PX275 - G3b - heat equation

a similar mechanism is heat transport, where the diffusion PDE is applicable
considering the density of heat, $Q (x, t) :$

\frac{\partial Q}{\partial t} \propto \frac{\partial^{2} Q}{\partial x^{2}}

since there is a local heat flux $\propto \frac{\partial Q}{\partial x}$ (fick's law again)
a simple example: a uniform, isolated bar of length, $L$ , with a constant heat capacity, $c$
the local temperature:

T \propto c Q

therefore, the heat equation:

\frac{\partial T (x, t)}{\partial t} = κ \frac{\partial^{2} T}{\partial x^{2}}

where, $κ$ is the thermal diffusivity
PX154 - B4 - heat transfer mechanisms

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