Stokes’ Hypothesis and Entropy Variation Within a Compression Shock

Abstract. Exact one-dimensional steady flow equations for viscous, heat conducting calorically perfect gases were derived in terms of a velocity potential. These nonlinear differential equations were integrated numerically thus predicting detailed variation of thermodynamic and flow properties through the normal steady compression shock waves for an entire range of ratios of secondary and primary viscosity coefficients, Reynolds numbers, and upstream Mach numbers. The results conform that entropy reaches its sharp maximum inside the shock wave and that shock wave strengths and losses correspond to Rankine-Hugoniot jump conditions only when Stokes hypothesis (zero bulk viscosity) is enforced.