Heat Conduction Equation -- from Eric Weisstein's World of Physics

see also

Heat conduction is the transfer of heat from warm areas to cooler ones, and effectively occurs by diffusion. The heat flux is therefore

where is the density, is the mass heat capacity in erg g^-1 K^-1, d is the diffusion distance, and is the thermal diffusivity in cm² s^-1.

Defining the thermal conductivity (with units of erg cm^-1 K^-1 s^-1)

and noting that is the temperature gradient, this becomes Fourier's law

Now find how temperature changes in time and space as a result of Fourier's law.

Heat Conduction Equation--1-Dimensional, Heat Conduction Equation--2-Dimensional, Heat Conduction Equation--3-Dimensional, Heat Diffusion Equation

References