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A characterization theorem in hydromagnetic double-diffusive convection coupled with cross diffusions

Mohan H.

Studia Geotechnica et Mechanica

2010

Vol. 32, nr 2

23-39

In the present paper, the governing equations of hydromagnetic double-diffusive convection problem of Veronis' type coupled with cross diffusion are linearized by the construction of a proper transformation and the relationship between various energies is established. The analysis made shows that total kinetic energy associated with a disturbance is greater than the sum of its total magnetic and concentration energies in the parameter regime. The result is valid for quite general boundary conditions.

Effect of rotation on double-diffusive convection in a magnetized ferrofluid with internal angular momentum saturating a porous medium

Sunil, Mahajan A.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 4

1059-1078

This paper deals with the theoretical investigation of the effect of rotation in a magnetized ferrofluid with internal angular momentum, heated and soluted from below saturating a porous medium and subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been employed to study the onset of convection. The influence of various parameters on the onset of stationary convection such as rotation, medium permeability, solute gradient, magnetization and internal angular momentum parameters (i.e., coupling parameter, spin diffusion parameter and heat conduction parameter) has been analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of buoyancy magnetization parameter and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferrofluid with internal angular momentum saturating a porous medium heated from below in the absence of rotation, coupling between vorticity and spin, microinertia and solute gradient. The oscillatory modes are introduced due to the presence of the rotation, coupling between vorticity and spin, microinertia and solute gradient, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.