Chapter 4

Heat transfer and diffusion of particles

Equation of heat diffusion

FondamentalOne-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.

AttentionOne-dimensional heat equation/ equation of thermal diffusion

  • Without source :

  • With sources :

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Equation of conservation of energy
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Heat transfers in a cylinder