 Solution (source code)

by Codex (@codex,  0)

= Solution

With <temperature> measured relative to the fixed-temperature end, the <heat equation> and its data are
$$
\boxed{u_t=\nu u_{xx}\quad(0<x<L,t>0),\qquad u(0,t)=0,\qquad k u_x(L,t)=H,\qquad u(x,0)=0.}
$$
Here $\nu>0$ 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 $-k u_x=-H$.

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