Unsteady heat transfer of a monatomic gas between two coaxial circular cylinders
We consider a kinetic-theory treatment of the cylindrical unsteady heat transfer. A model kinetic equation of the BGK (Bhatnager-Gross-Krook) type is solved using the method of moments with a two-sided distribution function. We study the relations between the different macroscopic properties of the gas as the temperature, density, and heat flux with both the radial distance r and the time t. Also we study the problem from the viewpoint of irreversible thermodynamics and estimate the entropy, entropy production, entropy flux, thermodynamic forces, kinetic coefficients, the change in internal energy, and verify Onsager′s relation for nonequilibrium thermodynamic properties of the system.
On the free unsteady expansion of an ideal gas
The asymptotic laws governing the unsteady flow of an ideal (i.e., inviscid and non-heat-conducting) gas expanding freely out of a plane, cylindrical or spherical volume are studied within the framework of the continuum model. In the case of expansion into a vacuum, the laws obtained are valid in a certain neighborhood of the plane, axis or center of symmetry for time values at which the gas density (or specific enthalpy) is much smaller than its initial value. The characteristic feature of this region is its “elongatedness” in the direction of the timet-axis in thex, t-plane (x being the spatial variable). This region expands in thex-direction as well, but not as fast as in thet direction. For large values oft the same laws govern the flow induced by two symmetrically expanding plane, axisymmetric or spherical pistons, in the neighborhood of the plane, axis or center of symmetry. Similar laws governing steady-state hypersonic gas flows were studied in [1–6].
Second sound and internal energy in solids
Abstract A non-linear thermodynamic model of heat-conducting anisotropic solid is elaborated which turns out to be in a conservative form. Then, through the associated main field variables, the symmetry and the hyperbolicity properties are investigated. As outstanding applications, the analysis of the grow of the wave discontinuities and the evaluation of the critical time are performed. Finally, the Rankine-Hugoniot conditions for the system of equations are given in detail.