Derivation of heat equation

Derivation of heat equation

Newton articulated some principles of heat flow through solids, but it was Fourier who created the correct systematic theory. Inside a solid there is no convective transfer of heat energy and little radiative transfer, so temperature changes only by conduction, as the energy we now recognize as molecular kinetic energy flows from hotter regions to cooler regions. The first basic principle of heat is:

1. the heat energy contained in a material is proportional to the temperature, the density of the material, and a physical characteristic of the material called the specific heat capacity. In mathematical terms,