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The least action principle is used in various disciplines including linear transport processes. However, non-equilibrium thermodynamic analyses of linear transport processes involve the dot product of the thermodynamic flux and the thermodynamic force which must be the entropy production rate in the linear phenomenological law for such processes; thus, Fourier’s heat conduction law cannot be derived based on the variation of the entropy production rate. A generalized linear phenomenological law for various types of linear transport processes, including heat conduction, mass diffusion, electric conduction and fluid flow in porous medium is introduced here where the dot product of a generalized flux and a generalized force is taken as the action to give the generalized linear phenomenological law. For heat conduction, the entransy dissipation rate, which is the dot product of the heat flux and the negative of the temperature gradient, is taken as the action, and the variation of the entransy dissipation rate then leads to Fourier’s heat conduction law with constant thermal conductivity. Hence, the action of heat conduction process is the entransy dissipation rate rather than the entropy production rate. A nonlinear constitutive relation for the heat conduction with temperature dependent thermal conductivity is then converted to a linear problem by introducing a generalized temperature, which gives a least generalized entransy dissipation principle for nonlinear heat conduction processes. Finally, the least entransy dissipation principle is applied to optimize a one-dimensional heat conduction problem without heat-work conversion as an example where the minimum entropy generation principle is not applicable. [ABSTRACT FROM AUTHOR]

Abstract: A new physical quantity, , has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction. This quantity, which will be referred to as entransy, corresponds to the electric energy stored in a capacitor. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes as a measure of the heat transfer irreversibility. The concepts of entransy and entransy dissipation were used to develop the extremum principle of entransy dissipation for heat transfer optimization. For a fixed boundary heat flux, the conduction process is optimized when the entransy dissipation is minimized, while for a fixed boundary temperature the conduction is optimized when the entransy dissipation is maximized. An equivalent thermal resistance for multi-dimensional conduction problems is defined based on the entransy dissipation, so that the extremum principle of entransy dissipation can be related to the minimum thermal resistance principle to optimize conduction. For examples, the optimum thermal conductivity distribution was obtained based on the extremum principle of entransy dissipation for the volume-to-point conduction problem. The domain temperature is substantially reduced relative to the uniform conductivity case. Finally, a brief introduction on the application of the extremum principle of entransy dissipation to heat convection is also provided. [Copyright &y& Elsevier]

The present discussion will focus on the size effect induced by the variation of dominant factors and phenomena in the flow and heat transfer as the device scale decreases. Due to the larger surface to volume ratio for microchannels and microdevices, factors related to surface effects have more impact to microscale flow and heat transfer. For example, surface friction induced flow compressibility makes the fluid velocity profiles flatter and leads to higher friction factors and Nusselt numbers; surface roughness is likely responsible for the early transition from laminar to turbulent flow and the increased friction factor and Nusselt number; the relative importance of viscous force modifies the correlation between Nu and Ra for natural convection in a microenclosure and, other effects, such as channel surface geometry, surface electrostatic charges, axial heat conduction in the channel wall and measurement errors, could lead to different flow and heat transfer behaviors from that at conventional scales. [Copyright &y& Elsevier]

Theoretical analysis and experimental confirmation for the principle to improve the thermal performance of heat exchangers is performed in this paper. The more uniform the temperature difference field (TDF), the higher the effectiveness of heat exchanger for the fixed Ntu and Cr. The uniformity of the TDF and the effectiveness of 13 types of heat exchangers are studied analytically and numerically, and the results support the uniformity principle of TDF. Further verification is given by the asymptotic solution for TDF in terms of a recurrence formula of heat transfer area distribution for the same kind of heat exchanger. The analysis of entropy generation caused by the heat transfer indicates that the uniformity principle of TDF satisfies the second law of thermodynamics. The results of the experimental setup, governed by the uniformity principle of TDF, show that the effectiveness increases with the increase of the uniformity of TDF. Heat exchanger effectiveness for the best flow distribution was found to be 11.2% greater than that of the conventional flow distribution without associated increase in pressure drop. Two ways, redistributing heat transfer areas and varying the connection between tubes, are presented for improving the uniformity of TDF and increasing effectiveness for the crossflow heat exchangers. [Copyright &y& Elsevier]

This note is to refute Bejan’s accusation (Bejan, 1983) that our work on field synergy (Guo, 1998) is a duplication of his idea of “heatline” (Kimura and Bejan, 1983), however in fact the two are significantly different. The former treats the convective heat transfer as heat conduction with heat sources which are the dot product of local velocity and temperature gradient, whereas the latter regards convective heat transfer as a flow of net energy which is simple combination between heat flow and enthalpy flow, and introduces a heat function borrowed from the streaming function in fluid mechanics,. The use and robustness of the two are also different. The field synergy is useful in enhancement/optimization of convective heat transfer, but heatline theory is only for visualization of convective heat transfer. [ABSTRACT FROM AUTHOR]

Heat conduction optimization with arbitrary boundary conditions is a challenging problem that lacks a universal optimization criterion. In the present work, the concept of generalized entransy dissipation (GED) is proposed through transforming heat conduction optimization problems with arbitrary boundaries into their homogeneous counterparts. It is demonstrated that minimizing GED leads to optimal thermal performance of heat conduction problems with arbitrary boundary conditions. In addition, GED-based continuous optimization problems are convex, guaranteeing the uniqueness and global optimality of the solution and benefitting numerical calculations. Two typical problems with complex boundary conditions are studied by applying the minimum principle of GED, and the results are compared with other optimization objectives. The numerical results show that GED achieves better thermal performance than entropy generation- (EG) and entransy dissipation- (ED) based optimizations. For the optimization of boundary average temperature under the given input heat flux of ▪, GED achieves the best result, where the optimized average temperature is ▪ and ▪ lower compared with EG and ED optimizations, respectively. In general, GED offers a reasonable and easy to implement optimization principle for heat conduction processes with arbitrary boundaries and may provide new insights for heat conduction optimization. • GED-criterion is proposed for optimizing heat conduction with arbitrary boundaries. • Minimizing GED leads to optimal thermal performance of complex boundary conditions. • Convexity of GED-based continuous optimization guarantees global optimality. • GED outperforms EGMP and EDEP, lowering average temperature by 48.8 and 27.5 K. • GED offers a universal and easy-to-use principle for heat conduction processes. [ABSTRACT FROM AUTHOR]

This note is our comments to the paper entitled, “Equivalence between the application of entransy and entropy generation” (Oliveira and Milanez, 2015). In this paper, the authors showed the equivalence between the application of the concepts of entransy and entropy by using several application examples including three physical models of solar energy collectors and a physical model of a sensible heat storage system. The main expressions regarding entransy in this paper come from our conference paper entitled, “Entransy transfer analysis and its application to optimizing irreversible thermodynamic cycles” (Wu and Guo, 2007). However, the authors did not distinguish between the entransy, the entransy transfer, and the thermodynamic entransy transfer. The application of which was shown to be equivalent to that of entropy generation by the authors using four examples, is the thermodynamic entransy transfer rather than the entransy transfer. Hence, the conclusion that the applications of entransy and entropy are equivalent is not appropriate. [ABSTRACT FROM AUTHOR]

Heat transfer optimization principle is critically important for further explaining the underlying mechanisms and guiding practical designs of heat transfer processes. Recently, the entransy theory has been successfully used to optimize various steady-state heat transfer processes. Nevertheless, it is still an open question whether this theory can be utilized in transient cases. Here, we examined the applicability of the entransy analyses on the one-dimensional transient heat conduction process. It was found that the entransy dissipation rate can neither derive the transient governing equation nor correspond to the optimal result in the transient optimization problem. Therefore, an extended entransy dissipation rate was defined as the convolution integral of heat flux and negative temperature gradient. The total extended entransy dissipation rate over the time and space domain can correspond to the optimal result of the transient optimization problem. Additionally, Fourier transform was used to convert the transient problem from the time domain into the frequency domain, and the total entransy dissipation rate in the frequency domain will give a convenient optimization criterion that the temperature gradient field should be spatially uniform to reach the shortest characteristic time. Also, the inverse Fourier transform of the entransy dissipation rate in the frequency will be the extended entransy dissipation rate in the time domain. Finally, these findings were used to optimize a practical transient heat conduction problem for a solid thermal energy storage unit. [ABSTRACT FROM AUTHOR]

Optimization analyses of two heat exchanger networks show that if the optimization objective of the heat exchanger network can be expressed as an explicit function of all the independent variables, its derivatives with respect to each variable can offer the optimal solution. If there is no explicit function, optimization problem can be solved by using the Lagrange multiplier method, which combines the optimization objective and the constraints. However, heat exchanger networks with many heat exchangers have a large number of variables and constraint equations in the Lagrange function, which slows the optimization solution. A crank mechanism is used as an example to indicate that the Lagrange multiplier method can be simplified in a generalized coordinate instead of Cartesian coordinates. Inspired by the use of generalized coordinates in multi-body systems, the entransy balance equation for the heat exchanger network is introduced here as a new constraint to replace the conventional constraints of heat transfer and energy conservation equations for the optimization of a loop-connected heat exchanger network. As a result, the number of variables and constraints in the Lagrange multiplier function is reduced and the solution is simplified. In this sense, the entransy balance equation can be termed as the generalized constraint. Finally, the reason for the simplification function of the entransy dissipation-based generalized constraint is explored. [ABSTRACT FROM AUTHOR]

• Propose the concept of irreversibility indicator for transport processes. • Entropy generation cannot measure irreversibility of standalone transport processes. • Entropy generation-based optimization may deteriorate process performance instead. • Irreversibility of a transport process should be measured by its energy dissipation. The entropy generation has been widely used for evaluating irreversibility of transport processes and optimize their performance. However, there still exist challenges against this methodology. This work revisits the irreversibility evaluation in typical transport processes. The irreversibility indicator of transport processes is proposed combining aspects of physical essence and practical application. It is expected to be able to recover the constitutive relation, characterize the evolution direction of process, and optimize standalone transport processes. The entropy generation rate is examined against these conditions, and results show that it fails to meet them. These failures challenge the legitimacy of entropy generation rate in characterizing transport processes' irreversibility. In contrast, the irreversibility of heat, mass, and momentum diffusion processes can be measured by the entransy dissipation, mass entransy dissipation, and momentum entransy dissipation, respectively. A one-dimensional "volume-to-point" heat conduction and a mass diffusion optimization problem are numerically studied, respectively. Results show that the entransy dissipation-based optimization reduces the average temperature by 3–5 K, giving a better performance than entropy generation optimization, which increases the average temperature up to 17.55 K. In the mass diffusion problem, the mass entransy dissipation-based optimization reduces the average concentration by 3.67%, showing a much better performance than the entropy generation optimization, which yields a 26% increase. Finally, these irreversibility indicators are found to be equivalent to their corresponding energy dissipations. [ABSTRACT FROM AUTHOR]

Abstract: Heat transfer optimization methods to effectively improve heat transfer performance is of great importance for energy conservation and pollution reduction. A recently developed heat transfer optimization method based on entransy theory and related peer-reviewed papers published between 2003 and 2010 are reviewed and updated in this paper to describe entransy, entransy dissipation, optimization criteria and optimization principles and their applications to different heat transfer modes (thermal conduction, convection and radiation) and to different levels (heat transfer element, heat exchanger, and heat exchanger network). Entransy theory is then compared with entropy theory in several aspects, including the heat transfer purpose, irreversibility and optimization principle for energy savings or weight reductions of thermal facilities. Finally, entransy theory is also compared with constructal theory in terms of optimization objective, optimization method and optimized results. [Copyright &y& Elsevier]

Abstract: Based on Einstein’s mass–energy relation, the equivalent mass of thermal energy or heat is identified and referred to as thermomass. Hence, heat conduction in carbon nanotubes (CNTs) can be regarded as the motion of the weighty phonon gas governed by its mass and momentum conservation equations. The momentum conservation equation of phonon gas is a damped wave equation, which is essentially the general heat conduction law since it reduces to Fourier’s heat conduction law as the heat flux is not very high and the consequent inertial force of phonon gas is negligible. The ratio of the phonon gas velocity to the thermal sound speed (the propagation speed of thermal wave) can be defined as the thermal Mach number. For a CNT electrically heated by high-bias current flows, the phonon gas velocity increases along the heat flow direction, just like the gas flow in a converging nozzle. The heat flow in the CNT is governed by the electrode temperature until the thermal Mach numbers of phonon gas at the tube ends reach unity, and the further reduction of the electrode temperature has no effect on the heat flow in the CNT. Under this condition, the heat flow is said to be choked and temperature jumps will be observed at the tube ends. In this case the predicted temperature profile of the CNT based on Fourier’s law is much lower than that based on the general heat conduction law. The thermal conductivity which is determined by the measured heat flux over the temperature gradient of the CNT will be underestimated, and this thermal conductivity is actually the apparent thermal conductivity. In addition, the heat flow choking should be avoided in engineering situations to prevent the thermal failure of materials. [Copyright &y& Elsevier]

Abstract: The turbulent heat transfer and flow resistance in an enhanced heat transfer tube, the DDIR tube, were studied experimentally and numerically. Water was used as the working fluid with Reynolds numbers between 15,000 and 60,000. The numerical simulations solved the three dimensional Reynolds-averaged Navier–Stokes equations with the standard k-ε model in the commercial CFD code, Fluent. The numerical results agree well with the experimental data, with the largest discrepancy of 10% for the Nusselt numbers and 15% for the friction factors. The heat transfer in the DDIR tube is enhanced 100∼120% compared with a plain tube and the pressure drop is increased 170∼250%. The heat transfer rate for the same pumping power is enhanced 30∼50%. Visualization of the flow field shows that in addition to the front and rear vortices around the ribs, main vortices and induced vortices are also generated by the ribs in the DDIR tube. The rear vortex and the main vortex contribute much to the heat transfer enhancement in the DDIR tubes. Optimum DDIR tube parameters are proposed for heat transfer enhancement at the same pumping power. [Copyright &y& Elsevier]

Abstract: In this paper the mechanism of heat transport in metallic nanofilms under ultra-short pulsed laser heating is examined theoretically and experimentally. In order to easily understand the non-equilibrium heat transport in metallic nanofilms the study of heat transport behavior is first carried out in dielectrics. The analyses indicate that there may be two kinds of wave phenomena in dielectrics subjected to a periodic surface temperature. One is the thermal wave governed by the C–V model based hyperbolic equation and the other is the diffusive wave governed by the Fourier model based parabolic equation. According to the hyperbolic two step model for non-equilibrium heat transport, such two kinds of wave phenomena can also occur simultaneously in the metallic nanofilms under pulsed laser heating, where the diffusive wave is induced by the electron temperature oscillation at the surface due to the non-equilibrium between electrons and lattices. Unlike the propagation speed of the thermal wave, the propagation speed of the diffusive wave depends not only on the medium properties but also the period of the temperature oscillation at the boundary. Hence, the propagation speed of the diffusive wave in the electron gas may be of as high as 106 ms−1, when the laser pulse duration is less than 1ps. A transient thermoreflectance (TTR) system has been built to measure the transient electron temperature responses caused by the femtosecond laser heating and a pump–probe technique is used to ensure the femtosecond temporal resolution in the experiments. Different from the commonly used front heating-front detecting (FF) method for measuring the material properties, a rear heating-front detecting (RF) method is applied, so that measuring the propagation speed of heat becomes available. The non-equilibrium heat diffusion model is used to fit the measured normalized electron temperature profiles of 27.2nm, 39.9nm and 55.5nm Au films. The best-fitted coupling factor G basically agrees with the theoretical value 2.3×1016 Wm−3 K−1. The propagation speed of the diffusive wave in the electron gas can be obtained by comparing the measured delay time of peak electron temperatures of Au films with different thicknesses. The average propagation speed of the temperature oscillation or diffusive wave in Au films for the range of thickness from 27.2nm to 55.5nm is equal to 8.1×105 ms−1, which is close to the value predicted by the non-equilibrium heat diffusion model. [Copyright &y& Elsevier]

Abstract: Following the brief introduction to the concept of a physical quantity, entransy, the equivalent thermal resistance of a heat exchanger couple is defined based on the entransy dissipation. The minimum thermal resistance principle is applied to obtain the optimal heat capacity rate of the medium fluid and the optimal allocation of heat exchangers thermal conductance, which correspond to the maximum heat transfer rate in the heat exchanger couple. In addition, analytical expression for the optimal heat capacity rate of the medium fluid is derived, whose reciprocal equals the sum of the reciprocal of the individual heat capacity rate of the hot and cold fluids, just like the case of two electrical capacitors in series. Numerical results in the variation of the thermal resistance and the heat transfer rate with the medium fluid heat capacity rate or the thermal conductance allocation agree with the theoretical analyses. Finally, for comparison, the entropy generation rate is also calculated to obtain its relation with the thermal performance of the heat exchanger couple. The results show that there is no one-to-one correspondence of the minimum entropy generation rate and the maximum heat transfer rate. This indicates that the minimum entropy generation principle cannot be used for optimizing the heat exchanger couple. [Copyright &y& Elsevier]