Volume 39, Issue 2

Abstract. A nonlinear stability threshold for convection in a rotating couple-stress fluid saturating a porous medium with temperature- and pressure-dependent viscosity using a thermal non-equilibrium model is found to be exactly the same as the linear instability boundary. This optimal result is important because it shows that linear theory has completely captured the physics of the onset of convection. The effects of couple-stress fluid parameter F , temperature- and pressure-dependent viscosity Γ, interface heat transfer coefficient H , Taylor number T A , Darcy–Brinkman number D˜a$\tilde{D}a$, and porosity modified conductivity ratio γ on the onset of convection have been investigated. Asymptotic analysis for both small and large values of interface heat transfer coefficient H is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions.

Abstract. Phonon transport in a two-dimensional thin silicon film is considered and the effect of heat source size and the film thickness on the transport characteristics is examined. Frequency dependent Boltzmann equation is incorporated in the analysis to account for the contribution of the ballistic phonons to the energy transport. Equivalent equilibrium temperature is introduced to assess the thermal resistance during the phonon transport in the film. The numerical scheme with the appropriate boundary conditions is used to predict the transport properties, including the effective thermal conductivity, of the thin film. It is found that the heat source size and the film thickness influence the thermal resistance of the film almost equally. The ballistic phonons reduce the film thermal resistance while suppressing the effective thermal conductivity in the thin film.

Abstract. Rapid solidification occurs under large driving force of transformation from the metastable undercooled liquid phase to the stable crystalline state. Using a formalism of extended irreversible thermodynamics, a phase-field model of rapid solidification in binary systems is derived. An entropy approach together with a grand potential density of a binary system is used to obtain the main governing equations of the model. Special attention is paid to equations of a rapidly solidifying binary system which are accompanied by essential deviations from local equilibrium in the transport of the conservative variables (such as inner energy and mass) and in the dynamics of non-conservative variables (such as phase field). The obtained equations are analyzed and compared with recent models and outcomes based on the grand potential approach to solidification.