ON ARRESTING THE COMPLEX GROWTH RATES IN FERROMAGNETIC CONVECTION IN A FERROFLUID SATURATED POROUS LAYER

Jyoti Prakash

doi:10.1615/JPorMedia.v16.i3.40

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Home > Journals > Journal of Porous Media > Volume 16, 2013 Issue 3 > ON ARRESTING THE COMPLEX GROWTH RATES IN FERROMAGNETIC CONVECTION IN A FERROFLUID SATURATED POROUS LAYER

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ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v16.i3.40
pages 217-226

ON ARRESTING THE COMPLEX GROWTH RATES IN FERROMAGNETIC CONVECTION IN A FERROFLUID SATURATED POROUS LAYER

Jyoti Prakash
Department of Mathematics and Statistics, Himachal Pradesh University Summer Hill, Shimla-171005, India

ABSTRACT

In the present paper it is shown that the complex growth rate σ = σ_r + iσ_i of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid saturated porous layer, for the case of free boundaries, lies inside a semicircle in the right half of the σ_r σ_i − plane whose center is at the origin and (radius)² = RM₁/P_r, where R is Rayleigh number, M₁ is magnetic numberand P_r is Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.

KEY WORDS: ferrofluid, complex growth rate, principle of exchange of stabilities, oscillatory motion, Pellew and Southwell technique