Volume 39, Issue 3

The non-equilibrium contact temperature is an internal variable which is independent of the internal energy. As an internal variable, also the contact temperature needs an evolution equation. Some ideas concerning these evolution equations are discussed for discrete systems and for systems in field formulation.

In this paper we study the penetrative convection in an anisotropic porous medium, for fluids with quadratic density law with the anisotropic permeability and thermal diffusivity effects. Both linear instability and global non-linear energy stability analyses are tested using a three-dimensional simulation. Our results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold.

In this paper, we implement and verify an algorithm based on the eigendecomposition method to solve the one-dimensional mono-energetic transport equation in a semi-infinite medium with isotropic scattering. Using our algorithm, we produce approximate closed-form expressions for the solution. Moreover, the algorithm does not utilize a Laplace transform, offers reasonable accuracy, and displays rapid convergence using a relatively small number of quadrature points.

Thermodynamic irreversibility in thin silicon film is considered and entropy generation in the film is predicted. The Boltzmann equation is incorporated to formulate the phonon transport in the film due to temperature disturbance across the film edges. Frequency-dependent and frequency-independent phonon transport are introduced to compare the entropy predictions due to both cases. The study is extended to include the effect of the film thickness on the entropy generation in the film. A numerical code is developed using the discrete ordinate method and the predictions are validated with the data presented in our previous study. It is found that entropy generation is higher in the close region of the high temperature film edge. As the film thickness increases towards the cold temperature of the film edge, entropy generation rate becomes gradual. Entropy generation due to the frequency-independent case is higher than that corresponding to the frequency-dependent case. This behavior is attributed to the ballistic phonons, which do not contribute to the film resistance; therefore, they do not contribute to entropy generation in the film.

A four-stroke free-piston engine with internal and external irreversibilities of finite combustion rate of the fuel, heat transfer and friction is investigated in this paper. Under the condition of the fixed fuel consumption per cycle, the optimal piston motion trajectory for maximizing the net work output of different cases is derived by applying optimal control theory. Considering the path constraints and boundary conditions of this free-piston Miller cycle, a Gauss pseudospectral method (GPM) is presented for solving optimal motion trajectory. The results show that the optimal piston trajectory improves the efficiency by more than 10% and also suitably reduces the heat transfer losses compared to the conventional piston motion. By optimizing the piston motion around the top dead center (TDC), the in-cylinder gas pressure and temperature have a remarkable improvement while the heat transfer losses have a suitable reduction. The effects of other parameters, such as combustion duration and the frictional coefficient on the piston trajectory, are also investigated. It is shown that optimizing the piston motion trajectory is a good approach for the free-piston engine to improve the efficiency and it can provide guidelines for the optimal control of the practical free-piston engine.