An upper bound on turbulent heat transport across a layer of electrically conducting Boussinesq fluid under a magnetic constraint
Abstract
The problem of finding an upper bound on the heat transport across a layer of electrically conducting Boussinesq fluid in the presence of a uniform magnetic field is considered. The analysis is restricted to statistically steady turbulent convection and the problem is studied using the variational theory of turbulence. The variational principle is formulated for a functional that includes the influence of the magnetic field. The resulting EulerLagrange equations are studied using a boundary layer approximation and the assumption of a single horizontal wave number. The results indicate that two regimes of turbulent hydromagnetic convection exist. The first occurs when the turbulence is strong or the size of the magnetic field is small. The maximum heat transport is only slightly reduced by the presence of the magnetic field and, as the intensity of the turbulence increases, the heat transport approaches the value for the nonmagnetic case. The other regime occurs for weak turbulence or a strong magnetic field. The heat transport is then inversely proportional to the size of the magnetic field, and it is found that a strong enough magnetic field completely suppresses the convection.
 Publication:

Ph.D. Thesis
 Pub Date:
 1975
 Bibcode:
 1975PhDT.......100M
 Keywords:

 Boussinesq Approximation;
 Heat Transfer;
 Magnetic Fields;
 Turbulent Flow;
 Boundary Layer Equations;
 Convection;
 Electrical Resistivity;
 Fluid Mechanics and Heat Transfer