On arresting the complex growth rates in ferromagnetic convection with magnetic field dependent viscosity in a rotating ferrofluid layer

• The linear stability analysis for a rotating ferrofluid layer with magnetic field dependent viscosity heated from below is made.
• Upper bounds for the complex growth rates are obtained for free and rigid boundaries.
• Bounds are important mainly when atleast one boundary is rigid so that exact solutions in closed form are not obtainable.
• Results derived involve only nondimensional quantities and are independent of the wave number; are, thus, of uniform validity and applicability.

It is proved analytically that the complex growth rate ω=ωr+iωi (ωrandωi are respectively the real and imaginary parts of ωω) of an arbitrary oscillatory motion of growing amplitude in ferromagnetic convection, with magnetic field dependent viscosity, in a rotating ferrofluid layer for the case of free boundaries, must lie inside a semicircle in the right half of the ωrωiωrωi- plane whose center is at the origin and (radius)2=max{(RM1/Pr),Ta}, where RR is the Rayleigh number, M1M1 is the magnetic number, PrPr is the Prandtl number and TaTa is the Taylor number. Further, bounds for the case of rigid boundaries are also derived separately.