Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2003 / Paper 1 / 2 / i

With temperature measured relative to the fixed-temperature end, the heat equation and its data areHere $\nu >0$ is thermal diffusivity and $k>0$ is thermal conductivity. The sign of the derivative condition describes incoming heat flux at $L$: the outward conductive heat flux is $-k{u}_x=-H$.