Search

The uniform distribution of certain physical quantities or functions, referred to as the corresponding equipartition principles, can be reflected in the optimization design of many physical processes. In this paper, three equipartition principles for the optimization of two- and three-stream heat exchangers are discussed, including the uniformity principle of thermodynamic force field, uniformity principle of the field of Δ T / T , and uniformity principle of temperature difference field. The main problems are highlighted for the first two principles. It is demonstrated that for a fixed heat transfer rate, the two principles cannot lead to the minimum entropy-generation rate or the highest heat exchanger effectiveness, and they cannot be satisfied when the best heat transfer performance is achieved. For the last principle, whether the heat transfer coefficient between cold and hot fluids is constant or not, it can be directly proved using the entransy theory, and theoretical derivation shows that for a fixed ratio of heat capacity flow rates and the number of heat transfer units, a larger uniformity factor of temperature difference field gives larger heat exchanger effectiveness. It is also demonstrated that when the temperature difference field is completely uniform, the entransy-dissipation-based thermal resistance has the minimum value. Therefore, the last principle can give the optimal heat transfer performance for heat exchangers. Some simple numerical examples for the application of the three principles are also presented, and the results directly verify the theoretical analyses. Theoretical analyses and simple examples show that the uniformity principles of the thermodynamic force field and the field of Δ T / T are obtained based on the entropy-generation concept and the uniformity principle of temperature difference field is derived with the entransy dissipation concept. The former concept describes the irreversibility of heat transfer from the viewpoint of the ability to do work, and the latter concept measures irreversibility from the viewpoint of heat transfer ability. This is why the first two principles are not consistent with heat transfer optimization, whereas the last principle is. Additionally, the heat transfer law does not conform to the actual heat transfer processes in the derivation of the first principle. Therefore, the first two principles are unsuitable for heat exchanger optimization, whereas the third principle is suitable; the statement that the uniformity principle of the temperature difference field is a duplicate of the uniformity principle of the field of Δ T / T for balanced counter-flow heat exchangers is unscientific and incorrect.

A newly developed frosting simulation method, pseudo-VOF (p-VOF) method, has applied to simulate the dynamic frost formation on the NACA0012 airfoil under strong convection. The p-VOF method is a pseudo volume of fraction simulation method of the multiphase flow with phase change. By solving a simplified mass conservation equation explicitly instead of the original volume fraction equations in CFD software, the efficiency and robustness of calculation are greatly improved. This progress makes it possible to predict a long-time frost formation. The p-VOF method was successfully applied to the simulation of dynamic frosting on the two-dimensional NACA0012 airfoil under strong convection conditions with constant frost physical properties. The simulation result shows that the average thickness of the frost layer increases, and the frost bulges and flow separation appear earlier, when the airfoil surface temperature decreases or the air humidity increases. The frost bulges and flow separation appear earlier, when the air velocity is faster, the growth rate of the frost layer at the early stage is greater, but the final frost layer is thinner.

Because of its high specific surface area, metal foam is expected to further enhance the flow and thermal performance of a minichannel heatsink. In this study, fully developed flow in minichannels with porous fins was studied. The porous geometry was constructed based on Laguerre-Voronoi tessellation and simulated in a pore scale, which eliminated the influence of parameter selection in a macroscale method. The influence of porosity, filling ratio, and Reynolds number on velocity field and pressure drop was analyzed. The general relationship between the Poiseuille number and filling ratio was determined, and a correlation was obtained using the study results. The results of this study were compared with those of the macroscale method, and finally, the influence of effective viscosity was discussed.

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.

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.

Recently, the analogy between the processes of heating a solid body and charging an electric capacitor was deemed as “heat-work analogy” and argued that it was false and violated the second law of thermodynamics. It was claimed that the two processes were not analogous because the process of heating a solid body was classified as a purely thermal system, while that of charging an electric capacitor was classified as a purely mechanical system. In response, this note discusses the analogy between heat and electric conductions and that between heating a solid body and charging an electric capacitor. It is shown that the analogies have nothing to do with heat-work conversion, and never violate the second law of thermodynamics. The classification of charging an electric capacitor as a purely mechanical system is inappropriate. It is also shown that what we concern in the analogy analysis are the commonalities between the processes, rather than the differences.

Spay cooling is a complicated flow and heat transfer process affected by multi-factors among which the environmental pressure is extremely important. However the influence of pressure is not investigated sufficiently, especially the reduced pressure. In the present study, spray cooling under low initial environmental partial pressures and vapor partial pressures with R21 are investigated with a closed spray and condensation system. To study the influence of initial environmental partial pressure, different amounts of nitrogen are inflated into the vacuum flash chamber, while the vapor partial pressure is kept constant. To study the influence of vapor partial pressure, a cascade refrigerator is used to condense the vapor with different condensation temperatures so that the vapor partial pressure can be maintained or adjusted, while the initial environmental partial pressure is kept constant. The experimental results show that the spray cooling power increases monotonically with the increasing spray flow rate in the experimental range, while the cooling efficiency decreases with the increasing spray flow rate. The spray cooling power and cooling efficiency vary with the initial environmental partial pressure or the vapor partial pressure non-monotonously, which indicates there is an optimal pressure for the heat transfer performance. Besides, the mechanism of the non-monotonous variation trend is discussed based on the key aspects including flash evaporation, convection and boiling. Especially, the boiling heat transfer curve is applied to explain the trend.

The entropy generation minimization and the entransy theory are widely used in the optimization of heat transfer. In this paper, the two theories are applied to coupled steady heat transfer systems. The two different definitions of radiative entransy flux are discussed. It is found that the extremum principle of entransy dissipation for coupled heat transfer systems can be obtained only when temperature is treated as the driving force of radiative heat transfer and the definition of entransy flux for radiative heat transfer is the same as that in conductive and convective heat transfer. Taking temperature as the driving force of radiative heat transfer, we have analyzed three coupled heat transfer examples, which are the one-dimensional coupled conductive and radiative heat transfer, the coupled convective and radiative heat transfer and the coupled conductive, convective and radiative heat transfer. The results show that the extremum principle of entransy dissipation always leads to the best system performance, while the entropy generation minimization does not always. The definition of radiative entransy flux in which the blackbody emissive power is treated as the driving force is also used for the three examples. However, the results show that neither the extremum radiative entransy dissipation rate nor the extremum conductive/convective entransy dissipation rate results in the best system performance. Therefore, this definition is not suitable for coupled heat transfer systems.

In this paper, the performance of a concentrating photovoltaic/thermal solar system is numerically analyzed with a mathematical and physical model. The variations of the electrical efficiency and the thermal efficiency with the operation parameters are calculated. It is found that the electrical efficiency increases at first and then decreases with increasing concentration ratio of the sunlight, while the thermal efficiency acts in an opposite manner. When the velocity of the cooling water increases, the electrical efficiency increases. Considering the solar system, the surface of the sun, the atmosphere and the environment, we can get a coupled energy system, which is analyzed with the entropy generation minimization and the entransy theory. This is the first time that the entransy theory is used to analyze photovoltaic/thermal solar system. When the concentration ratio is fixed, it is found that both the minimum entropy generation rate and the maximum entransy loss rate lead to the maximum electrical output power, while both the minimum entropy generation numbers and the maximum entransy loss coefficient lead to the maximum electrical efficiency. When the concentrated sunlight is not fixed, it is shown that neither smaller entropy generation rate nor larger entransy loss rate corresponds to larger electrical output power. Smaller entropy generation numbers do not result in larger electrical efficiency, either. However, larger entransy loss coefficient still corresponds to larger electrical efficiency.

The analysis and the design of turbojet engines are of great importance to the improvement of the system performance. Many researchers focus on these topics, and many important and interesting results have been obtained. In this paper, the thermodynamic cycle in a turbojet engine is analyzed with the entransy theory and the T-Q diagram. The ideal thermodynamic cycle in which there is no inner irreversibility is analyzed, as well as the influences from some inner irreversible factors, such as the heat transfer process, the change of the component of the working fluid and the viscosity of the working fluid. For the discussed cases, it is shown that larger entransy loss rate always results in larger output power, while smaller entropy generation rate does not always. The corresponding T-Q diagrams are also presented, with which the change tendencies of the entransy loss rate and the output power can be shown very intuitively. It is shown that the entransy theory is applicable for analyzing the inner irreversible thermodynamic cycles discussed in this paper. Compared with the concept of entropy generation, the concept of entransy loss and the corresponding T-Q diagram are more suitable for describing the change of the output power of the analyzed turbojet engine no matter if the inner irreversible factors are considered.

The influence of gravity on flow boiling poses a challenge to the development of two-phase thermal systems for space applications. The present study investigates the heat transfer coefficient of flow boiling in a mini-channel evaporator in both horizontal and vertically downward flow directions to observe the effect of gravity. The evaporator has 23 channels that are 624 μm in width and 923 μm in depth. The experiments show that nucleate boiling dominates the heat transfer. The heat transfer and flow patterns for the two directions differ when the mass flow rate is less than 264.3 kg/m2 s and the heat flux is less than 3.0 W/cm2. The experimental results are compared with five general correlations. The outlet Froude number is more suitable for correlating the results than existing gravity-independent criteria. Gravity may influence the heat transfer through instabilities and changes in the flow patterns.

Partial coalescence is a complicated flow phenomenon. In the present study, the coalescence process is simulated with the volume of fluid (VOF) method. The numerical results reveal that a downward high-velocity region plays a significant role in partial coalescence. The high-velocity region pulls the droplet downward continuously which is an important factor for the droplet turning into a prolate shape and the final pinch-off. The shift from partial coalescence to full coalescence is explained based on the droplet shape before the pinch-off. With the droplet impact velocity increasing, the droplet shape will get close to a sphere before the pinch-off. When the shape gets close enough to a sphere, the partial coalescence shifts to full coalescence. The effect of film thickness on the coalescence process is also investigated. With large film thickness, partial coalescence happens, while with small film thickness, full coalescence happens. In addition, the results indicate that the critical droplet impact velocity increases with the increase of surface tension coefficient but decreases with the increase of viscosity and initial droplet diameter. And there is a maximum critical Weber number with the increase of surface tension coefficient and initial droplet diameter.

With the aim to improve overall thermal-hydraulic and thermodynamic performance of parabolic trough solar receiver (PTR), a new configuration with partial insertion of gradient metal foam (GMF) is proposed. The effects of GMF with pore density gradient or porosity gradient on turbulent forced convection heat transfer, flow resistance, entropy generation rate and exergetic efficiency of PTR tube are numerically analyzed. The distribution of non-uniform heat flux on receiver tube wall is calculated by Monte Carlo Ray-Trace Method, and the local thermal non-equilibrium model is used, which considers the temperature difference between metal skeleton and fluid. The numerical method is validated by experimental data. The results show that GMF enhances the heat transfer of PTR tube, with Nusselt number being increased by 43.7%–812.6%; brings the increase of flow resistance, with friction factor being 4.2 to 16.7 times of empty tube; improves the overall thermal-hydraulic performance with performance evaluation criteria ranging from 1.5–3.6. The GMF causes maximum reduction of total entropy generation rate and maximum enhancement of exergetic efficiency to be 92.6% and 24.4%, respectively. The PTR tube partially filled with GMF can obtain higher thermal-hydraulic and thermodynamic performance than that with uniform metal foam.

Droplet impact onto thin film is a ubiquitous phenomenon in many industrial applications. In the present study, the VOF method is adopted to simulate the crown evolution during the impact process with different surface tension coefficient, viscosity and gravity. Especially, the crown behavior is investigated in the energy aspect. The kinetic energy, gravitational potential energy, surface energy and viscous dissipation are taken into consideration. The results reveal that higher surface tension coefficient leads to larger crown diameter. The evolution of gravitational potential energy can be divided into three phases: decrease phase, increase phase and collapse phase. Similarly, the evolution of surface energy can be divided into four phases: increase phase, drop phase, flat phase and collapse phase. The drop phase is caused by the film rupture in the center zone. In the case with zero gravity the flat phase is replaced by a second increase phase. In particular, it is found that larger viscosity will postpone the film rupture and the film even doesn't break at high viscosity.

The electrical power generation from low temperature heat source attracts more and more attentions but the temperature mismatching between the heat sources and working medium in the organic Rankine cycle (ORC) becomes an issue. The organic flash cycle (OFC) is an effective solution to this issue. In this paper, the OFC is analyzed by the concept of entransy loss and the T-Q (temperature-heat flow rate) diagram for the heat-work conversion. The equations for cycles of the basic OFC and the OFC whose heat source is the exhaust gas of the turbine in a Brayton cycle (the combined cycle) are derived theoretically and the results indicate that larger entransy loss rate leads to larger output power with prescribed inlet parameters of the hot stream in the discussed cases, which is displayed by the T-Q diagram intuitively. Two numerical examples demonstrate that the optimal mass flow rate of the working medium for the maximum entransy loss rate is the same as that for the maximum output power. The T-Q diagram analyses is in accordance with the numerical results. The concept of entransy loss can be used as the criteria for the OFC optimization.

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.

Based on the entropy generation minimization and entransy theory, we discuss the applicability of the concepts of entropy generation rate, entropy generation number, revised entropy generation number, exergy efficiency, entransy increase rate, entransy increase coefficient and entransy efficiency to the analyses of heat pump systems in this paper. The theoretical analyses show that all the concepts except for the entransy increase rate decrease monotonically with increasing COP, while only the entransy increase rate increases monotonically with increasing heat flow pumped into the high temperature heat sink. It is shown that the entransy increase rate is not as convenient as the other concepts for the COP analyses, while it is suitable for the analyses of the heat flow into the high temperature heat sources. Some numerical examples are also presented, and the results have verified the theoretical analyses. Therefore, the applicability of entropy generation minimization and entransy theory to the analyses of heat pump systems is conditional, depending on the design objectives.

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 netwo...

This paper presents the optimization of an air conditioning system, in which the heat from the hot stream is transported to do work first, and then the work is used to pump heat from the environment into the room. It is shown that the system can deliver more heat into the room than the direct heating by the hot stream. A functional is set up to optimize the distribution of the total thermal conductance for the system, and the numerical results show that the functional is effective. The system is also discussed with the concepts of entropy and entransy. It is found that the minimum values of the entropy generation rate, entropy generation number, revised entropy generation number, entransy loss and entransy loss coefficient all correspond to the maximum heat flow rate into the room with prescribed heat flow rate from the hot stream, but the values of the parameters all increase with increasing heat flow rate from the hot stream and that into the room.

The optimization model of the district heating system for an N-floor building is set up. The mass flow rate and thermal conductance distributions are optimized for prescribed total mass flow rate and prescribed total thermal conductance respectively by the Newton method. Two numerical examples are presented, and the effects of the parameters, such as the heat load, its distribution and the room temperature, on the optimal results are discussed. It is shown that for a three-floor building with two users on each floor, larger heat load requires larger mass flow rate on the corresponding floor when the total mass flow rate is prescribed. Putting the user of larger heat load nearest to the upstream flow reduces the total mass flow rate for fixed total heat load on the floor. For the three-floor building with one user on each floor, larger thermal conductance of the corresponding heat exchanger is required for the room with higher temperature when the total thermal conductance is prescribed. With fixed total heat load of two floors, distributing more heat load to the room with lower temperature reduces the total mass flow rate.

In this paper, the entransy expressions of the three thermodynamic laws are discussed. The entransy expression of the first law is that the entransy of any thermodynamic system is in balance. For the second law, the entransy expression for heat transfer is that the entransy flow will never be transported from a low temperature body to a high temperature body automatically and entransy dissipation always exists. The entransy expression for heat-work conversion is that it is impossible for any device to operate in a cycle that receives heat entransy flow from a single reservoir and results in an equivalent amount of work entransy flow. The two entransy expressions of the second law are proved to be equivalent to each other. For the third law, its entransy expression is that it is impossible to achieve the zero entransy for any body through limited processes. With these expressions, the Clausius inequality is proved, and the concept of entransy loss is defined. The application of entransy loss to heat transfer and heat-work conversion is discussed.

The Rankine cycle has been widely used in industry, and the optimization of the Rankine cycle is of great significance to energy utilization improvement. In this paper, both the concepts of entropy generation and entransy loss are applied to analyzing the thermodynamic processes of the Rankine cycle that receives heat from the exhaust-heat boiler with a hot stream and releases heat to a cold stream. In order to get the maximum output power, the mass flow rate of the working medium is optimized. Theoretical analysis and numerical results show that both the maximum entransy loss rate and the minimum entropy generation rate correspond to the maximum output power when the inlet temperatures and the heat capacity flow rates of the streams are prescribed. When the inlet temperatures or the heat capacity flow rates of the streams is not prescribed, smaller entropy generation rate does not lead to larger output power but larger entransy loss rate still leads to larger power output for this kind of cases.

The one-stream hybrid thermal network is analyzed and discussed based on the entransy theory, and the results are compared with those from the entropy generation optimization. The theoretical analysis indicates that the minimum heat-flow-weighted temperature of the thermal networks corresponds to the minimum entransy dissipation rate and the minimum thermal resistance. For a simple hybrid thermal network consisting of three thermal components, the expression of entransy dissipation is conducted, and the heat transfer area and the mass flow rate are calculated and optimized. The optimal results are obtained in order to minimize the entransy dissipation and the thermal resistance. The optimal results are calculated for various combinations, such as series connection, parallel connection and other hybrid connections. The numerical results are in accordance with the theoretical analysis. Both the theoretical analysis and the numerical results show that the minimum entransy dissipation and the minimum thermal resistance correspond to the minimum heat-flow-weighted temperature of the thermal networks while the minimum entropy generation does not.

The two-stream heat exchanger networks (THENs) are widely used in industry. The effectiveness of the THENs is analyzed in this paper. The general expressions for the entransy dissipation, the entransy-dissipation-based thermal resistance and the entropy generation for a generalized THEN are developed. It is found that the expressions are independent of the specific constitution of the THENs. Only the entransy-dissipation-based thermal resistance always decreases monotonously with the increase in effectiveness, while the entransy dissipation and the entropy generation do not. Therefore, the entransy-dissipation-based thermal resistance is most applicable for the optimization of the THENs.

Heat exchangers are widely used in industries and daily life. The optimization design of heat exchangers is of great significance to the consumption reduction of energy. This paper analyzes and discusses two-/three-stream heat exchangers based on the concepts of the entransy dissipation, the entropy generation and the entransy–dissipation-based thermal resistance of multi-stream heat exchangers. It is found that the minimum thermal resistance based on entransy dissipation always corresponds to the best performance of heat exchangers, while the minimum entropy generation and the extreme entransy dissipation do not always correspond to the best performance of heat exchangers. The relationship between the thermal resistance and uniformity factor of temperature difference field, the relationship between the thermal resistance and the effectiveness of heat exchangers are derived for the two-stream heat exchangers. The results indicate that the uniformity factor of temperature difference field and the effectiveness of heat exchangers would both increase with the decrease of the thermal resistance. In addition, it is found that a larger uniformity factor always leads to a higher effectiveness of heat exchangers. The physical meaning of the phenomenological principle of the uniformity of temperature difference field is discussed for the two-stream heat exchangers, and the uniformity principle of temperature difference field is proved directly.

The spectral radiative entransy flux and the total radiative entransy flux are defined for the steady radiative heat transfer processes in enclosures composed of non-isothermal or non-grey, opaque, diffuse surfaces. Based on the definitions, the radiative entransy flux balance equation and the radiative entransy dissipation functions are introduced under spectral and total wavelength condition. Furthermore, the minimum principle of radiative entransy loss, the extreme principle of radiative entransy dissipation and the minimum principle of radiative thermal resistance are developed. The minimum principle of radiative entransy loss shows that the potential and the net radiative heat flux distribution which meet the control equations and the boundary conditions would make the radiative entransy loss minimum if the net radiative heat flux or the potential distribution of the radiative heat transfer system is given. The extreme principle of radiative entransy dissipation indicates that the minimum radiative entransy dissipation leads to the minimum average potential difference for the prescribed total radiative heat exchange and the maximum radiative entransy dissipation leads to the maximum radiative heat exchange for the prescribed average potential difference. Moreover, the minimum principle of radiative thermal resistance tells us that the aforementioned extreme values of radiative entransy dissipation both correspond to the minimum value of radiative thermal resistance. Application examples are given for the extreme principle of spectral radiative entransy dissipation and the minimum principle of spectral radiative thermal resistance, and the principles are proved to be applicable.

Entransy is a new concept developed in recent years to measure the transport ability of heat at a temperature in conduction and convection. This paper develops the concept of entransy flux for thermal radiation in enclosures with opaque surfaces. The entransy balance equation and entransy dissipation function are derived. The minimum principle of radiative entransy loss is developed. The potentials and the heat fluxes distribution which meet the Stefan–Boltzmann’s law and the energy balance equation would make the radiative entransy loss minimum if the net heat flux of each surface or the thermal potentials of the surfaces are given. The extremum entransy dissipation principles (EEDP) for thermal radiation are developed. The minimum radiative entransy dissipation leads to the minimum average radiative thermal potential difference for prescribed total heat exchange and the maximum radiative entransy dissipation leads to the maximum heat exchange for prescribed average radiative thermal potential difference. The minimum and maximum principle can be concluded into the minimum thermal resistance principle (MTRP) for thermal radiation by defining the thermal resistance with the entransy dissipation. The EEDP or MTRP is proved to be reliable when they are used to optimize some radiative heat transfer problems, and a comparison is made between the minimum principle of entropy generation and the EEDP.

The experiments are carried out to study the transient heat transfer characteristics of a minichannel heat sink under high heat flux density that varies from 150 W/cm 2 to 200 W/cm 2 , in an enclosed loop. The heat flux is supplied by the ethyne flame. The average rate of the cooling water is from 1.00 m/s to 1.86 m/s. The temperature rise of the heated surface and the temperature rise of the cooling water are measured. The results show that the temperature rise of the heated top surface rises quickly at the startup period of heating, and then increases slowly. The variation of the top surface temperature is similar to the voltage in the RC circuit. The surface temperature is a function of thermal resistance and thermal capacity of the heat sink. The temperature of the cooling water at outlet also rises quickly at the startup period of heating, and then becomes stable. The temperature increases are related to the heat flux density and the rate of the cooling water. There is a time delay between the temperature rise of the inlet cooling water and the startup of heating. This delay is related to the length of the enclosed loop and the rate of the cooling water. The pressure drop across the heat sink decreases slightly with time at high heat flux since the water viscosity reduces with the increasing temperature.

The homogenization of temperature field and temperature gradient field are very important for many devices, systems and equipments, such as satellites and electronic devices. This paper discusses the distribution optimization of the limited high conductivity material with the simulated annealing algorithm to homogenize the temperature field in a two-dimensional heat conduction problem. At the same time, the temperature gradient field is homogenized with the bionic optimization method. The results show that the two optimization targets are consistent to some extent, while the bionic optimization method could save much computing time. In addition, there are threshold values for the amount of high conductivity material and the ratio of the high conductivity to the low conductivity beyond which further increasing these values brings very little improvement on the homogenization of temperature field and temperature gradient field.

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 extremum principle are presented.

The interfacial effects on flow and heat transfer on micro/nano scale are discussed in this paper. Different from bulk cases where interfaces can be simply treated as a boundary, the interfacial effects are not limited to the interface on a microscale but could extend into a significant, even the whole domain of the flow and heat transfer field when the characteristic size of the domain is close to the mean free path (MFP) of the carriers inside an object. Most of microscale thermal phenomena result from interfacial interactions. Any changes in the interactions between the object and boundary particles, such as the force between fluid and solid wall particles, microstructure of interfaces, could affect thermal properties, flow and heat transfer characteristics and hence change thermal conductivity, velocity and temperature profiles, friction coefficient and thermal radiative properties, etc. The properties of nano-structure or flow and heat transfer features of fluid in micro/nanostructures not only depend on themselves, but also on the interaction with the interface because the interface impact can go deep inside the flow. The same fluid, same channel geometry but different wall materials could have different flow and heat transport characteristics on microscale.

The present work discusses the scaling effect on steady and unsteady thermal processes at mini/microscale that behave differently from the bulk case. Fast transient thermal processes could not be realized at bulk scale because of large thermal inertia and seldom have applications for practical use. However, due to the development of state-of-the-art technology, the miniaturization of device size makes it possible to utilize thermal responses due to the significantly reduced thermal inertia. For the steady case, the thermal effect varies with the boundary conditions and flow parameters because the relative importance of different forces changes with size at mini/microscale. Thus, the thermal phenomena are different from the conventional cases and vary with size.

For enhancing the heat energy release from a phase change material (PCM) the conductive fin is designed according to a proposed constructal rule, in which the high conductivity material (HCM) should be located at the place where the heat flux density is the largest. The local temperature gradient integration over time is taken as a criterion to determine where to distribute the limited HCM during a given time period. This rule is applicable to heat conduction of steady and unsteady conditions, as well as to the problems with and without phase change. Numerical simulations show that the constructal design of a conductive fin has much better performance than arbitrary ones. The constructal rule is an effective technique that designs the fin with high performance for enhancing heat conduction.

The field synergy equation for steady laminar convection heat transfer was derived by conditional variation calculus based on the least dissipation of heat transport potential capacity. The optimum velocity field with the best heat transfer performance and least flow resistance increase can be obtained by solving the synergy equation. The numerical simulation of laminar convection heat transfer in a straight circular tube shows that the multi-longitudinal vortex flow in the tube is the flow pattern that enhances the heat transfer enormously. Based on this result, a novel enhanced heat transfer tube, the discrete double-inclined ribs tube (DDIR-tube), is developed. The flow field of the DDIR-tube is similar to the optimal velocity field. The experimental results show that the DDIR-tube has better comprehensive heat transfer performance than the current heat transfer enhancement tubes. The present work indicates that new heat transfer enhancement techniques could be developed according to the optimum velocity field.

Experiments are carried out on the convection inside a novel alternating elliptical axis tube. The unified correlations of heat transfer and flow resistance for 500

A systematic study has been carried out numerically and compared with some experimental data to examine the heating effect on the corner recirculation zone (CRZ) in sudden-expansion gas flows. The heat addition to such flows will lead to the reduction of the CRZ length, and the CRZ can even disappear if the heating intensity is sufficiently large. The concept of thermal drag (heating induced pressure drop in duct flows) has been used to clarify the underlying mechanism of the heating effect on CRZ. The heating induced reduction of the adverse pressure gradient in sudden-expansion flows should be largely responsible for the shrinkage of the CRZ due to heating. Computational results also show that heating the CRZ and the upstream part of expansion flow are more efficient for changes of the CRZ.

This work discusses the interfacial effects on flow and heat transfer at micro/nano scale. Different from bulk cases where interfaces can be simply treated as a boundary, the interfacial effects are not limited to the interface at microscale but extend into a significant, even the whole domain of the flow and heat transfer field when the characteristic size of the domain is close to the mean free path (MFP) of fluid particles. Most of microscale flow phenomena result from interfacial interactions. Any changes in the interactions between the fluid and solid wall particles could affect the flow and heat transfer characteristics, such as flow and temperature profiles, friction coefficient. The interactions depend on many parameters, such as the force between fluid and solid wall particles, microstructure of interfaces. The flow and heat transfer features does not only depend on the fluid itself, but also on the interaction with the solid wall because the interface impact can go deep inside the flow. Same fluid, same channel shape but different wall materials could have different flow characters.Copyright © 2006 by ASME

The concepts of entransy and entropy are applied to the analyses of the irreversible Carnot engines based on the finite time thermodynamics. Taking the maximum output power and the maximum heat-work conversion efficiency (HWCE) as objectives, the applicability of the entransy theory and the entropy generation minimization method to the optimizations is investigated. For the entransy theory, the results show that the maximum entransy loss rate always relates to the maximum output power, while the maximum entransy loss coefficient always leads to the maximum HWCE for all the cases discussed in this paper. For the concept of entropy generation, the maximum entropy generation rate corresponds to the maximum output power when the Carnot engine works between infinite heat reservoirs, while the entropy generation number cannot be defined in this case. When the Carnot engine works between the finite heat reservoirs provided by streams, the minimum entropy generation rate corresponds to the maximum output power with prescribed heat flow capacity rates and inlet temperatures of the streams, while the minimum entropy generation number corresponds to the maximum HWCE. When the heat capacity flow rate of the hot stream is not prescribed, the entropy generation rate increases with increasing output power, while the entropy generation number decreases with increasing HWCE. When the inlet temperature of the hot stream is not prescribed, the entropy generation rate increases with increasing output power, and the entropy generation number also increases with increasing HWCE.

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.

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 taken as an expression of the second law of thermodynamics for heat transfer. The thermal equilibrium criteria for an isolated system and a closed system are also introduced. It is found that when an isolated system reaches thermal equilibrium, its entransy is a minimum value. This criterion is referred to as the minimum entransy principle. When a closed system reaches thermal equilibrium, its free entransy is also a minimum value. This criterion is referred to as the minimum free entransy principle. Therefore, like entropy, entransy can be considered an arrow of time in heat transfer and used to describe the thermal equilibrium state.

The concept of entransy developed in recent years can describe the heat transport ability. This paper extends this concept to the open thermodynamic system and defines the concept of enthalpy entransy. The entransy balance equation of steady open thermodynamic systems, as well as the concept of entransy loss, is developed. The entransy balance equation is applied to analyzing and discussing the air standard cycle. It is found that the entransy loss rate can describe the change in net power output from the cycle but the entropy generation rate cannot when the heat absorbed by the working medium is from the combustion reaction of the gas fuel. When the working medium is heated by a high temperature stream, both the maximum entransy loss rate and the minimum entropy generation rate correspond to the maximum net power output from the cycle. Hence, the concept of entransy loss is an appropriate figure of merit that describes the cycle performance.