Fay-Riddell equation

The Fay-Riddell equation is a fundamental relation in the fields of aerospace engineering and hypersonic flow, which provides a method to estimate the stagnation point heat transfer rate on a blunt body moving at hypersonic speeds in dissociated air.^[1] The heat flux for a spherical nose is computed according to quantities at the wall and the edge of an equilibrium boundary layer.

where ${\displaystyle {\text{Pr}}}$ is the Prandtl number, ${\displaystyle {\text{Le}}}$ is the Lewis number, ${\displaystyle h_{0,e}}$ is the stagnation enthalpy at the boundary layer's edge, ${\displaystyle h_{w}}$ is the wall enthalpy, ${\displaystyle h_{D}}$ is the enthalpy of dissociation, ${\displaystyle \rho }$ is the air density, ${\displaystyle \mu }$ is the dynamic viscosity, and ${\displaystyle (du_{e}/dx)_{s}}$ is the velocity gradient at the stagnation point. According to Newtonian hypersonic flow theory, the velocity gradient should be:$${\displaystyle \left({\frac {du_{e}}{dx}}\right)_{s}={\frac {1}{R}}{\sqrt {\frac {2(p_{e}-p_{\infty })}{\rho _{e}}}}}$$where ${\displaystyle R}$ is the nose radius, ${\displaystyle p_{e}}$ is the pressure at the edge, and ${\displaystyle p_{\infty }}$ is the free stream pressure. The equation was developed by James Fay and Francis Riddell in the late 1950s. Their work addressed the critical need for accurate predictions of aerodynamic heating to protect spacecraft during re-entry, and is considered to be a pioneering work in the analysis of chemically reacting viscous flow.^[2]