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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.....

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  • $\begingroup$ Could it be Stagnation point flow? I just googled third order ode and was lucky... $\endgroup$ – Emil Dec 19 '18 at 7:02
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    $\begingroup$ @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 $\endgroup$ – WeiShan Ng Dec 22 '18 at 3:26

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