Analyses of an air conditioning system with entropy generation minimization and entransy theory

In this paper,based on the generalized heat transfer law,an air conditioning system is analyzed with the entropy generation minimization and the entransy theory.Taking the coefficient of performance（denoted as COP） and heat flow rate Qout which is released into the room as the optimization objectives,we discuss the applicabilities of the entropy generation minimization and entransy theory to the optimizations.Five numerical cases are presented.Combining the numerical results and theoretical analyses,we can conclude that the optimization applicabilities of the two theories are conditional.If Qout is the optimization objective,larger entransy increase rate always leads to larger Qout,while smaller entropy generation rate does not.If we take COP as the optimization objective,neither the entropy generation minimization nor the concept of entransy increase is always applicable.Furthermore,we find that the concept of entransy dissipation is not applicable for the discussed cases.

Analyses of the endoreversible Carnot cycle with entropy theory and entransy theory

The endoreversible Carnot cycle is analyzed based on the concepts of entropy generation, entropy generation number, entransy loss, and entransy loss coefficient. The relationships of the cycle output power and heat-work conversion efficiency with these parameters are discussed. For the numerical examples discussed, the preconditions of the application for these concepts are derived. When the inlet temperatures and heat capacity flow rates of hot streams and environment temperature are prescribed, the results show that the concepts of entropy generation and entransy loss are applicable. However, in the presence of various inlet temperatures of streams, larger entransy loss rate still leads to larger output power, while smaller entropy generation rate does not. When the heat capacity flow rates of hot streams are various, neither larger entransy loss rate nor smaller entropy generation rate always leads to larger output power. Larger entransy loss coefficient always leads to larger heat-work conversion efficiency for the cases discussed, while smaller entropy generation number does not always.

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 black body 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 prin ciples 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.

Entransy analyses of heat–work conversion systems with inner irreversible thermodynamic cycles

In this paper, we try to use the entransy theory to analyze the heat–work conversion systems with inner irreversible thermodynamic cycles. First, the inner irreversible thermodynamic cycles are analyzed. The influences of different inner irreversible factors on entransy loss are discussed. We find that the concept of entransy loss can be used to analyze the inner irreversible thermodynamic cycles. Then, we analyze the common heat–work conversion systems with inner irreversible thermodynamic cycles. As an example, the heat–work conversion system in which the working fluid of the thermodynamic cycles is heated and cooled by streams is analyzed. Our analyses show that larger entransy loss leads to larger output work when the total heat flow from the high temperature heat source and the corresponding equivalent temperature are fixed.Some numerical cases are presented, and the results verify the theoretical analyses. On the other hand, it is also found that larger entransy loss does not always lead to larger output work when the preconditions are not satisfied.

Entransy dissipation analysis of interfacial convection enhancing gas–liquid mass transfer process based on field synergy principle

An exploration of the gas CO2 absorbed into liquid ethanol accompanied with Rayleigh convection is performed by analyzing the mass entransy dissipation;this new statistical quantity is introduced to describe the irreversibility of mass transfer potential capacity. Based on the general advection–diffusion differential equation for an unsteady mass transfer process, the variation of the included angle between the velocity vector and concentration gradient fields is investigated to reveal the underlying mechanism of interfacial convection enhancing mass transfer. Results show some identical characteristics with the qualitative analyses of the synergy effects generated by the concentration and velocity fields after interfacial convection occurring for a boundary condition of fixed surface concentration. And the equivalent mass resistance for convective mass transfer process presents the similar variation with the reciprocal of instantaneous mass transfer coefficient. Accordingly, it is reasonable to be seen that mass transfer dissipation rate could be provided to assess the convection strength and explain fundamentally how Rayleigh convection improves mass transfer performance through establishing a close relationship between the mass transfer capacity and field synergy principle from the view of mass transfer theory.

Optimization of fin geometry in heat convection with entransy theory

The entransy theory developed in recent years is used to optimize the aspect ratio of a plate fin in heat convection.Based on a two-dimensional model,the theoretical analysis shows that the minimum thermal resistance defined with the concept of entransy dissipation corresponds to the maximum heat transfer rate when the temperature of the heating surface is fixed.On the other hand,when the heat flux of the heating surface is fixed,the minimum thermal resistance corresponds to the minimum average temperature of the heating surface.The entropy optimization is also given for the heat transfer processes.It is observed that the minimum entropy generation,the minimum entropy generation number,and the minimum revised entropy generation number do not always correspond to the best heat transfer performance.In addition,the influence factors on the optimized aspect ratio of the plate fin are also discussed.The optimized ratio decreases with the enhancement of heat convection,while it increases with fin thermal conductivity increasing.

Application of entransy dissipation extremum principle in radiative heat transfer optimization

The concepts of entransy flux and entransy dissipation in radiative heat transfer were introduced based on the analogy with heat conduction and heat convection processes. Entransy will be partially dissipated during the radiative heat transfer processes due to the irreversibility. The extremum principle of entransy dissipation was developed for optimizing radiative heat transfer processes. This principle states that for a fixed boundary temperature the radiative heat transfer is optimized when the entransy dissipation is maximized, while for a fixed boundary heat flux the radiative heat transfer process is optimized when the entransy dissipation is minimized. Finally, examples for the application of the entransy dissipation extre- mum principle are presented.

Principle of equipartition of entransy dissipation for heat exchanger design

In the present work,a principle of equipartition of entransy dissipation(EoED) for heat exchanger design is established,which says that for a heat exchanger design with given heat duty and heat transfer area,the total entransy dissipation rate reaches the minimum when the local entransy dissipation rate is uniformly distributed along the heat exchanger.When the heat transfer coefficient is unfixed,the total entransy dissipation obtained by the EoED principle is less than that obtained by the principle of equipartition of temperature difference(EoTD).Furthermore,the exchanger effectiveness obtained by the EoED principle is larger than that obtained by the EoTD principle.When the heat transfer coefficient is fixed,the EoED principle is equivalent to the EoTD principle.We show that the equipartition of entropy production(EoEP) and EoED principles give rise to difference in entropy generation and entransy dissipation for a heat exchanger optimization design.The discrepancies are caused by distinct features of entropy production minimization and entransy dissipation minimization principles,the former is to optimize the design of heat exchanger by making the lost available work minimum,while the latter is not involved with heat-work conversion.It is found that the entropy generation number is not suitable for evaluating heat exchanger performance,since it directly depends on the inlet and outlet temperatures of working fluids.On the contrary,the entransy dissipation number is not directly related to the inlet and outlet temperatures of working fluids.Therefore,the entransy dissipation number is more suitable for serving as a criterion to evaluate heat exchanger performance.

“Volume-Point” heat conduction constructal optimization with entransy dissipation minimization objective based on rectangular element

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.

Constructal optimization of discrete and continuous-variable cross-section conducting path based on entransy dissipation rate minimization

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.

Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective

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.

Entransy dissipation minimization for liquid-solid phase change processes

The liquid-solid phase change process of a simple one-dimensional slab is studied in this paper.By taking entransy dissipation minimization as optimization objective,the optimal external reservoir temperature profiles are derived by using optimal control theory under the condition of a fixed freezing or melting time.The entransy dissipation corresponding to the optimal heat exchange strategies of minimum entransy dissipation is 8/9 of that corresponding to constant reservoir temperature operations,which is independent of all system parameters.The obtained results for entransy dissipation minimization are also compared with those obtained for the optimal heat exchange strategies of minimum entropy generation and constant reservoir temperature operations by numerical examples.The obtained results can provide some theoretical guidelines for the choice of optimal cooling or heating strategy in practical liquid-solid phase change processes.

Constructal multidisciplinary optimization of electromagnet based on entransy dissipation minimization

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.

Constructal entransy dissipation rate and flow-resistance minimizations for cooling channels

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.

Entransy functions for steady heat transfer

In this paper, the entransy functions for steady heat transfer are summarized and discussed based on the variational theory and the entransy theory. The entransy functions for steady convective heat transfer are derived for the first time. In steady heat transfer processes, it is shown that the steady distributions of heat flux and temperature(radiative thermal potential) should make the corresponding entransy functions reach their minimum values when the temperature(radiative thermal potential) or the heat flux of the boundary is given. The extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles are compared with the entransy functions. It is shown that the entransy functions can describe a steady state,but cannot directly give a way to optimize heat transfer processes, while the extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles act in an opposite way.

Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory

Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory. Three types of 3-D circular disc heat sink models, i.e. without collection microchannels, with center collection microchannels, and with edge collection microchannels, are established respectively. Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels, that of circular disc heat sink with center collection microchannels is the minimum, so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages. Furthermore, the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes. With the mass flow rate increasing, both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease. With the heat flux increasing, the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged. With the same mass flow rate and heat flux, the larger the microchannel branch number, the smaller the maximum thermal resistance. While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.

Constructal entransy dissipation rate minimization for X-shaped vascular networks

Combining with entransy theory, constructal designs of the X-shaped vascular networks(XSVNs) are implemented with fixed total tube volumes of the XSVNs. The entransy dissipation rates(EDRs) of the XSVNs are minimized, and the optimal constructs of the XSVNs are derived. Comparison of the optimal constructs of the XSVNs with two optimization objectives(EDR minimization and entropy generation rate(EGR) minimization) is conducted. It is found that when the dimensionless mass flow rate(DMFR) is small, the optimal diameter ratio of the elemental XSVN derived by EDR minimization is different from that derived by EGR minimization. For the multilevel XSVN, when the DMFR is 100, compared the XSVN with the corresponding H-shaped vascular network(HSVN), the dimensionless EDRs of the elemental, second and fourth order XSVNs are reduced by 26.39%, 15.34% and 9.81%, respectively. Compared with the entransy dissipation number(EDN) of the second order XSVN before angle optimization, the EDN after optimization is reduced by 26.15%, which illustrates that it is significant to conduct angle optimization of the XSVN. Entransy theory is applied into the constructal design of the vasculature with heat transfer and fluid flow in this paper, which provides new directions for the vasculature designs.

Generalized constructal optimization of strip laminar cooling process based on entransy theory

A strip laminar cooling process is investigated in this paper. Entransy theory and generalized constructal optimization are introduced into the optimization. Total water flow amount(WFA) in the laminar cooling zone(LCZ) and complex function are taken as the constraint and optimization objective, respectively. The entransy dissipation(ED) and maximum temperature different(MTD) of the strip are simultaneously considered in the complex function. WFA distributions of the headers in the LCZ are optimized. The effects of the total WFA, strip thickness and cooling water temperature on the optimal results are analyzed.The optimal cooling scheme is the eleventh cooling mode for the considered total 257 cooling schemes, and the complex function,ED and MTD of the strip are decreased by 11.59%, 5.59% and 17.58% compared with the initial cooling scheme, respectively.The total WFA and strip thickness have the obvious influences on the optimal cooing scheme, but the cooling water temperature has no influence in the parameter analysis range of this paper. The "generalized optimal construct" derived by minimum complex function shows a compromise between the energy retention and quality of the strip.

Role of viscous heating in entransy analyses of convective heat transfer

The entransy theory is widely used and found to be effective in thermal analyses and optimizations.Some researchers considered the entransy variation due to viscous heating as part of entransy dissipation and analyzed convective heat transfer based on the differential relationship between entropy and entransy.However,it has been pointed out that the derivation of the differential relationship between entropy and entransy is incorrect.In this paper,the convective heat transfer processes with viscous heating is reconsidered and analyzed from the viewpoint of the energy conservation and the entransy balance equation.It is shown that the influence of the viscous heating is equivalent to that of an inner heat source.Therefore,the contribution of viscous heating to system entransy should not be treated as part of entransy dissipation,but entransy flow into the system.Two-stream parallel and counter flow heat exchangers with viscous heating and a thermal insulation transportation problem of heavy oil are taken as examples to verify the theoretical analyses intuitively.In the examples,the numerical results show that the entransy dissipation rates could be negative when the influence of the viscous heating on the system entransy is treated as part of the entransy dissipation.This is obviously unreasonable.Meanwhile,when the entransy contribution from the viscous heating to the system entransy is treated as entransy flow into the system,it is shown that the entransy dissipation rate is always positive,and the heat transfer processes can be well explained with the entransy theory.

Optimization of combined endoreversible Carnot heat engines with different objectives

Taking the output power, thermal efficiency, and thermo-economic performance as the optimization objectives, we optimize the operation parameters of a thermodynamic system with combined endoreversible Carnot heat engines in this paper. The applicabilities of the entropy generation minimization and entransy theory to the optimizations are discussed. For the discussed cases, only the entransy loss coefficient is always agreeable to the optimization of thermal efficiency. The applicabilities of the other discussed concepts to the optimizations are conditional. Different concepts and principles are needed for different optimization objectives, and the optimization principles have their application preconditions. When the preconditions are not satisfied, the principles may be not applicable.