Solving a streamline function PDE

Hi,

I am trying to solve an streamline function. I have found this PDE for the steamline function, $\displaystyle \psi $.

$\displaystyle \frac{\partial}{\partial z}\left(f\frac{\partial \psi }{\partial z} \right)+ \frac{\partial}{\partial x}\left(a.f\frac{\partial \psi }{\partial x} \right)-\frac{\partial F}{\partial z}=0$

with the boundary conditions of:

$\displaystyle \frac{\partial \psi }{\partial x}=0$ at $\displaystyle z=0$

$\displaystyle \frac{\partial \psi }{\partial x}=0$ at $\displaystyle z=h$

$\displaystyle \frac{\partial \psi }{\partial z}=b$ at $\displaystyle x=0$

$\displaystyle \frac{\partial \psi }{\partial z}=b$ at $\displaystyle x=\infty $

where $\displaystyle a$, $\displaystyle b$ and $\displaystyle h$ are constants. $\displaystyle f$ and $\displaystyle F$ are functions of (x,z). Does anybody know if this PDE can be solved? Thanks.