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3 Mechanics and Mechanical Engineering

3 2004

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The transformational analytical solution for nonlinear convection in the presence of two-way rotation

El-Kholy S. A., Ismail I. A.

Mechanics and Mechanical Engineering

2004

Vol. 7, nr 1

119-130

Steady two-dimensional finite amplitude solutions are obtained for the problem of convection in a horizontal fluid layer heated from below and rotated about its vertical axis. The flow is assumed to be laminar and two-dimensional. The density variation is taken into account by the Boussinesq approximation. Different boundaries with prescribed constant temperature are assumed and the solutions are obtained. The transform for summing the variables, which reduce the nonlinear partial differential equation into ordinary differential equation of the high order, is used. The existence of steady subcritical finite amplitude solutions is demonstrated for different Prandtl numbers. A strong reduction in the domain of stable rolls that occurs as the rotation rate is increasing. Convection driven by thermal buoyancy in the presence of the Coriolis force occurs in planetary atmospheres and interiors. Asymptotic expressions for the onset of convection in a horizontal fluid layer of finite extent heated from below and rotating about a vertical axis are derived in the limit of large rotation rates in the case of stress-free upper and lower boundaries. In the presence of the vertical sidewalls the critical Rayleigh number R is much lower than the classical value of the infinity extended layer.

The exact solution of nonlinear stress-free convection under the influence of magnetic fields

El-Kholy S. A.

Mechanics and Mechanical Engineering

2004

Vol. 7, nr 2

13-22

This paper aims at transforming nonlinear equations (Navier-Stokes, energy and magnetic induction) in steady state into ordinary high order differential equations. The exact solution for it has been found using a suitable transformation. The second goal is studying the state conditions of heating from below in a horizontal layer and studying the influence of the magnetic field on the phenomenon of convection itself. This model paper has uncovered the properties of electricity-conducting fluid elements. These properties have been disclosed neither in theory nor in practice. This study has been applied on the stress-free boundaries. All of which have realistic manifestation, in nature. They study convection in geophysics and astrophysics. Results have been illustrated in three dimensions to generalize the study and use it practically.

Axisymmetric MHD oscillation of a compressible hollow jet

Radwan A. E., Eltaweel M. A.

Mechanics and Mechanical Engineering

2004

Vol. 7, nr 2

127-130

The capillary oscillation of compressible hollow Jet under the action of the electromagnetic force for axisymmetric perturbation is discussed. Some published results are recovered as limiting cases on utilizing the dispersion relation of the present model. The capillary force has a destabilizing effect in a small range (0 ≤ χ < 1, where χ is the dimensionless longitudinal wavenumber) of perturbation. While it is stabilizing as 1 ≤ χ < ∞. The compressibility has a strong destabilizing tendency of the model for all wavenumber values χ ≠ 0. Each of the magnetic fields pervaded in the gas and liquid regions has a stabilizing effect for all short and. long wavelengths. As that effect is so strong, the capillary instability is suppressed and stability sets in. But in fact here the model is unstable due to the strong destabilizing effect of the compressibility.