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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]

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]

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]