Shock structure for heat conducting and viscid fluids
Abstract
The shock structure problem is investigated for a class of theories offering relativistic generalizations developed by Muller (1966), which showed that a regular shock structure may exist only at low Mach numbers. Balance equations for a continuum are defined for a plane steady shock, and evolution equations are presented. Conditions are found within which the system of wave propagation is hyperbolic, and the structure of a steady plane shock wave is explored analytically. An asymptotic theory for weak shocks is studied, yielding a form which is independent of the form of the transport coefficients. A critical Mach number is obtained which limits the shock speed which will yield a stable structure, and the Muller equations in the stable regime are demonstrated to be equivalent to the NavierStokesFourier theory for the same speeds.
 Publication:

Meccanica
 Pub Date:
 September 1981
 Bibcode:
 1981Mecc...16..149A
 Keywords:

 Conducting Fluids;
 Conductive Heat Transfer;
 Flow Theory;
 Gas Transport;
 Shock Wave Propagation;
 Viscous Fluids;
 Asymptotic Methods;
 Flow Stability;
 Fourier Law;
 Mach Number;
 NavierStokes Equation;
 Plane Waves;
 Steady Flow;
 Transport Properties;
 Fluid Mechanics and Heat Transfer