reasonably employing the insulating wall with small number of cavities.The complex function has better selfadaptability,and the results in the recent literature are special cases of this paper.展开更多
Entropy generation minimization for heat and mass transfer process in a solid-gas reactor is carried out based on constructal theory by using triangular elemental area. The aspect ratio of the triangular elemental are...Entropy generation minimization for heat and mass transfer process in a solid-gas reactor is carried out based on constructal theory by using triangular elemental area. The aspect ratio of the triangular elemental area is optimized under constraint conditions. A number of optimal triangular elements are assembled to a new large rectangular area, which is optimised again. The procedure is repeated until the control-volume is covered, and the complete analytical results are obtained. The effects of some parameters on minimum entropy generation are analysed by nu-merical examples. The results show that smaller entropy generation can be ob-tained when the optimization for a given volume is carried out on the basis of tri-angular elements than those obtained on the basis of rectangular elements.展开更多
In this paper,constructal optimization of the twice Y-shaped assemblies of fins with six freedom degrees (characteristic parameters of geometry) is performed by employing finite element method and taking dimensionless...In this paper,constructal optimization of the twice Y-shaped assemblies of fins with six freedom degrees (characteristic parameters of geometry) is performed by employing finite element method and taking dimensionless maximum thermal resistance as a performance index,and the heat transfer performance of the twice Y-shaped assemblies of fins under various conditions with different freedom degrees are analyzed. The results show that the twice assemblies can improve the heat transfer performance of Y-shaped fin remarkably,and the minimum maximum thermal resistance of the twice Y-shaped assemblies of fins decreases by 36.37% compared with that of once Y-shaped assembly of fins. It is also proved again that the larger the number of freedom degrees for evolving is,the more perfect the system performance is. The effects of different characteristic parameters of geometry on the performance of the twice Y-shaped assemblies of fins are different,one should pay different attention to these parameters in practical engineering designs. The effects of two angles on the maximum thermal resistance are larger,but the optima of the two angles are robust. The effects of two height ratios on the maximum thermal resistance are more remarkable than those of two thickness ratios.展开更多
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 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 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 (10905093)the Program for New Century Excellent Talents in University of China (NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation of China (200136)
文摘Based on constructal theory,"disc-to-point" heat conduction is optimized by minimizing the entransy dissipation rate whereby a critical point is determined that distributes the high-conductivity material according to optimized radial or branch patterns.The results show that the critical point is determined by the product of the thermal conductivity ratio of the two materials and the volume fraction of the high-conductivity material allocated to the entire volume.The notion of optimal heat transfer performance can be attributed to the disc based on the entransy dissipation extremum principle.Comparing the results based on EDR minimization (entransy dissipation rate minimization) with those based on MTD minimization (maximum temperature difference minimization),one finds that the performance derived from the two optimization procedures are different.When the product of the thermal conductivity ratio and volume fraction is 30,the critical point of the former procedure is that for which the nondimensional radius of the disc equals 1.75,while that of the latter procedure is that for which this radius of the disc equals 2.18.Comparing heat transfer performances from the two procedures,the mean heat transfer temperature difference is decreased more for the former procedure thereby receiving an improved performance quota.
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 Program for New Century Excellent Talents in Universities of China (Grant No. 20041006)Foundation for the Authors of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For a heat transfer model of a rectangular solid wall with an open T-shaped cavity, a dimensionless equivalent thermal resistance based on entransy dissipation is taken as optimization objective, and constructal optimization for the model is carried out when the system volume, the cavity volume and the volume of rectangle occupied by T-shaped cavity are fixed. Numerical results indicate that the optimal geometry construct of cavity can be schemed out based on entransy dissipation extremum principle. The formulation of dimensionless global (maximum) thermal resistance presented in a literature is modified; some new rules which are different from those reported in the literature are obtained based on the minimization of the modified objective. Comparisons of the numerical results show that the optimal system constructs deduced respectively from the two thermal resistance objectives are very different. The optimization by taking equivalent thermal resistance minimization as objective can more effectively reduce mean temperature difference of heat transfer than the optimization by taking maximum thermal resistance minimization as objective, so that the performance of heat transfer for the total system can be improved. The more freedom the cavity has, the better the total system performance is. The correlations of the equivalent thermal resistance and the maximum thermal resistance of the system and three geometric degrees of freedom are found by using function fitting.
文摘The analysis of the “tree-like network” construct method has been repeated. The high effective conduction channel distribution has been optimized again, without the premise that the new order assembly construct must be assembled by the optimized last order construct. It is proved that the “tree-like network” construct method is faultiness. A more optimal construct is obtained,; when the thermal conductivity; the proportion of the two heat conduction materials are constant, the limit of the minimum heat resistance is derived. All these conclusions can be used to guide the engineering application.
基金supported by the National Natural Science Foundation of China(Grant No.10905093)the Program for New Century Excellent Talents in University of China(Grant No.NCET-04-1006)the Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.200136)
文摘For a vertical insulating wall,a product function of heat flow and strength with power weight is introduced as the complex optimization objective to compromise between insulating performance and mechanical performance.Under the global constraints of fixed external dimensions and safety requirements,the constructal optimization of the wall is carried out by taking the complex function maximization as the objective.It is shown that the maximum of the complex-objective function and its corresponding optimal internal structure design under a certain environmental condition can be obtained by allowing the internal structure of the wall to vary(evolve)freely.The validity,effectivity and applicability of the complex function are proved by the results and the power weight parameter in the range from 0.4 to 4 can compromise between the requirements of insulating and strength simultaneously and preferably.The constructal optimization with coequal attention to heat flow and strength and the corresponding results are discussed in detail.The optimal structure design and the corresponding performance analyses under various environmental conditions of application are presented.When the change of environment is greater and the total Rayleigh number is bigger,the insulating wall with large number of cavities should be employed.When the total Rayleigh number is small,the better performance can be obtained by reasonably employing the insulating wall with small number of cavities.The complex function has better selfadaptability,and the results in the recent literature are special cases of this paper.
基金the Program for New Century Excellent Talents in Universities of China (Grant No. NCET-04-1006)Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200136)
文摘Entropy generation minimization for heat and mass transfer process in a solid-gas reactor is carried out based on constructal theory by using triangular elemental area. The aspect ratio of the triangular elemental area is optimized under constraint conditions. A number of optimal triangular elements are assembled to a new large rectangular area, which is optimised again. The procedure is repeated until the control-volume is covered, and the complete analytical results are obtained. The effects of some parameters on minimum entropy generation are analysed by nu-merical examples. The results show that smaller entropy generation can be ob-tained when the optimization for a given volume is carried out on the basis of tri-angular elements than those obtained on the basis of rectangular elements.
基金supported by the National Natural Science Foundation of China(Grant No.10905093)the Program for New Century Excellent Talents in University of China(Grant No.NCET-04-1006)the Foun-dation for the Author of National Excellent Doctoral Dissertation of China(Grant No.200136)
文摘In this paper,constructal optimization of the twice Y-shaped assemblies of fins with six freedom degrees (characteristic parameters of geometry) is performed by employing finite element method and taking dimensionless maximum thermal resistance as a performance index,and the heat transfer performance of the twice Y-shaped assemblies of fins under various conditions with different freedom degrees are analyzed. The results show that the twice assemblies can improve the heat transfer performance of Y-shaped fin remarkably,and the minimum maximum thermal resistance of the twice Y-shaped assemblies of fins decreases by 36.37% compared with that of once Y-shaped assembly of fins. It is also proved again that the larger the number of freedom degrees for evolving is,the more perfect the system performance is. The effects of different characteristic parameters of geometry on the performance of the twice Y-shaped assemblies of fins are different,one should pay different attention to these parameters in practical engineering designs. The effects of two angles on the maximum thermal resistance are larger,but the optima of the two angles are robust. The effects of two height ratios on the maximum thermal resistance are more remarkable than those of two thickness ratios.
