Constructal entransy dissipation rate minimization for a heat generating volume cooled by forced convection

The geometry of a heat generating volume cooled by forced convection is optimized by applying the entransy dissipation extremum principle and constructal theory, while the optimal spacing between the adjacent tubes and the optimal diameter of each tube are obtained based on entransy dissipation rate minimization. The results of this work show that the optimal constructs based on entransy dissipation rate minimization and maximum temperature difference minimization, respectively, are clearly different. For the former, the porosity of the volume of channels allocated to the heat generating volume is 1/2; while for the latter, the larger the porosity is, the better the performance will be. The optimal construct of the former greatly decreases the mean thermal resistance and improves the global heat transfer performance of the system compared with the optimal construct of the latter. This is identical to the essential requirement of the entransy dissipation extremum principle that the required heat transfer temperature difference is minimal with the same heat transfer rate (the given amount of heat generated in the heat generating volume) based on the entransy dissipation extremum principle.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization

In the viewpoint of heat transfer,heat transport potential capacity and its dissipation are defined based on the essence of heat transport phenomenon,Rspectively,their physical menings are the overall heat transfer capability and the dissipation rate of the heat transfer capacity.Then the least dissipation principle of heat transport potential cpacity is presented to enhance the heat conduction efficiency in the heat conduction optimization .The principle is, for a conduction process with the constant integral of the thermal conductivity over the region ,the optimal distribution of thermal conductivity,which corresponds to the highest heat conduction efficiency ,is characterized by the least dissipation of heat transport potential capacity .Finally the principle is applied to some cases in heat conduction optimization.     

Entransy-dissipation-based thermal resistance analysis of heat exchanger networks

Heat exchanger network optimization has an important role in high-efficiency energy utilization and energy conservation. The thermal resistance of a heat exchanger network is defined based on its entransy dissipation. In two-stream heat exchanger networks, only heat exchanges between hot and cold fluids are considered. Thermal resistance analysis indicates that the maximum heat transfer rate between two fluids corresponds to the minimum entransy-dissipation-based thermal resistance; i.e. the minimum thermal resistance principle can be exploited in optimizing heat exchanger networks.     

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.     

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: its physical basis,applications and limitations

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.     

The optimal configuration of reciprocating engine based on maximum entransy loss

A class of two-heat-reservoir heat engine model with heat leakage,finite heat capacity high-temperature source and infinite heat capacity low-temperature heat sink,is researched with the finite-time thermodynamic theory and the entransy theory.The optimal configuration based on the minimum entropy generation and the maximum entransy loss under the given cycle is searched,which are compared with the optimal configuration based on the maximum output work,and all the heat transfer in the model is assumed to obey the Newton’s law.The results show that,for the infinite heat capacity high-temperature source,the optimal configuration does not change whether heat leakage exists or not;however,for the finite hightemperature reservoir,the optimal configuration is different among which based on the minimum entropy generation,the maximum entransy loss,and the maximum output work when the heat leakage exists.     

Effect of charge on growth of droplets with ionic condensation nuclei

A growth kinetics model of droplets with ionic condensation nuclei based on the chemical potential and the kinetic equation of mass transfer is established. The model is simplified and the effect of charge on droplet growth is examined. The theoretical results show that the critical radius for droplet growth with an ionic condensation nucleus is less than that of those without an ionic nucleus. Furthermore, our results also indicate that if the initial droplet with an ionic nucleus has a radius shorter than the critical radius, the droplet will not vanish, but will reach a steady-state radius. As the ionic charge increases, the critical radius for droplet growth will decrease and the corresponding steady-state droplet radius will increase. In addition we show that once a critical charge is reached, all droplets will grow regardless of initial radius.     

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.     

Relationship between microstate number and available entransy

Based on the relationship between entransy and microstate number, we discuss the variations of the available transport entransy, the unavailable transport entransy, the available conversion entransy and the unavailable conversion entransy with the microstate number. We focus on physical processes in which heat is used for heating/cooling or doing work. When heat is transported for heating or cooling, the available transport entransy increases if the increase in microstate number is due to the increase in internal energy of the system, and decreases if the increase in microstate number is due to spontaneous heat transfer. When heat is used to do work, both the available conversion entransy and the unavailable conversion entransy increase if the increase in microstate number relates to the growth in internal energy of the system. The available conversion entransy decreases and the unavailable conversion entransy increases if the increase in microstate number results from spontaneous heat transfer.