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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]

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]