An exact solution in closed form, in terms of elliptic functions, is obtained for the one-dimensional steady flow of a polytropic gas with finite constant electrical conductivity which is influenced by an oblique magnetic field and a transverse electric field in the absence of viscosity, thermal conductivity and all other non-electrical dissipative mechanisms. The solution is presented in terms of elementary functions and the many possible flow patterns are discussed in detail in the case when, at some position, the transverse momentum equals the transverse Maxwell stress; a case which is appropriate to the structure of switch-on and switch-off shock waves.
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The research reported in this paper was supported in part by the United States Air Force under Grant No. AF-EOAR-65-58 and monitored by the European Office, Office of Aerospace Research.
Communicated by C. C. Lin
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Helliwell, J.B. One-dimensional steady magnetogasdynamic flow in oblique fields and the structure of shock waves. Arch. Rational Mech. Anal. 26, 237–256 (1967). https://doi.org/10.1007/BF00281972
- Thermal Conductivity
- Electrical Conductivity
- Shock Wave
- Flow Pattern
- Closed Form