No abstract

This paper analyses the effects of small injection/suction Reynolds number, Hartmann parameter, permeability parameter and wave number on a viscous incompressible electrically conducting fluid flow in a parallel porous plates forming a channel. The plates of the channel are parallel with the same constant temperature and subjected to a small injection/suction. The upper plate is allowed to move in flow direction and the lower plate is kept at rest. A uniform magnetic field is applied perpendicularly to the plates. The main objective of the paper is to study the effect of the above parameters on temporal linear stability analysis of the flow with a new approach based on modified Orr-Sommerfeld equation. It is obtained that the permeability parameter, the Hartmann parameter and the wave number contribute to the linear temporal stability while the small injection/suction Reynolds number has a negligible effect on the stability.

This paper considers the nonlinear dynamics of the oscillations of an individual plant forced by the fluctuating aerodynamic drag and significantly influenced by collisions with its close neighbors. In this study, a row of identical and flexible oscillators is considered. The flexible beams theory is used to model the equation of motion of an individual plant and then plant collisions were modelled as a simple spring, linear dashpot and nonlinear dashpot interactions between adjacent plants. The multiple scales method is used to obtain the amplitude of the plant relative to wind forcing in the resonant and nonresonant oscillations cases. Numerically, chaotic oscillations, hysteresis and coexistence of attractors have been found using the bifurcation diagram, the Lyapunov exponents and the phase portraits. The influences of both type of dashpot collisions on the dynamics behaviors of the plant have been analyzed.

The linear and nonlinear dynamics of thermal convection of a rotating hybrid nanofluid layer heated from below with the Cattaneo–Christov heat flux model are studied in this paper. Starting from the flow equations of a hybrid nanofluid and exploiting the free boundary conditions, the analytical expressions of the stationary and oscillatory Rayleigh numbers of the base fluid are determined as a function of the dimensionless parameters of the heat transfer fluid and the thermophysical properties of the hybrid nanofluid. The effects of hybrid nanoparticles and Taylor number on the onset of stationary convection in the base fluid are investigated graphically. Then, a numerical study of the transition from natural convection to chaotic behaviour of the hybrid nanofluid is made using the truncated Galerkin approximation. This approximation allowed us to find a novel six-dimensional nonlinear system depending on the parameters of the base fluid and the thermophysical properties of the hybrid nanofluid that can be reduced to five, four, or three dimensions when we tend some parameters to zero. The different results showed that the addition of hybrid nanoparticles (alumina-copper) to a thermal fluid (water) subjected to the rotation force in the presence or absence of the thermal relaxation time allows control of the chaotic convection in the base fluid. On the other hand, the increase of the rescaled Taylor number and the Cattaneo number widens the domain of chaos in the hybrid nanofluid with the increase of the rescaled Rayleigh number of the base fluid.