This article presents an analytical and experimental study of magnetohydrodynamic
Rayleigh–Bénard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The
test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number
of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103<
Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.When a horizontal magnetic field is imposed on a heated liquid metal layer, the
electromagnetic forces give rise to a transition of the three-dimensional convective roll
pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls
become more and more aligned with the magnetic field. A linear stability analysis
based on two-dimensional model equations shows that the critical Rayleigh number
for the onset of convection of quasi-two-dimensional flow is shifted to significantly
higher values due to Hartmann braking at walls perpendicular to the magnetic field.
This finding is experimentally confirmed by measured Nusselt numbers. Moreover,
the experiments show that the convective heat transport at supercritical conditions is
clearly diminished. Adjacent to the onset of convection there is a significant region
of stationary convection with significant convective heat transfer before the flow
proceeds to time-dependent convection. However, in spite of the Joule dissipation
effect there is a certain range of magnetic field intensities where an enhanced heat
transfer is observed. Estimates of the local isotropy properties of the flow by a four-element
temperature probe demonstrate that the increase in convective heat transport
is accompanied by the formation of strong non-isotropic time-dependent flow in the
form of large-scale convective rolls aligned with the magnetic field which exhibit a
simpler temporal structure compared to ordinary hydrodynamic flow and which are
very effective for the convective heat transport.
Two-Dimensional Computation Model for Simultaneous Soil Water and Heat Transport in Bare Soil with Various Topography
