ABSTRACT
In the present chapter, mathematical models for the heat conduction are developed. Particular 1D problems were discussed in Chapter 6. The heat conduction is taken for definiteness. The same equation, here called the heat equation, describes diffusion, electrostatics etc. (see Batchelor’s Table in Sec.8.7). It is not surprising that this equation is also called the diffusion equation. This is the standard situation in Mathematical Modeling when processes from different topics of science are described by the same equation. Roughly speaking the automatic replacements: “heat conduction” → “diffusion”, “heat flux” → “diffusion flux”, “thermal conductivity” → “diffusivity” etc. transforms a course on the heat conduction to a course on the diffusion with the fitting 90%. At least a short comparative review of the both topics could be useful to argue with the above assertion.
