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This paper concerns with unsteady two-dimensional temperature laminar
magnetohydrodynamic (MHD) boundary layer of incompressible fluid. It is
assumed that induction of outer magnetic field is function of
longitudinal coordinate with force lines perpendicular to the body
surface on which boundary layer forms. Outer electric filed is neglected
and magnetic Reynolds number is significantly lower then one i.e.
considered problem is in inductionless approximation. Characteristic
properties of fluid are constant because velocity of flow is much lower
than speed of light and temperature difference is small enough (under 50oC).
Introduced assumptions simplify considered problem in sake of
mathematical solving, but adopted physical model is interesting from
practical point of view, because its relation with large number of
technically significant MHD flows. Obtained partial differential
equations can be solved with modern numerical methods for every
particular problem. Conclusions based on these solutions are related
only with specific temperature MHD boundary layer problem. In this
paper, quite different approach is used. First new variables are
introduced and then sets of similarity parameters which transform
equations on the form which don't contain inside and in corresponding
boundary conditions characteristics of particular problems and in that
sense equations are considered as universal. Obtained universal
equations in appropriate approximation can be solved numerically once
for all. So-called universal solutions of equations can be used to carry
out general conclusions about temperature MHD boundary layer and for
calculation of arbitrary particular problems. To calculate any
particular problem it is necessary also to solve corresponding momentum
equation. |
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