# Fluid dynamics - boundary later equation $f'''+ff''-f'^2+\theta = 0$ and $\theta''+Prf\theta' = 0$

Our lecturer gave us a system of boundary layer equations:

\begin{align}f'''+ff''-f'^2+\theta &= 0 \\ \theta''+Prf\theta'&=0 \end{align} subject to boundary conditions:
$$f=f'=0, \qquad \theta'=-1 \qquad \mathrm{at} \quad y=0 \\ f'\rightarrow 0, \qquad \theta \rightarrow = 0 \qquad \mathrm{as} \quad y \rightarrow \infty$$

and ask us to solve for the wall temperature $$\theta(0)$$ and the reduced skin friction $$f''(0)$$ numerically for different Prandtl number. I have finished that part and found the required value, but I still don't know what's the equation all about. Can someone please point me to the right direction (i.e. relevant paper or book) that discuss this set of equations??? I have limited knowledge on the subject and only know they are non-dimensional equations.....

• Could it be Stagnation point flow? I just googled third order ode and was lucky... – Emil Dec 19 '18 at 7:02
• @Emil You did point me to the right direction! Thank you!!!It's the stagnation point of free convection boundary layer flow on a horizontal cylinder. url:core.ac.uk/download/pdf/159188580.pdf – WeiShan Ng Dec 22 '18 at 3:26