Heat-flow model

The heat-flow model $T' = -(Ak/cm)(T - T_{\mathrm{out}})$ of section 2.3, p. 56-61, is the first-order, linear, nonhomogeneous alternative to the emigration model P' = kP - E. It appears throughout chapters 3 and 4 to illustrate numerical methods, steady states, and the various analytic solution methods.

Although its derivation involves possibly elusive notions like energy, thermal conductivity, and specific heat, it is a natural candidate for a plausibility argument:

The temperature of the body falls if it is hotter than its surroundings ($T \gt T_{\mathrm{out}}$). The rate of decrease of temperature increases if there is more surface area A to transfer heat energy or if thermal conductivity k is larger (i.e., if insulation is poorer).

The concept of heat flow appears again in section 9.4, Time-dependent Diffusion, p. 460-467, where the heat equation $T_t = \kappa T_{xx}$ is derived.