Volume 25, Issue 2

The thermal instability of a rotating plasma in a porous medium is considered in the presence of a uniform vertical magnetic field to include the Hall-current, finite-Larmor-radius (FLR) and variable gravitational field effects. It is found that the principle of exchange of stabilities is valid in the absence of rotation and magnetic field (hence Hall-current). The uniform vertical magnetic field (and hence an FLR and Hall-current) and rotation effects introduce oscillatory modes in the system which were non-existent in their absence. The system is stable/unstable depending upon certain conditions in the presence of rotation, medium permeability and magnetic field (hence Hall-current and an FLR). The Rayleigh number is found to increase with the increase of the magnetic field (and hence an FLR and Hall-current), rotation and medium permeability.

The formalism of internal state variables is proposed for describing the processes of deformation in muscles. Due to the complicated hierarchical microstructure of soft tissues where macroscopic stress states depend upon the sliding of molecules and ion concentrations, the internal variables are switched in successively forming a certain hierarchy. This hierarchy is a general property for complicated materials with different microscopic processes influencing the macroscopic behaviour. Based on that property a novel concept of hierarchical internal variables is defined (up to the knowledge of authors first time) and embedded into the framework of the existing formalism. The discussion based on an example of cardiac muscle contraction illustrates the advantages of this approach.

In this paper, we use an averaged entropy inequality and employ it together with an entropy principle to develop thermodynamically consistent rate-dependent turbulence models and governing equations at the first order level for describing the turbulence. In particular, a thermodynamically consistent evolution equation of the dissipation rate of the turbulent kinetic energy is presented in contrast to other recent works [1–3]. The domain of validity of the model is defined by the restrictions placed upon the model parameters imposed by the entropy inequality, so that only physically realizable processes can be described. As a consequence, it is shown that the so-called “realizability-constraints” in [4, 5] which are often presented and applied to ensure physically sound solutions of the models in the literature, alone are not able to guarantee conformity with the irreversibility of the turbulent processes; they are only one among other conditions required by the second law of thermodynamics. On this basis the thermodynamic consistency of some existing nonlinear eddy-viscosity models as well as anisotropic models is analysed and discussed. It appears from this critical evaluation that many of the existing models are thermodynamically inadmissible.

The current description of a formation cell using nonequilibrium thermodynamics gives an overall picture. It does not consider the behaviour of the temperature, chemical potential and electric potential locally. Thus it is unclear where temperature and potential change in the cell. Are these quantities discontinuous at the electrode surfaces, and if yes: how this should be described. Using methods developed in our earlier work we present such a local description. A differential equation is derived and solved for the transference coefficient of the salt in the electrolyte between the electrodes. Boundary conditions are essential for this purpose.

The mesoscopic concept in continuum mechanics consists of extending the domain of the balance equations by the set of mesoscopic variables and of introducing a local distribution function of these variables as a statistical element. The balance equations defined on this extended domain and an example concerning liquid crystals of biaxial molecules are discussed.