Volume 27, Issue 1

Given the premise that a set of dynamical equations must possess a definite, underlying mathematical structure to ensure local and global thermodynamic stability, as has been well documented, several different models for describing liquid crystalline dynamics are examined with respect to said structure. These models, each derived during the past several years using a specific closure approximation for the fourth moment of the distribution function in Doi's rigid rod theory, are all shown to be inconsistent with this basic mathematical structure. The source of this inconsistency lies in Doi's expressions for the extra stress tensor and temporal evolution of the order parameter, which are rederived herein using a transformation that allows for internal compatibility with the underlying mathematical structure that is present on the distribution function level of description.

It is not unusual for a Soret coefficient to change sign with temperature. We develop the theory for the onset of convection in such systems, heated from below or from above, provided that the mean temperature is precisely that at which the change of sign occurs. We also consider the realistic case of rigid, conducting, impervious boundaries for later comparison with laboratory experiments.

This paper treats the simple example of heating a system from a given initial to a given final temperature with minimum entropy production. The allowed control for the process is the selection of K temperatures for intermediate heat baths. The problem is sufficiently simple to allow analytic approaches and we compare the optimal solution with the solution prescribed by equal thermodynamic distance (ETD). We find that ETD coincides with the optimum if the heat capacity is constant. For a temperaturedependent heat capacity, ETD deviates from the exact optimum. ETD however matches the optimal solution to second order in 1/ K .

The irreversibilities resulting from the finite-rate heat transfer between the working substance and the external heat reservoirs and the regenerative losses in regenerative processes are considered in the cycle model of a magnetic Ericsson refrigerator. The fundamental optimum relations between the cooling rate and the coefficient of performance and between the power input and the coefficient of performance are derived, based on a class of heat-transfer laws and the Curie law. The general characteristic curves of the cycle are presented. The effect of the different forms of the regenerative time and heat-transfer laws on the performance of the cycle is discussed in detail. The results obtained here will be useful to further understand the general optimum performance of real magnetic Ericsson refrigerators.

Experimental results on the convective instability of a transient evaporating thin liquid layer are reported. Evaporation is identified as an agent causing Rayleigh-Bénard convection and/or Marangoni-Bénard convection. Convective flow occurs in the evaporating liquid layer as long as the evaporation is strong enough, regardless of whether the layer is heated or cooled from below. The wavelength of the cells maintains a preference value in steady evaporation. When an evaporating thin layer is strongly cooled from below, both the nonlinear temperature profile of the layer and the flow pattern change rapidly during the transient evaporation process. The wavelength of convection cells increases with time and tends towards the preference value with the approach of a steady evaporation stage. A modified Marangoni number and a modified Rayleigh number serve as the dimensionless control parameters for this system.

In this paper a realizable area in the parametric space of a thermodynamic system is defined. A system can operate without violating thermodynamic constraints only if its parameters remain within this area. We show how this area can be constructed using finite-time thermodynamic's technique. Realizability areas for a heat engine, a heat exchanger and a mass-transfer system are constructed.