The dynamics of a buoyant plume rising above a horizontal line heat source in a transverse, horizontal magnetic field is investigated. Similarity is shown to occur when the magnetic field strength varies as the -2/5 power of vertical distance from the source. The plume depends on two parameters -the Prandtl number (Pr) and the Lykoudis number (ZL). Families of exact closed form solutions are derived for Pr = 5/9 and Pr _> 2. A family of numerical integrations for Pr = 0.01 (typical of liquid metals) is also reported. The magnetic field is shown to affect the profiles of velocity and temperature by altering the similarity functions, the coefficients, and the value of the independent similarity variable corresponding to a fixed physical position. An approximate closed form solution valid for low Pr and high Z L is presented. Possible experimental tests of the theory are proposed.
Nomenclature
B magnetic field strength B 0 constant introduced in (9) C constant introduced in (35) C~ constant of integration Cp specific heat at constant pressure D constant introduced in (35) f non-dimensional similarity stream function g acceleration due to gravity Gr Grashof number I non-dimensional heat flux integral J integral defined by (34) * Research sponsored by the U.S. Energy Research and Development Administration under interagency agreement with Union Carbide Corporation.