Volume 27, Issue 3

Biological thought suggests that organisms tend toward optimal design through evolution. This optimization should be evident in the physiology of organs and organ systems. However, a given organ often has multiple roles to play in the optimization of the organism, and sometimes the logical optimization criteria for the different roles may be contradictory. In this paper we consider the case of skeletal muscle. One of its obvious functions is movement of the organism, for which efficiency is clearly a goal. However, muscle is also important for temperature regulation through shivering. In this latter function muscle should produce heat; i.e. it should be maximally inefficient. The thermodynamic optimizations desired for these two roles appear diametrically opposed. We show a way out of this dilemma by constructing a simple, physiologically motivated model of the contraction-relaxation cycle of muscle. This model muscle can be both an efficient mover in a ‘purposeful contraction’ regime, characterized by large movements of low frequency, and a good heat producer in a distinct ‘shivering’ regime characterized by small movements of high frequency.

In this paper we obtain the existence of solutions and continuous dependence on the supply terms and initial conditions for the equation of the dual-phase-lag heat conduction theory. When the phase-lag constants satisfy a certain condition we can prove exponential stability with respect to time and spatial variables. When this condition is not satisfied we can prove the instability of solutions.

A link is developed between the work that thermally-driven winds are capable of performing and the entropy of the windspeed history: this information entropy is minimized when the minimum work required to transport the heat by wind is dissipated. When the system is less constrained, the information entropy of the windspeed record increases as the windspeed fluctuates to dissipate its available work. Fluctuating windspeeds are a means for the system to adjust to a peak in entropy production.

Graphical representations of the first and second-law effciencies of heat engines, refrigerators and heat-pumps are used to compare these real devices with their corresponding reversible counterparts. Other representations, such as the temperature-energy diagram, also known as the Bejan/Bucher diagram, illustrate the conservation nature of the first and second-law of thermodynamics. This work intends to combine the major benefits of these thermodynamical representations by means of a dimensionless approach and using the concepts behind the Bejan/Bucher diagram into a new diagram. The proposed chart allows a direct reading of the first and second law effciencies and of the entropy generation. It may be used as well to compare different thermal machines among them, with the available thermodynamical models and with the observed performance of state of the art devices, from both first and second-law viewpoints. Using simple geometrical concepts, a number of thermodynamical principles can also be easily deduced. This is illustrated, in Appendix A, through the derivation of the Curzon-Ahlborn formula for the efficiency of endoreversible engines; the most complex case of the Curzon-Ahlborn engine–different cold and hot thermal resistances–is considered.

A distillation column with the possibility of heat exchange on every tray (a fully diabatic column) is optimized in the sense of minimizing its total entropy production. This entropy production counts the interior losses due to heat and mass flow as well as the entropy generated in the heat exchangers. It is observed that the optimal heating distribution, i.e. the heat exchange required on each tray, is essentially the same for all trays in the stripping and rectification sections, respectively. This makes a column design with consecutive interior heat exchanger and only one exterior supply for each of the two sections very appealing. The result is only slightly dependent on the heat transfer law considered. In the limit of an infinite number of trays even this column with resistance to transfer of heat becomes reversible.

This paper sets out a framework for discussing operations whose cost can be made to approach zero by subdividing the operation into an increasing number ( K ) of stages. Examples of such processes include what thermodynamics books call quasistatic processes taking place with near-equilibrium conditions between the participants. For any fixed value of K , there are always many ways to carry out the subdivision. This paper addresses some questions related to the asymptotic (large K ) behavior of the minimum total cost. In particular, we show that corresponding points in optimal subdivisions for objective functions differ by O(1/ K 2 ). Our main result is the construction of a geometrically motivated near-optimal partition scheme whose total cost (for each K ) differs from the true minimum by O(1/ K 3 ). The research is motivated by recent efforts in the analysis of entropy production minimization for thermodynamic processes. In that context, our result shows that the equal thermodynamic distance subdivision will come within O(1/ K 3 ) of the true minimum entropy production.

Measurements have recently been made of the thermodynamic conditions at the interface during steady state, liquid-vapour phase transitions. In these stationary, nonequilibrium states discontinuities were recorded in the temperature and other intensive properties. Independently of whether evaporation or condensation was taking place, it was found that the interfacial temperature was higher in the vapour phase than that in the liquid. The expression for the interfacial entropy production during these phase change processes is formulated using statistical rate theory. The interfacial entropy production rate is not a minimum when there is a phase change process taking place, but if the system is required to be closed (no net phase change), the interfacial entropy production rate is a minimum. States of minimum entropy production rate can exist arbitrarily far from equilibrium, provided a certain relation exists between the properties of the substance undergoing the phase change. For water, it is found that states of minimum entropy production rate are only slightly displaced from the stationary, nonequilibrium states existing when a net phase change rate is present.