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In the presence that most books are either too mathematical or too physical, this book is written with the belief that mathematical methods should be communicated to a wider audience than just mathematicians. It offers new physical models and new mathematical approaches that are disperse throughout the research journals in the last years. The physical objective is to model thermoelectric and thermoelectrochemical phenomena. The mathematical aim is to establish existence results in a simple setting from existence theory on PDE for providing quantitative estimates, and in such way their...

A complete study of heat conducting viscous flows presents several nonlinearities: the convections, the Joule effect and energy dependent conductivity and viscosities. Adopting the general thermodynamics process, the constitutive relations for the Cauchy stress tensor and the heat flux are nonlinear with p and q coercivity parameters, respectively, when non- Newtonian fluids are taken care of. We investigate what we call the (p-q) coupled fluid-energy system. We deal with the initial and boundary value problems of (p-q) coupled fluid-energy systems under Dirichlet-Newton boundary...