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The Quarterly Journal of Mechanics and Applied Mathematics 1965 18(1):31-40; doi:10.1093/qjmam/18.1.31
© 1965 by Oxford University Press
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HEAT TRANSFER IN HYDROMAGNETICS

P. RAMAMOORTHY

( Department of Mathematics, Queen Mary College London )

The classical theory of heat transfer in a boundary layer is extended to the hydromagnetic case in which a viscous, electrically conducting, incompressible liquid flows past an electrically insulated semi-infinite flat plate in the presence of a uniform magnetic field parallel to the plate. The equations governing the flow and the magnetic field have been integrated numerically on analogue and digital computers and the results used to integrate the equations governing the temperature. Two different cases have been considered. In the first, the problem of the ‘plate thermometer’ we find the surface temperature of a thermally insulated surface and the distribution in the boundary layer. In the second, we find the heat convection from the plate to the liquid, the plate being kept at a given temperature.

In both cases, we find that the temperature distribution in the boundary layer is considerably reduced because of the slowing down of the flow by the magnetic field. The dissipation of currents due to Joule heating is small.

It is found that the presence of the magnetic field increases both the viscous and temperature boundary layer thicknesses.


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