What question did this study set out to answer?

To derive exact analytical solutions for steady normal shock waves within the Navier–Stokes–Fourier framework for calorically perfect Newtonian gases across a wide range of Prandtl numbers.

August 1, 2026Studies in Applied Mathematics

Exact Normal‐Shock Solutions at Intermediate Prandtl Numbers

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Authors

RPRaimund Feodor Perschke

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Implication

Mathematical analysis derives exact steady normal-shock solutions in calorically perfect Newtonian gases, revealing explicit shock structures across intermediate Prandtl numbers up to 36.

Key Points

To derive exact analytical solutions for steady normal shock waves within the Navier–Stokes–Fourier framework for calorically perfect Newtonian gases across a wide range of Prandtl numbers.
Transformed the steady Navier–Stokes–Fourier equations into an Abel differential equation of the second kind for transport laws maintaining a constant longitudinal Prandtl number.
Identified one-parameter analytical solution curves in parameter space defined by the specific heat ratio, longitudinal Prandtl number, and upstream Mach number.
Evaluated shock profiles by direct quadrature under constant-coefficient transport assumptions.
Derived exact shock solutions covering longitudinal Prandtl numbers extending from near zero up to 36.
Generated implicit velocity profiles for most parameter combinations, alongside a unique explicit closed-form expression for fluid velocity as a spatial coordinate.

Cite This Study

Raimund Feodor Perschke (2026) studied this question.

synapsesocial.com/papers/6a9076d54ca7c096eec90f24 https://doi.org/10.1111/sapm.70287

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Implication

Mathematical analysis derives exact steady normal-shock solutions in calorically perfect Newtonian gases, revealing explicit shock structures across intermediate Prandtl numbers up to 36.

Exact Normal‐Shock Solutions at Intermediate Prandtl Numbers

Discussion

Member takes

Implication

Key Points

Cite This Study

Exact Normal‐Shock Solutions at Intermediate Prandtl Numbers

Discussion

Member takes

Implication

Key Points

Cite This Study

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