Non-linear Convection in Couple Stress Fluid with Non-classical Heat Conduction Under Magnetic Field Modulation

Abstract The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.

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Non-linear dynamic analysis of bearing—rotor system lubricating with couple stress fluid

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes814 ◽

2008 ◽

Vol 222 (4) ◽

pp. 599-616 ◽

Cited By ~ 2

Author(s):

C-W Chang-Jian ◽

C-K Chen

Keyword(s):

Dynamic Analysis ◽

Chaotic Motion ◽

Couple Stress ◽

Couple Stress Fluid ◽

Speed Ratio ◽

Non Linear ◽

System Life ◽

The Stability ◽

Suitable System ◽

Bearing System

The current study performs a dynamic analysis of a rotor supported by two couple stress fluid film journal bearings with non-linear suspension. The dynamics of the rotor centre and bearing centre are studied. The analysis of the rotor—bearing system is investigated under the assumptions of a couple-stress lubricant and a short journal bearing approximation. The displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The analysis methods employed in this study include the dynamic trajectories of the rotor centre and the bearing centre, Poincaré maps, and bifurcation diagrams. The Lyapunov exponent analysis is also used to identify the onset of chaotic motion. Numerical results show that the stability of the system varies with the non-dimensional speed ratios. Specifically, it is found that the system is quasi-periodic at a small speed ratio ( s = 0.5). At speed ratios of s = 0.6–0.7, the system is periodic. At s = 0.8–1.9, the system is quasi-periodic, but the system is periodic at s = 2.0–2.6. However, the system exhibits chaotic motion at the speed ratios s = 2.7–2.74. At the speed ratios s = 2.75–3.16, the system becomes periodic. At s = 3.17–3.30, the system is unstable. The Poincaré map has a particular form at s = 3.17, indicative of a chaotic motion. At s = 3.31–6.0, the system finally becomes periodic. The results also confirm that the stability of the system varies with the non-dimensional speed ratios s and l∗. The results of this study allow suitable system parameters to be defined such that undesirable behaviour of the rotor centre can be avoided and the bearing system life extended as a result.

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