Oscillatory states in thermal convection of a paramagnetic fluid in a cubical enclosure subjected to a magnetic field gradient

Abstract

We report experimental and numerical studies of combined natural and magnetic convection of a paramagnetic fluid inside a cubical enclosure heated from below and cooled from above and subjected to a magnetic field gradient. Values of the magnetic field gradient are in the range 9≤|grad|b(0)|(2)|≤900 T(2)/m for imposed magnetic field strengths in the center of the superconducting magnet bore of 1≤|b(0)|(max)≤10 T. Very good agreement between experiments and simulation is obtained in predicting the integral heat transfer over the entire range of working parameters (i.e., thermal Rayleigh number 1.15×10(5)≤Ra(T)≤8×10(6), Prandtl number 5≤Pr≤700, and magnetization number 0≤γ≤58.5). We present a stability diagram containing three characteristic states: steady, oscillatory (periodic), and turbulent regimes. The oscillatory states are identified for intermediate values of Pr (40≤Pr≤70) and low magnetic field (|b(0)|(max)≤2 T). Turbulent states are generated from initially stable flow and heat transfer regimes in the range of 70≤Pr≤500 for sufficiently strong magnetic field (|b(0)|(max)≥4 T).