The structure of MHD shock waves

The MHD equations are used to discuss the formation and structure of shock waves in channel flow of an ionized gas with finite viscosity, thermal and electrical conductivity. The fundamental resulting complicated nonlinear differential equations are solved exactly, and the shock structure is determined completely. A necessary compatibility condition for the evolution of shock waves is obtained in the form:

where Pr and Pr_m are ordinary and magnetic Prandtl numbers and γ the ratio of specific heats. The flow quantities and parameters are found to depend, in a non-analytical manner, on Pr and Pr_m, so that special cases of interest are to be treated separately. Numerical results are given and discussed.