Constructal entransy dissipation rate minimization for ＂disc-to-point＂ heat conduction

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.     

Constructal entransy dissipation rate minimization for heat conduction based on a tapered element

Based on constructal theory,the structure of a tapered element and high-conductivity link is optimized by taking the minimization of the entransy dissipation rate as the optimization objective.The results show that the mean temperature difference of the heat transfer cannot always decrease when the internal complexity of the control-volume increases.There exists an optimal constructal order leading to the minimum mean temperature difference for heat transfer.The thermal current density in high-conductivity links with variable shapes does not linearly depend on the length.Therefore,the optimized constructs based on the minimization of the entransy dissipation rate are different from those based on the minimization of the maximum temperature difference.Compared with the construct based on the minimization of the maximum temperature difference,the construct based on the minimization of the entransy dissipation rate can reduce the mean temperature difference,and improve the heat transfer performance significantly.Because entransy describes the heat transfer ability more suitably,various constructal problems in heat conduction may be addressed more effectively using this basis.     

Constructal optimization on T-shaped cavity based on entransy dissipation minimization

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.     

Constructal entransy optimizations for insulation layer of steel rolling reheating furnace wall with convective and radiative boundary conditions

Based on the entransy dissipation extremum principle for thermal insulation process, the constructal optimizations for a plane insulation layer of the steel rolling reheating furnace wall with convective and radiative boundary conditions are carried out by taking the minimization of entransy dissipation rate as optimization objective. The optimal construct of the plane insulation layer is obtained. The results show that for the convective heat transfer boundary condition, the optimal constructs of the insulation layer obtained based on the minimizations of the entransy dissipation rate and heat loss rate are obvi- ously different. Comparing the optimal construct obtained based on the minimization of the entransy dissipation rate with that based on the minimization of the heat loss rate, the entransy dissipation rate is reduced by 5.98 %, which makes the global thermal insulation performance of the insulation layer improve. For the combined convective and radiative heat transfer boundary condition, compared the insulation layer having an increasing thickness with that having constant thickness and a decreasing thickness, the entransy dissipation rates are reduced by 16.59 % and 39.72 %, respectively, and the global thermal insulation performance of the insulation layer is greatly improved.There exits an optimal constant coefficient α2,opt which leads to the minimum dimensionless entransy dissipation rate of the insulation layer. The difference between the optimal constant coefficients α2,opt obtained based on the minimizations of the entransy dissipation rate and the maximum temperature gradient of the insulation layer is small. This makes the corresponding thermal stress obtained based on the minimum dimensionless entransy dissipation rate also be small, and the global thermal insulation performance and thermal safety of the insulation layer are improved simultaneously. The results obtained can provide some guidelines for the optimal designs of the insulation layers.     

The entransy dissipation minimization principle under given heat duty and heat transfer area conditions

Under given heat duty and heat transfer area conditions, the equipartition of the entransy dissipation (EoED) principle, the equipartition of the temperature difference (EoTD) principle, and the equipartition of the heat flux (EoHF) principle are applied to the optimization design of a heat exchanger with a variable heat transfer coefficient. The results show that the difference between the results obtained using the EoED and EoTD principles is very small, far smaller than that between the results obtained using the EoED and EoHF principles. The correct entransy dissipation minimization principle is chosen to optimize the parameters in the hot and cold fluids in a two-fluid heat exchanger, under given heat duty and heat transfer area conditions. The results indicate that the proper choice of the two alternative fluids has an important role in the successful application of the entransy dissipation minimization principle. The fluid that could improve the total heat transfer coefficient should be chosen, or the fluid that makes the temperature profiles of the hot and cold fluids parallel and decreases the temperature difference between the hot and cold fluids after optimization simultaneously, could be the proper one.     

Optimization of flue gas turbulent heat transfer with condensation in a tube

Conservation equations for sensible and latent entransy are established for flue gas turbulent heat transfer with condensation in a tube, and the entransy dissipation expression is deduced. The field synergy equation is obtained on the basis of the extremum entransy dissipation principle for flue gas turbulent heat transfer with condensation. The optimal velocity field is numerically obtained by solving the field synergy equation. The results show that the optimal velocity field contains multiple longitudinal vortices near the tube surface. These improve the synergy not only between the velocity and temperature fields but also between the velocity and vapor concentration fields. Therefore, the turbulent heat and mass transfers are significantly enhanced.     

Optimization of flue gas convective heat transfer with condensation in a rectangular channel

Conservation equations of sensible entarnsy and latent entransy are established for flue gas convective heat transfer with condensation in a rectangular channel and the entransy dissipation expression is deduced. The field synergy equation is obtained on the basis of the extremum entransy dissipation principle for flue gas convective heat transfer with condensation. The optimal velocity field is numerically obtained by solving the field synergy equation. The results show that the optimal velocity field has multiple longitudinal vortices, which improve the synergy not only between the veloctiy and temperature fields but also between the velocity and vapor concentration fields. Therefore, the convective heat and mass transfers are significantly enhanced. Flow with multiple longitudinal vortices close to the optimal velocity field can be generated by discrete double-inclined ribs set in the rectangular channel. The numerical results show that the total heat transfer rate in the discrete double-inclined rib channel increases by 29.02% and the condensing heat transfer rate increases by 27.46% for Re = 600 compared with the plain channel.     

An equation of entransy transfer and its application

Entransy is a physical quantity describing heat transfer ability, and heat transfer is accompanied by entransy transfer. Thermal energy is conserved in its transfer process, while entransy is dissipated because of the irreversibility of its transfer process. As a result, entransy transfer must have its rules which are different from those of thermal energy transfer. Based on the definition of entransy, an entransy transfer equation is derived, which describes the entransy transfer processes of a multi-component viscous fluid subject to heat transfer by conduction and convection, mass diffusion and chemical reactions. The expressions of entransy flux and entransy dissipation are obtained simultaneously, and their physical mechanism is clarified. And further, the theory and method of optimizing heat transfer applying the entransy transfer equation to the steady-state convection heat transfer process are expounded. The minimum thermal resistance principle and the entransy dissipation extremum principle are obtained by applying the steady-state entransy transfer equation to the steady-state convection heat transfer process. The cases of the single-component steady-state convection heat transfer and the steady-state heat conduction show the application of the theory and method.     

Entropy generation extremum and entransy dissipation extremum for heat exchanger optimization

The applicability of the extremum principles of entropy generation and entransy dissipation is studied for heat exchanger optimization. The extremum principle of entransy dissipation gives better optimization results when heat exchanger is only for the purpose of heating and cooling, while the extremum principle of entropy generation is better for the heat exchanger optimization when it works in the Brayton cycle. The two optimization principles are approximately equivalent when the temperature drops of the streams in a heat exchanger are small. Supported by Major State Basic Research Development Program of China (Grant No. 2007CB206901)     

Entransy dissipation number and its application to heat exchanger performance evaluation

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 demonstrates some distinct advantages. Furthermore, the entransy dissipation number reflects the degree of irreversibility caused by flow imbalance.     

The extremum principle of mass entransy dissipation and its application to decontamination ventilation designs in space station cabins

In terms of the analogy between mass and heat transfer phenomena, a new physical quantity, i.e. mass entransy, is introduced to represent the ability of an object for transferring mass to outside. Meanwhile, the mass entransy dissipation occurs during mass transfer processes as an alternative to measure the mass transfer irreversibility. Then the concepts of mass entransy and its dissipation are used to develop the extremum principle of mass entransy dissipation and the corresponding method for convective mass transfer optimization, based on which an Euler＇s equation has been deduced as the optimization equation for the fluid flow to obtain the best convective mass transfer performance with some specific constraints. As an example, the ventilation process for removing gaseous pollutants in a space station cabin with a uniform air supply system has been optimized to reduce the energy consumption of the ventilation system and decrease the contaminant concentration in the cabin. By solving the optimization equation, an optimal air velocity distribution with the best decontamination performance for a given viscous dissipation is firstly obtained. With the guide of this optimal velocity field, a suitable concentrated air supply system with appropriate air inlet position and width has been designed to replace the uniform air supply system, which leads to the averaged and the maximum contaminant concentrations in the cabin been decreased by 75% and 60%, respectively, and the contaminant concentration near the contaminant source surface been decreased by 50%, while the viscous dissipation been reduced by 30% simultaneously.     

Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation

In order to further analyze and optimize convective heat transfer process further, the concepts of heat flux weighted average heat temperature and heat flux weighted average heat temperature difference in multi-dimensional heat transfer system were introduced in this paper. The ratio of temperature differ- ence to heat flux is defined as the generalized thermal resistance of convective heat transfer processes, and then the minimum thermal resistance theory for convective heat transfer optimization was devel- oped. By analyzing the relationship between generalized thermal resistance and entansy dissipation in convective heat transfer processes, it can be concluded that the minimum thermal resistance theory equals the entransy dissipation extremum theory. Finally, a two-dimensional convective heat transfer process with constant wall temperature is taken as an example to illustrate the applicability of generalized thermal resistance to convective heat transfer process analysis and optimization.     

Entransy and entropy analyses of heat pump systems

In this paper, heat pump systems are analyzed with entransy increase and entropy generation. The extremum entransy increase principle is developed. When the equivalent temperatures of the high and low temperature heat sources are fixed, the theoretical analyses and numerical results both show that the maximum COP leads to the maximum entransy increase rate for fixed input power, while it leads to the minimum entransy increase rate for fixed heat flow absorbed from the low temperature heat source. The minimum entropy generation principle shows that the minimum entropy generation rate always leads to the maximum COP for fixed input power or fixed heat flow absorbed from the low temperature heat source when the equivalent thermodynamic forc- es of the high and low temperature heat sources are given. Further discussions show that only the entransy increase rate always increases with increasing heat flow rate into the high temperature heat source for the discussed cases.     

Entransy dissipation minimization for optimization of heat exchanger design

In this paper,by taking the water-water balanced counterflow heat exchanger as an example,the entransy dissipation theory is applied to optimizing the design of heat exchangers.Under certain conditions,the optimal duct aspect ratio is determined analytically.When the heat transfer area or the duct volume is fixed,analytical expressions of the optimal mass velocity and the minimal entransy dissipation rate are obtained.These results show that to reduce the irreversible dissipation in heat exchangers,the heat exchange area should be enlarged as much as possible,while the mass velocity should be reduced as low as possible.     

Progress in entransy theory and its applications

The entransy and entransy dissipation extremum principle proposed have opened up a new direction for the heat transfer optimi-zation. The emergence and development of entransy theory are reviewed. Entransy theory and its applications are summarized from several aspects, such as heat conduction, heat convective, heat radiation, heat exchanger design and mass transfer, etc. The emphases are focused on four aspects, i.e., the comparison between entropy generation rate and entransy dissipation rate, the combination of entransy dissipation extreme principle with finite time thermodynamics, the combination of entransy dissipation extreme principle with the heat conduction constructal theory, and the combination of entransy dissipation extreme principle with the heat convective constructal theory. The scientific features of entransy theory are emphasized.     

Entransy dissipation and irreversibility of some thermodynamic processes

The relationship between entransy dissipation and the irreversibility of some thermodynamic processes, such as heat transfer, work-heat conversion, free expansion, isothermal diffusion etc., are analyzed in this paper. The results show that there is entropy generation but no entransy dissipation in irreversible work-heat conversion, free expansion and isothermal diffusion. Therefore, entransy dissipation cannot be used to describe the irreversibility of these processes. Both entropy generation and entransy dissipation exist in heat transfer process, which indicates that the entransy dissipation can be used to describe the irreversibility of heat transfer processes. Furthermore, the irreversibility of endoreversible cycles is analyzed. As all the irreversibility in endoreversible cycles is attributed to heat transfer between the heat sources and the working medium, entransy dissipation can be used to describe the irreversibility of this kind of cycles. To verify this conclusion, numerical examples of the endoreversible Carnot cycle are discussed.     

A comparison of optimization theories for energy conservation in heat exchanger groups

In general,thermal processes can be classified into two categories: heat-work conversion processes and heat transfer processes. Correspondingly,the optimization of thermal processes has to have two different criteria:the well known entropy generation minimization method and the recently proposed entransy dissipation maximization method. This study analyzes the thermal issues in a heat exchanger group,and optimizes the unit arrangements under different constraints based on a suitable optimization crite-rion. The result indicates that the principle of minimum entropy generation rate is valid for optimizing heat exchangers in a ther-modynamic cycle with given boundary temperatures. In contrast,the entransy dissipation maximization is more suitable in heat exchanger optimizations involving only heat transfer processes. Furthermore,the entropy generation rate induced by dumping used streams into ambient surroundings has to be taken into account,except for that originating from the hot and cold-ends of heat exchangers,when using the entropy generation minimization to optimize heat exchangers undergoing a thermodynamic cycle.     

Entransy decrease principle of heat transfer in an isolated system

The entropy increase principle for an isolated system and the criteria of thermal equilibrium for an isolated system and systems with prescribed temperature and volume can be derived on the basis of the concept of entropy and the first and second laws of thermodynamics. In this paper, the entransy decrease principle for an isolated system is introduced on the basis of the concept of entransy. It is found that the entransy of an isolated system always decreases during heat transfer. This principle can be tak...     

火积理论在高炉冷却壁性能评价中的应用

基于火积理论分析得出了高炉冷却壁的火积平衡方程式以及冷却壁中的火积耗散.在此基础上定义了高炉冷却壁的热阻.根据最小热阻原理,提出用高炉冷却壁的热阻来评价其传热性能的优劣的观点,通过实例说明了高炉冷却壁热阻的计算方法,比较了不同冷却水管间距下冷却壁热面最高温度及热阻之间的关系.结果表明,随着冷却水管间距的改变,冷却壁热阻与热面最高温度有相同的变化趋势.在一定的边界条件下,高炉冷却壁的热阻可以评价其传热性能的优劣.     

Optimization for entransy dissipation minimization in heat exchanger

A common of two-fluid flow heat exchanger, in which the heat transfer between high- and low-temperature sides obeys Newton＇s law [q∝△（T）], is studied in this paper. By taking entransy dissipation minimization as optimization objective, the optimum parameter distributions in the heat exchanger are derived by using optimal control theory under the condition of fixed heat load. The condition corresponding to the minimum entransy dissipation is that corresponding to a constant heat flux density. Three kinds of heat exchangers, including parallel flow, condensing flow and counter-flow, are considered, and the results show that only the counter-flow heat exchanger can realize the entransy dissipation minimization in the heat transfer process. The obtained results for entransy dissipation minimization are also compared with those obtained for entropy generation minimization by numerical examples.