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Transport and diffusion processes are central in many scientific and technical applications. Prominent examples are the temperature distribution in continuous media, the flow of liquids or gases, the dynamics of reaction-diffusion systems, or the concentration distribution in a binary mixture. The key to the description of these systems is provided by nonlinear partial differential equations, derived from basic conservation laws like those for mass, momentum and energy. In non-equilibrium thermodynamics fluxes are defined and caused by generalized forces. Finally, linear relations between fluxes and forces allow for a closed description. The first part of the textbook discusses the concept of local equilibrium. Using the Onsager relations, conservation equations for mass (continuity), momentum (Euler or Navier-Stokes), and energy (temperature) are derived and solved analytically or numerically for several examples. The second part is based on the kinetic gas theory describing a classical many particle system. At the example of a perfect gas the conservation equations derived phenomenologically in the first part are thereby put on statistical grounds. The textbook addresses advanced Bachelor or Master students of physics, mechanical engineering and applied mathematics.
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