PDEs boundary conditions

Question

I have this boundary conditions question where $u(0,t)=0$, $u_x(\pi,t)=B$, $t>0$ So it asks what is the physical meaning of the boundary condition at $x=\pi$ in the three cases $B<0,B=0,B>0$.

Does it just means for $B=0$, there is no heat flowing, for $B<0$, the heat flow is decreasing and for $B>0$, the heat flow is increasing?

Answer 1

HINT

Fourier's law establishes a connection between heat flux and temperature gradient

$$ {\bf q} = -k\nabla u $$