The end x = 0 of a uniform rod is maintained at a constant temperature and the end x = L is maintained at temperature zero. After the steady state has been reached, it is found that the flux out of the end of the rod at x = L has the value F. What is the temperature at x = 0?

$\displaystyle \displaystyle\text{B.C.}=\begin{cases} u(0,y)=C\\ u(L,y)=0\end{cases}$

How do I obtain the flux at x = L?