Nomenclature
Abbreviations
| Abbreviation | Meaning |
|---|---|
| BL | Boundary layer |
| NS | Navier-Stokes |
| FS | Falkner-Skan |
| FSC | Falkner-Skan-Cooke |
Coordinates and Velocity
| Symbol | Description |
|---|---|
| \(x\) | Streamwise coordinate |
| \(y\) | Wall-normal coordinate |
| \(z\) | Crossflow (spanwise) coordinate (3D only) |
| \(u\) | Streamwise velocity component |
| \(v\) | Wall-normal velocity component |
| \(w\) | Crossflow velocity component |
Thermodynamic and Transport Properties
| Symbol | Description |
|---|---|
| \(\rho\) | Density |
| \(p\) | Pressure |
| \(T\) | Temperature |
| \(\mu\) | Dynamic viscosity |
| \(k\) | Thermal conductivity |
| \(c_p\) | Specific heat at constant pressure |
| \(R\) | Specific gas constant |
| \(\gamma\) | Ratio of specific heats (\(= c_p/c_v\)) |
| \(\mathrm{Pr}\) | Prandtl number (\(= \mu c_p / k\)) |
Similarity Variables
| Symbol | Description |
|---|---|
| \(\eta\) | Similarity (wall-normal) coordinate |
| \(f\) | Streamwise stream function (\(f' = u/u_e\)) |
| \(f'\) | Streamwise velocity ratio \(u/u_e\) |
| \(f''\) | Streamwise velocity gradient |
| \(g_{cf}\) | Crossflow velocity ratio \(w/w_e\) |
| \(g_{cf}'\) | Crossflow velocity gradient |
| \(\tau\) | Normalised temperature \(T/T_e\) |
| \(\tau'\) | Normalised temperature gradient |
| \(N\) | Chapman-Rubesin parameter (\(= \rho\mu/\rho_e\mu_e\)) |
Flow Parameters
| Symbol | Description |
|---|---|
| \(M_e\) | Edge Mach number |
| \(\Lambda\) | Sweep angle |
| \(m\) | Wedge / power-law exponent (\(u_e \propto x^m\)) |
| \(\beta\) | Hartree pressure-gradient parameter (\(= 2m/(m+1)\)) |
| \(S\) | Stagnation enthalpy parameter (\(= 1 + \tfrac{\gamma-1}{2}M_e^2\cos^2\!\Lambda\)) |
| \(K\) | Crossflow recovery factor (\(= (1 + \tfrac{\gamma-1}{2}M_e^2)/S\)) |
| \(r\) | Adiabatic recovery factor (\(\approx \mathrm{Pr}^{1/2}\) for laminar flow) |
| \(T_{ad}\) | Adiabatic wall temperature |
| \(T_0\) | Stagnation temperature |
Subscripts
| Subscript | Meaning |
|---|---|
| \(e\) | Boundary layer edge (outer inviscid flow) |
| \(w\) | Wall |
| \(0\) | Stagnation (total) condition |
| \(\infty\) | Freestream condition |