Volume 29, Issue 3

A non-linear simplified model for a thermoacoustic engine is presented in this work, which assumes the form for the spatial dependence of the state variables and considers only effects inside the stack. For such a model the limit cycle solution is found numerically using a shooting technique in the ∇ T > ∇ T crit region, where the stationary, fixed-point, trivial solution is unstable. With this solution a bifurcation diagram for thermoacoustic phenomena is built. Through such diagram an analysis of the non-linear nature of the generated oscillations is conducted, focusing on the presence of harmonics and the higher-order time-average pressure.

A model of polarizable media investigated by Maugin and coworkers is considered as the domain of application of a recent method for the geometrization of the thermo-elasticity of continua with internal variables. The polarization together with its space gradient are assumed as state variables expressed in terms of internal variables evolving according to a relaxation law driven by external and internal electric fields. The entropy productions in Clausius-Duhem inequalities are calculated explicitly.

A systematic description of the interaction between two systems is presented within the framework of thermodynamics of discrete systems. We distinguish between two situations: a contact between an equilibrium system and a non-equilibrium one, and a contact between two non-equilibrium systems. In the second case the state space includes replacement quantities, which reduce the situation to a contact between an equilibrium system and a non-equilibrium one. Interacting discrete systems form a composite (compound) system which is also a discrete one. Thus a compound system can be described as if it were composed of two subsystems, or by ignoring this fact, as a plain single discrete system, whose composition of sub-systems is not taken into consideration. These descriptions cause different degrees of accuracy which are expressed by excess quantities. Such an excess quantity vanishes if the discrete system is really not composed of subsystems. Aim of this paper is to calculate the excess quantities of power and energy exchange and to derive the excess entropy in the special case of an endoreversible compound system.

Moment’s methods devised to solve the Boltzmann kinetic equation for a simple, inert, dilute gas exhibit inconsistencies. These are brought up in a general way for the ordinary Boltzmann equation (BE), the Bhatnagar-Gross-Krook (BGK) model, and the Mott-Smith ansatz. Although also present in the Chapman-Enskog method the nature of its perturbation expansion in terms of Knudsen’s number takes care of the problem in a natural way. We show that indeed another step based on this idea is required to arrive at a closure condition in the moment’s solution. Also, a general proof is offered showing why these inconsistencies appear when appealing to moment expansions.

Direct contact membrane distillation process has been studied using microporous polytetrafluoroethylene and polyvinylidene fluoride membranes. The membranes were characterized in terms of their non-wettability, pore size distribution and porosity. The mean pore sizes and pore size distributions were obtained by means of wet/dry flow method. The mean pore size and the effective porosity of the membranes were also determined from the gas permeation test. A theoretical model that considers the pore size distribution together with the gas transport mechanisms through the membrane pores was developed for this process. The contribution of each mass transport mechanism was analyzed. It was found that both membranes have pore size distributions in the Knudsen region and in the transition between Knudsen and ordinary diffusion region. The transition region was the major contribution to mass transport. The predicted water vapor permeability of the membranes were compared with the experimental ones. The effect of considering pore size distribution instead of mean pore size to predict the water vapor permeability of the membranes was investigated.

Periodic operating systems can conserve energy by temporarily transferring one form of energy into another. However, every transfer of energy Δ E in a system of mass M has a characteristic time scale τ. Thus the power flux per unit mass q ′ = Δ E /( M τ) is not arbitrary. Time scales τ = C t · M α and energy fluxes P = C p · M β for various processes are expressed here as power functions of M . The scaling law constants C t and C p depend on various internal parameters, occasionally allowing the performance of systems to be optimized. When energy changes its form reversibly inside abody there is no mass dependence on the time scale and on the specific power transfer: α, β = 0. In most other cases beta is negative in the range -2/3 ≤ β ≤ 0, and alpha is positive in the range 0 ≤ α ≤ 1/2.