Application of the method of characteristics to the solution of the universal equation for a plane boundary layer in a conducting fluid

Yu. E. Karyakin - V. E. Karyakin - T. V. Demidova

Abstract
We discuss the application of the method of characteristics to the solution of the universal equation for a plane magnetohydrodynamic boundary layer in an incompressible fluid in a transverse magnetic field. The system of characteristics of the universal equation is a family of curves issuing from a singular point of the "nodal" type. Along each of the characteristics the universal equation reduces to a set of partial differential equations in two independent variables and a system of ordinary differential equations. It is shown that solution of the universal characteristic equation is particularly simple in the two-parameter approximation. Then the characteristics are rays issuing from the singular point f₁ = κ₁ = 0. In the two-parameter approximation the equation was integrated by computer. Plots of the universal functions are given and methods for solution of specific problems on the motion of a conducting fluid in the boundary layer are indicated.