Does anyone know how to derive the following one-dimensional heat equation from the laws of thermodynamic?
$\rho\ c \frac{\partial\ T}{\partial\ t} - div(\kappa\ \frac{\partial\ T}{\partial\ x}) = \dot{q}_v$
2026-03-28 04:43:40.1774673020
How to derive the heat equation from the laws of thermodynamic?
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After struggling a lot with the problem. It seems that all I have to do is to formulate the potential form of the heat equation in such a way that the derivative of the potential with respect to the variable yield the weak form of the equilibrium.