I'm trying to solve these equations of hypersonic adiabatic flow over a flat plate. I did all the simplifications and got these equations for the stagnation point flow. $$\left(Cf''\right)' + f f'' = \left(f'\right)^2-g$$ $$\left(\frac{C}{p_r} g'\right) + fg'=0$$
For a calorically perfect gas, $g=h/he$, and $he = \rm stagnation ~enthalpy$
$p_r$ is a constant and $C=g^{-1/3}$
$f(0)=0$ (over the streamline of the body)
$f'(0)=0$ (this is $u$, the velocity over the body which is null)
$f''(0)=?$ white suggests to try as a first value $0.664/\sqrt{C_w}$
I'm doing this for the adiabatic case so
$g(0)=g_{wall}$
$g'(0)=0$ (no thermic flux)
UPDATE
Control conditions:
$f'(\delta)=1$ and $g(\delta)=1$
I want to integrate from $\delta=0$ to $\delta=6$, in the end, if $f'(\delta)$ is different than $1$ I'll have to change the value assumed for $f''(0)$.
How can I solve these equations, someone suggested me using the shooting method but how could I code this in matlab? I would like just a help on how to implement the equations on matlab, not a final solution.