Natural convection in a horizontal cylindrical enclosure filled with a magnetic nanofluid: Influence of the uniform outer magnetic field

An analytical and numerical study of laminar convection in a horizontal cylindrical enclosure heated from below is performed. It is found analytically that uniform outer magnetic field can cause instability of the equilibrium state of magnetic nanofluid or influence gravity convection. Particular attention is paid to the steady convection, structure transients and the onset of unsteadiness. The Prandtl number from 0.7 to 700, different Rayleigh numbers (up to 106) and magnetic Rayleigh number are considered. For a nonmagnetic fluid, we studied the influence of the Prandtl number on the Rayleigh number values for which the equilibrium state becomes unstable, convective flow becomes bi-cellular, or becomes nonstationary. The effect of the magnetic Rayleigh number and the thermal conductivity of the solid block surrounding the enclosure on the onset of the convection is investigated. It is found that the magnetic permeability of the magnetic fluid filling the enclosure is an important factor. Four modes of fluid flow are studied analytically and then two of them are demonstrated during numerical simulation. It is shown that the outer uniform magnetic field turns to nonuniform in the magnetic fluid heated from below with not only the vertical, but also with the horizontal components of the gradient. So, there is a weak no-threshold convective flow even for very small magnetic Rayleigh numbers. The influence of the convective flow on magnetic field structure in the volume of a non-conducting magnetic fluid is found. Critical temperature difference for the experiment is predicted.