# heat equation,radiating at 1 end, find boundary conditions at that end

Right end : Energy leaving right end is given by $-\lambda A \frac{\partial u}{\partial x}(4,t) = 2(u(4,t)-23)$ which becomes
$-\frac{\partial u}{\partial x}(4,t) = 2(u(4,t)-23)$ and then... not sure. I assume they want 2 boundary conditions at the right end because they ask for boundary conditions.
I would say the other boundary condition could be $u(4,t) = u(4,0)-t\frac{\partial u}{\partial x}(4,t)$