The shock ahead of a high-speed body decelerates the air to the stagnation point and raises its temperature to thousands of degrees. At those temperatures air no longer behaves as an ideal gas: molecules dissociate, ionisation begins, and heat transfer becomes dependent on the chemical state.
The 1958 work of Fay and Riddell establishes the fundamental relation for stagnation-point heat transfer in dissociated air, treating separately the cases of a boundary layer in chemical equilibrium or frozen, and of a wall that is catalytic or non-catalytic [1].
Nose radius: where aerodynamics and thermal design conflict
Stagnation-point heat flux varies inversely with the square root of the nose radius. The practical consequence: sharpening the nose lowers drag but sends the heat flux up.
That is why re-entry capsules are blunt — a blunt nose pushes the shock away from the surface and brings the heat flux down to a manageable level. Aerodynamic and thermal requirements pull in opposite directions here, and the design is a compromise.
Wall catalycity: the large neglected uncertainty
Dissociated atoms recombining at the surface release additional heat. The more readily the surface material promotes that recombination (its catalycity), the higher the heat load. The difference between the fully-catalytic and non-catalytic wall assumptions can be a factor in heat flux.
This is not a modelling preference but an uncertainty item, and it should be reported. Running both extremes and quoting the range is far more honest than quoting a single value. See the note on significant digits.
Modelling requirements
Shock resolution. Because the heat flux depends on the post-shock state, the shock position must come out right. The mesh has to be fine normal to the shock; adaptive refinement more than repays itself here. See the compressible flow note.
Wall resolution. Heat flux is the temperature gradient at the wall; it is not computed by a wall function. y+ < 1 is mandatory. See the cell type note.
Radiation. At high enough speeds the gas behind the shock radiates in its own right, and this becomes a non-negligible part of the total heat load. See the radiation note.
Conjugate solution. If the temperature distribution within the thermal protection material is the question, fluid and solid have to be solved together; the thermal inertia of the material sets the surface temperature directly along the flight profile. See the conjugate heat transfer note.
References
- Fay, J. A. & Riddell, F. R. (1958). Theory of stagnation point heat transfer in dissociated air. Journal of the Aerospace Sciences, 25(2), 73–85. DOI: 10.2514/8.7517
- Modest, M. F. & Mazumder, S. (2021). Radiative Heat Transfer, 4th ed. Academic Press. ISBN 978-0-323-98406-5.