Chapter 13.1, Problem 4P

Obtain the heat flow equation (1.3) as follows: The quantity of heat $Q$ flowing across a surface is proportional to the normal component of the (negative) temperature gradient, $(-\nabla T)\cdot$

n. Compare Chapter 6, equation $(10.4),$ and apply the discussionHow of water given there to the flow- of heat per unit volume per unit time is proportional to $\nabla \cdot \nabla T$.

But $\partial T/\partial t$ is proportional to this gain in heat; thus show that $T$ satisfies (1.3).