Exact Normal‐Shock Solutions at Intermediate Prandtl Numbers

ABSTRACT

Exact solutions for the steady normal shock in the Navier–Stokes–Fourier framework for calorically perfect Newtonian gases are presented. The governing equations are reduced to an Abel differential equation of the second kind for general local transport laws of the longitudinal viscosity and thermal conductivity that maintain a constant longitudinal Prandtl number, while shock profiles are obtained by subsequent quadrature. For certain combinations of the specific heat ratio , longitudinal Prandtl number and upstream Mach number , exact solutions are obtained on one‐parameter curves in ‐space. The resulting longitudinal Prandtl numbers range from values close to zero up to 36. Exact shock profiles are developed for the constant‐coefficient case. Most solutions determine the fluid velocity implicitly, while one solution yields an explicit representation of the velocity as a function of the spatial coordinate.