Heat transfer and diffusion of particles
Equation of heat diffusion
Fondamental : One-dimensional heat equation / equation of thermal diffusion (with or without source)
Using Fourier's law :
We deduce :
Heat equation (without source) :
Heat equation with sources :
Analytical solutions to this equation only exist in particular cases that we will study in the following lessons.
The solution to this partial differential equation depends on integration constants that are found by spatial and temporal boundary values.
Attention : One-dimensional heat equation/ equation of thermal diffusion
Without source :
With sources :