Entransy Dissipation Extremum Research Articles

Progress in optimization of mass transfer processes based on mass entransy dissipation extremum principle

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 dissipation extremum principle are reviewed. Secondly, the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for optimizing the mass transfer processes of one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, and isothermal throttling and isothermal crystallization are summarized. Thirdly, the combination of the mass entransy dissipation extremum 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 extremum principle are emphasized.

Performance optimization of two-stage latent heat storage unit based on entransy theory

In order to enhance the performance of the latent heat storage (LHS) process and provide the criterion for the selection and match of the multistage PCMs, the effects of PCMs melting temperatures on the heat storage rate, entransy dissipation rate and heat storage quality were numerically analyzed based on the entransy theory. For the single stage LHS unit, although decreasing the PCM melting temperature can augment the heat storage rate, the lower melting temperature causes larger entransy dissipation and reduces the heat storage quality. The larger heat storage rate results in the larger entransy dissipation rate, which is accordant with the entransy dissipation extremum theory. For the two-stage LHS unit with reasonably matching the PCMs melting temperature, the heat storage rate can be augmented and the entransy dissipation rate can be reduced. Then the optimization for the match of the two-stage PCMs melting temperatures was performed based on the entransy theory. The results show that there is an optimal match of the two-stage PCMs melting temperatures to achieve the maximum heat transfer rate or the minimum entransy dissipation rate. And the formulas for the optimum two-stage PCMs temperatures were presented, which can provide the criterions for the selection and match of the PCMs.

Numerical studies on the inherent interrelationship between field synergy principle and entransy dissipation extreme principle for enhancing convective heat transfer

In 1998 Guo et al. integrated the boundary-layer energy equation along the thermal boundary layer thickness, and noted that at outside boundary the temperature gradient is zero and the convection term is actually the inner production of vector velocity and temperature gradient, they found that for a fixed flow rate and temperature difference, the smaller the intersection angle between velocity and temperature gradient the larger the heat transfer rate. This idea is called field synergy principle (FSP). Later it has been shown that FSP can unify all mechanisms for enhancing single phase heat transfer. In 2007 Guo and his co-workers proposed a new concept: entransy to describe the potential of a body to transfer thermal energy and the entransy dissipation extreme principle (EDEP). It is indicated that for any heat transfer process the entransy of the system is always dissipated, which can be regarded as the indication of the irreversibility of the transport process. For a heat transfer process with given boundary temperature condition the best one has the maximum entransy dissipation, while for that with given boundary heat flux condition the best one has minimum entransy dissipation. The combination of the two cases is called the entransy dissipation extremum principle.The purpose of this paper is to reveal the inherent interrelationship between the ideas of field synergy principle and the entransy extremum principle. Numerical simulations are conducted for five examples of convective heat transfer. All the numerical results demonstrate the inherent consistency between FSP and EDEP.

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 obviously 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 \( a_{{2,{\text{opt}}}} \) which leads to the minimum dimensionless entransy dissipation rate of the insulation layer. The difference between the optimal constant coefficients \( a_{{2,{\text{opt}}}} \) 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.

Application of Entransy Optimization to One-Stream Series-Wound and Parallel Heat Exchanger Networks

Entransy theory has developed in recent years to describe heat transfer behavior from another point of view. Entransy dissipation is proposed to evaluate the irreversibility of heat transfer and is used to optimize heat transfer processes. We apply this theory to the one-stream series-wound and parallel heat exchanger (HE) networks. The heat transfer optimization for the HE networks includes the distribution of the heat transfer area or heat load. The distribution of the cold fluid flow rate in parallel HE networks can also be optimized. For these problems, physical and mathematical models are set up, analyzed, and discussed with the entransy theory. It is found that the optimization objectives of these problems and the optimization directions of the extremum entransy dissipation principle are consistent. The optimized results for the distribution optimization problem with given heat load are in agreement with the uniformity principle of temperature difference field. Examples of simple one-stream HE networks are given; the distributions of the heat transfer area or heat load are optimized by the extremum entransy dissipation method.

Constructal entransy dissipation rate minimization for variable cross-section insulation layer of the steel rolling reheating furnace wall

A variable cross-section (distributed thickness and width) insulation layer of the steel rolling reheating furnace wall is investigated subjected to the constraints of the total volume and cross-sectional area of the insulation material. According to the entransy dissipation extremum principle of the thermal insulation process, the thickness of the insulation layer is optimized by taking minimum entransy dissipation rate as optimization objective, and the optimal construct of the insulation layer is obtained. The results show that when the temperature distribution of the furnace is linear with the length, the optimal thickness of the insulation layer with minimum entransy dissipation rate is linear with the dimensionless longitudinal position, which is evidently different from that with minimum heat loss rate. When the dimensionless temperature at the low temperature side ε=0, the minimum entransy dissipation rate of the insulation layer with distributed thickness is decreased by 33.33% than that with uniform thickness, and is decreased by 8.85% than that based on minimum heat loss rate. Essentially, the temperature gradient field obtained based on minimum entransy dissipation rate is more homogenous than that based on minimum heat loss rate, and the corresponding thermal stress performance is better. The decrement of the entransy dissipation rate tends to increase for the exponential temperature distribution case with a large exponent. Moreover, the insulation layer with triangular cross-section has a better global thermal insulation performance derived from entransy dissipation than those with rectangular and trapezoidal cross-sections. Therefore, the optimal construct obtained by adopting variable cross-section insulation layer (distributed thickness and width) and based on minimum entransy dissipation rate can improve the global thermal insulation performance of the insulation layer derived from entransy dissipation, and can reduce its average heat loss rate defined based on entransy dissipation simultaneously. The optimal construct obtained based on minimum entransy dissipation rate can provide a new scheme for the design of practical thermal insulation system different from that based on minimum heat loss rate, which can satisfy the different requirements in the design of practical thermal insulation systems.

A comparison of different entransy flow definitions and entropy generation in thermal radiation optimization

In thermal radiation, taking heat flow as an extensive quantity and defining the potential as temperature T or the blackbody emissive power U will lead to two different definitions of radiation entransy flow and the corresponding principles for thermal radiation optimization. The two definitions of radiation entransy flow and the corresponding optimization principles are compared in this paper. When the total heat flow is given, the optimization objectives of the extremum entransy dissipation principles (EEDPs) developed based on potentials T and U correspond to the minimum equivalent temperature difference and the minimum equivalent blackbody emissive power difference respectively. The physical meaning of the definition based on potential U is clearer than that based on potential T, but the latter one can be used for the coupled heat transfer optimization problem while the former one cannot. The extremum entropy generation principle (EEGP) for thermal radiation is also derived, which includes the minimum entropy generation principle for thermal radiation. When the radiation heat flow is prescribed, the EEGP reveals that the minimum entropy generation leads to the minimum equivalent thermodynamic potential difference, which is not the expected objective in heat transfer. Therefore, the minimum entropy generation is not always appropriate for thermal radiation optimization. Finally, three thermal radiation optimization examples are discussed, and the results show that the difference in optimization objective between the EEDPs and the EEGP leads to the difference between the optimization results. The EEDP based on potential T is more useful in practical application since its optimization objective is usually consistent with the expected one.

Study on flow and heat transfer characteristics of composite porous material and its performance analysis by FSP and EDEP

In this paper, the heat transfer characteristics of porous material adopted in the receiver of a concentrated solar power (CSP) with different structure parameters are numerically investigated. The commercial software FLUENT and the user defined function program (UDF) are adopted to implement the simulation. The porous material geometry is represented by periodic structures formed with packed tetrakaidecahedron. The air flow and heat transfer characteristics under the boundary conditions of constant heat flux and constant wall temperature are studied. The field synergy principle (FSP) and the entransy dissipation extremum principle (EDEP) are used to analyze the flow and heat transfer performance of the composite porous material. From the numerical results the best composite of the porous material is obtained. The effects of different boundary conditions are revealed. It is also demonstrated that the FSP and the EDEP are inherently consistent.

Application of entransy in the analysis of HVAC systems in buildings

The main task of HVAC systems in the cooling condition is to remove heat from indoor environment to outdoor environment. HVAC systems are complex networks of various processes, e.g., heat transfer, heat–work conversion, heat–humidity conversion, etc. These processes correspond to equipment such as heat exchangers, indoor cooling terminals, heat pumps, and cooling towers. Single analysis method or thermal parameter could hardly describe all the processes in an HVAC system. Exergy destruction refers to the loss of heat–work conversion ability. Reducing exergy destruction indicates less supplied exergy (input work) of HVAC systems. Entransy is a new parameter defined as heat transfer ability. Entransy dissipation refers to the loss of heat transfer ability. When the purpose of heat transfer is cooling or heating, entransy analysis is a direct method for optimizing heat transfer processes. Loss of HVAC system is mainly in heat transfer process. The entransy dissipation extremum principle or the minimum thermal resistance principle is suitable for analyzing heat transfer process in HVAC system. For indoor cooling, reducing entransy dissipation will increase chilled water temperature. Flow unmatched coefficient ξ represents an increase of thermal resistance of heat exchanger if the calorific capacities of the fluids are different.

Constructal entransy dissipation rate minimization the problem of constracting “disc-point” cooling channels

Based on configucation theory, the construction of a “disc-point” heat transfer with cooling channels can be optimized by taking minimum entransy dissipation rate. Thus an optimal construction of the disc-shaped assembly with cooling channels is obtained. The results show that there exists an optimal aspect ratio of the elemental sector which leads to the minimum dimensionless equivalent thermal resistance of the elemental sector at the fixed pumping power; there also exists an optimal width ratio of the elemental and first-order cooling channel to the optimal dimensionless radius of the elemental sector, which leads to the minimum dimensionless equivalent thermal resistance of the first-order branched-pattern disc at the fixed total pumping power. Moreover, the optimal width ratio of the elemental and first-order cooling channels is only relative to the number of elemental tributaries. When the radius of the central disc tends to zero, the branch-pattern disc is simplified into a radial-pattern disc, and the radius of the first-order branch-pattern disc becomes the critical radius at this point. When the radius of the branch-pattern disc is higher than the critical radius, the branch-pattern design should be adopted, otherwise the radial-pattern design should be adopted. There exists an optimal number of elemental tributaries which lead to the minimum dimensionless equivalent thermal resistance of the first-order branch-pattern disc, which is obviously different from the results of the “disc-point” heat conduction constructional optimization with high-conductivity channels. The optimal constructions of the first-order branch-pattern disc based on the minimizations of entransy dissipation rate and maximum temperature difference are different. The dimensionless equivalent thermal resistance of the disc with cooling channels based on the minimization of entransy dissipation rate is greatly reduced as compared with that based on the minimization of maximum temperature difference, and its global heat transfer performance is obviously improved simultaneously. Therefore, the combination of the entransy dissipation extremum principle and the heat convection constructional optimization further illustrates the advantages of minimization of entransy dissipation rate for heat transfer optimizations.

Constructal entransy dissipation rate minimization of a disc on micro and nanoscales

Based on constructal theory, the constructal optimization of a disc on micro and nanoscales is carried out by taking minimum entransy dissipation rate as optimization objective; and the optimal construction of the disc with minimum dimensionless equivalent thermal resistance is obtained. The result shows that the optimal construction of the disc when the size effectis taken into account is obviously different from that without considering the size effect. There exists an optimal dimensionless channel length of the high conductivity material which leads to the minimum dimensionless equivalent thermal resistance. With the increase in the number of the elemental sectors, the minimum dimensionless equivalent thermal resistance decreases first and then increases, and there exists an optimal number of the elemental sectors which leads to the double minimum dimensionless equivalent thermal resistance, which is different from the performance characteristic of the disc on a conventional scale. The entransy dissipation rate of the disc, based on the minimization of entransy dissipation rate, is reduced by 7.31% as compared with that based on maximum temperature difference, that is, the average heat transfer temperature difference of the disc is reduced by 7.31%. The optimal construction on micro and nanoscales, obtained based on minimum entransy dissipation rate, can reduce the average heat transfer temperature difference of a disc, and improves its global heat transfer performance simultaneously. The work in this paper can help to further extend the application range of the entransy dissipation extremum principle.

Generalized thermal resistance and its application to thermal radiation based on entransy theory

Entransy is a novel concept developed in recent years to measure the transport ability of heat in heat transfer processes. In order to analyze and optimize thermal radiation process more conveniently and intuitively, we develop the entransy-theory-based method to the field of thermal radiation problems to define the generalized thermal resistance for multi-dimensional steady state thermal radiation systems, with a consistent dimension of those for heat conduction and convection systems proposed in previous studies. Based on it, the minimum generalized thermal resistance principle for thermal radiation is developed and its equivalence with the entransy dissipation extremum principle can be concluded by defining the concept of heat flux weighted average temperature difference for thermal radiation systems. We point out that these two principles emphasize particularly on the optimization of the mean performance for heat transfer processes. A steady state thermal radiation process in an enclosure with three opaque surfaces is taken as an example to illustrate the applicability and reliability of generalized thermal radiation resistance when it is used to optimize thermal radiation problems. Finally, a comparison between the principles of minimum generalized thermal resistance and minimum entropy generation is discussed to show that the latter might not be appropriate to optimize some thermal radiation problems.

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 optimization. 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.

Power output analyses and optimizations of the Stirling cycle

Based on the finite time thermodynamics theory, the entransy theory and the entropy theory, the Stirling cycles under different conditions are analyzed and optimized with the maximum output power as the target in this paper. The applicability of entransy loss (EL), entransy dissipation (ED), entropy generation (EG), entropy generation number (EGN) and modified entropy generation number (MEGN) to the system optimization is investigated. The results show that the maximum EL rate corresponds to the maximum power output of the cycle working under the infinite heat reservoirs whose temperatures are prescribed, while the minimum EG rate and the extremum ED rate do not. For the Stirling cycle working under the finite heat reservoirs provided by the hot and cold streams whose inlet temperatures and the heat capacity flow rates are prescribed, the maximum EL rate, the minimum EG rate, the minimum EGN and the minimum MEGN all correspond to the maximum power output, but the extremum ED rate does not. When the heat capacity flow rate of the hot stream increases, the power output, the EL rate, the EG rate and the ED rate increase monotonously, while the EGN and the MEGN decrease first and then increase. The EL has best consistency in the power output optimizations of the Stirling cycles discussed in this paper.

Thermal insulation constructal optimization for steel rolling reheating furnace wall based on entransy dissipation extremum principle

Analogizing with the heat conduction process, the entransy dissipation extremum principle for thermal insulation process can be described as: for a fixed boundary heat flux (heat loss) with certain constraints, the thermal insulation process is optimized when the entransy dissipation is maximized (maximum average temperature difference), while for a fixed boundary temperature, the thermal insulation process is optimized when the entransy dissipation is minimized (minimum average heat loss rate). Based on the constructal theory, the constructal optimizations of a single plane and cylindrical insulation layers as well as multi-layer insulation layers of the steel rolling reheating furnace walls are carried out for the fixed boundary temperatures and by taking the minimization of entransy dissipation rate as optimization objective. The optimal constructs of these three kinds of insulation structures with distributed thicknesses are obtained. The results show that compared with the insulation layers with uniform thicknesses and the optimal constructs of the insulation layers obtained by minimum heat loss rate, the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate are obviously different from those of the former two insulation layers; the optimal constructs of the insulation layers obtained by minimum entransy dissipation rate can effectively reduce the average heat loss rates of the insulation layers, and can help to improve their global thermal insulation performances. The entransy dissipation extremum principle is applied to the constructal optimizations of insulation systems, which will help to extend the application range of the entransy dissipation extremum principle.

“Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale

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.

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.

Two energy conservation principles in convective heat transfer optimization

Improving heat transfer performance is very beneficial to energy conservation because heat transfer processes widely existed in energy utilization systems. In this contribution, in order to effectively optimize convective heat transfer, such two principles as the field synergy principle and the entransy dissipation extremum principle are investigated to reveal the physical nature of the entransy dissipation and its intrinsic relationship with the field synergy degree. We first established the variational relations of the entransy dissipation and the field synergy degree with the heat transfer performance, and then derived the optimization equation of the field synergy principle and made comparison with that of the entransy dissipation extremum principle. Finally the theoretical analysis is then validated by the optimization results in both a fin-and-flat tube heat exchanger and a foursquare cavity. The results show that, for prescribed temperature boundary conditions, the above two optimization principles both aim at maximizing the total heat flow rate and their optimization equations can effectively obtain the best flow pattern. However, for given heat flux boundary conditions, only the optimization equation based on the entransy dissipation extremum principle intends to minimize the heat transfer temperature difference and could get the optimal velocity and temperature fields.

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.

Constructal design for a steam generator based on entransy dissipation extremum principle

Steam generator is optimized by applying entransy dissipation extremum principle and constructal theory and adopting analytical method. The obtained results show that the optimal spacing between adjacent tubes, the mass flow rate of gas and the maximum entransy dissipation rate all depend on the dimensionless diameter of one tube, the dimensionless pressure difference number and the dimensionless length of flow channel of gas. Besides the three dimensionless groups, the optimal numbers of riser tubes and downcomer tubes and their summation all depend on the dimensionless height of one tube. The maximum entransy dissipation rate increases as the pressure difference that drives the gas flowing increases, and as the diameter of one tube and the length of flow channel both decrease. The mean heat flux in the heat transfer process of hot gas grows greatly, and the performance of the system is improved. Compared with the optimal construct with heat transfer rate maximization, the optimal construct with entransy dissipation rate maximization can improved the heat transfer effect of the steam generator more.