Nonisothermal Shock Structure and Universal Flow-Index Thresholds in a Hyperbolic Power-Law Fluid

We investigate whether the two flow-index thresholds previously found for isothermal shock profiles persist when the full nonisothermal dynamics is taken into account in a hyperbolic power-law relaxation model of Rational Extended Thermodynamics. The nonisothermal profile problem is structurally different from its isothermal counterpart; restoring the energy balance determines the temperature along the traveling wave and feeds it back into the pressure, the relaxation production, and the temperature-dependent consistency coefficient. We derive an exact global characteristic-ordering identity and prove that the positive nonequilibrium characteristic speed has its strict global minimum at the unperturbed upstream state. Consequently, a monotone continuous profile exists for 1< M 0 < M∗ 0, while for M 0 > M∗ 0 the Boillat–Ruggeri theorem excludes a C 1 profile. Despite the thermomechanical coupling, the shock-thickness classification remains unchanged with m= 2 as the weak-shock threshold and m= 1 as the near-critical threshold as M 0 approaches M ∗ 0. The corresponding exponents are constitutive-independent, while finite limiting values depend on the equation of state, internal energy, and temperature-dependent coefficient. For the Tait–Murnaghan example, increasing the reference temperature lowers the critical Mach number.