© 1967 by Oxford University Press
THE MAGNETOGASDYNAMIC BOUNDARY LAYER FOR A THERMALLY CONDUCTING PLATE
( Department of Mathematics, The University Leeds )
This paper is concerned with the flow in the boundary layer on a semi-infinite flat plate placed at zero incidence to a uniform stream of electrically conducting gas with an aligned magnetic field at large distances from the plate. The equations governing the flow, magnetic field and temperature are derived for any heat-transfer condition at the plate.
Six parameters are involved, namely Pr, 
,
= 4
µ
, ß = µH2/4
U2, M2 =U2/c2 and the temperature difference Tp—T or the temperature gradient (
T/ y)p; a complete solution would therefore be difficult to obtain. Two different cases are considered;
(i) the plate is thermally insulated, i.e. the problem of the ‘plate thermometer’;
(ii) the plate is maintained at any given temperature which for the purpose of the numerical PARTof this paper has been taken to be that of the main stream.
The equations have been integrated numerically taking = 0.1, ß = 0.3 and 0.5, and = 0, ß = 0 in all three cases for Pr = 1, = 1.4, and M2 = 0, ½, 1, 2, 5, 10, and 25. For given values of ß and M the effect of changing the boundary conditions from (i) to (ii) is to increase both the skin friction and tangential component of magnetic field at the plate and also to increase the width of the boundary layer slightly.
It is found that increasing the magnetic field for a given Mach number, or decreasing the Mach number for a given magnetic field thickens the boundary layer.