Magnetohydrodynamic Peristaltic flow of a couple stress with heat and mass transfer of a Jeffery fluid in a tube through porous medium
The effects couple stress on the unsteady flow of a couple stress fluid an incompressible non-Newtonian (Jeffrey) fluid through porous medium have been discussed. The thermal diffusion thermo effect are taken to our consideration. Analytical expression for the axial velocity, stream function and axial pressure gradient are established. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The non-linear partial differential equations which govern this problem are simplified by making the assumptions of long wave length approximation. The analytical formula of the velocity and temperature have been obtained in terms of Bessel function of first and second kinds. In addition, it has been illustrated graphically for significant various parameters such as, magnetic parameter, couple stress parameter, permeability parameter, and thermal parameters .
Linear and Non-Linear Stability Analysis for Thermal Convection in A Bidispersive Porous Medium with Thermal Non-Equilibrium Effects
     The linear instability and nonlinear stability analyses are performed for the model of bidispersive local thermal non-equilibrium flow. The effect of local thermal non-equilibrium on the onset of convection in a bidispersive porous medium of Darcy type is investigated.  The temperatures in the macropores and micropores are allowed to be different. The effects of various interaction parameters on the stability of the system are discussed. In particular, the effects of the porosity modified conductivity ratio parameters,  and , with the inter-phase momentum transfer parameters and, on the onset of thermal Convection are also considered. Furthermore, the nonlinear stability boundary is found to be below the linear instability threshold. The numerical results are presented for free-free boundary conditions.
MODELLING LIVING FLUIDS WITH THE SUBDIVISION INTO THE COMPONENTS IN TERMS OF PROBABILITY DISTRIBUTIONS
As it follows from the results of C. H. Waddigton, F. E. Yates, A. S. Iberall, and other well-known bio-physicists, living fluids cannot be modelled within the frames of the fundamental assumptions of the statistical-mechanics formalism. One has to go beyond them. The present work does it by means of the generalized kinetics (GK), the theory enabling one to allow for the complex stochasticity of internal properties and parameters of the fluid particles. This is one of the key features which distinguish living fluids from the nonliving ones. It creates the disparity of the particles and hence breaks the each-fluid-component-uniformity requirement underlying statistical mechanics. The work deals with the corresponding modification of common kinetic equations which is in line with the GK theory and is the complement to the latter. This complement allows a subdivision of a fluid into the fluid components in terms of nondiscrete probability distributions. The treatment leads to one more equation that describes the above internal parameters. The resulting model is the system of these two equations. It appears to be always nonlinear in case of living fluids. In case of nonliving fluids, the model can be linear. Moreover, the living-fluid model, as a whole, cannot have the thermodynamic equilibrium, only partial equilibriums (such as the motional one) are possible. In contrast to this, in case of nonliving fluids, the thermodynamic equilibrium is, of course, possible. The number of the fluid components is treated as the number of the modes of the particle-characteristic probability density. In so doing, a fairly general extension of the notion of the mode from the one-dimensional case to the multidimensional case is proposed. The work also discusses the variety of the time-scales in a living fluid, the simplest quantum-mechanical equation relevant to living fluids, and the non-equilibrium nonlinear stochastic hydrodynamics option. The latter is simpler than, but conceptually comparable to, stochastic kinetic equations. A few directions for future research are suggested. The work notes a cohesion of mathematical physics and fluid mechanics with the living-fluid-related fields as a complex interdisciplinary problem.