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This is the second edition of "Thermodynamics of Fluids under Flow," which has now been corrected, expanded and updated. It provides macroscopic and microscopic approaches to assessing flow contributions to thermodynamic quantities.

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This is the second edition of the book "Thermodynamics of Fluids under Flow," which was published in 2000 and has now been corrected, expanded and updated. This is a companion book to our other title Extended irreversible thermodynamics (D. Jou, J. Casas-Vázquez and G. Lebon, Springer, 4th edition 2010), and of the textbook Understanding non-equilibrium thermodynamics (G. Lebon, D. Jou and J. Casas-Vázquez, Springer, 2008. The present book is more specialized than its counterpart, as it focuses its attention on the non-equilibrium thermodynamics of flowing fluids, incorporating non-trivial thermodynamic contributions of the flow, going beyond local equilibrium theories, i.e., including the effects of internal variables and of external forcing due to the flow. Whereas the book´s first edition was much more focused on polymer solutions, with brief glimpses into ideal and real gases, the present edition covers a much wider variety of systems, such as: diluted and concentrated polymer solutions, polymer blends, laminar and turbulent superfluids, phonon hydrodynamics and heat transport in nanosystems, nuclear collisions, far-from-equilibrium ideal gases, and molecular solutions. It also deals with a variety of situations, emphasizing the non-equilibrium flow contribution: temperature and entropy in flowing ideal gases, shear-induced effects on phase transitions in real gases and on polymer solutions, stress-induced migration and its application to flow chromatography, Taylor dispersion, anomalous diffusion in flowing systems, the influence of the flow on chemical reactions, and polymer degradation. The new edition is not only broader in scope, but more educational in character, and with more emphasis on applications, in keeping with our times. It provides many examples of how a deeper theoretical understanding may bring new and more efficient applications, forging links between theoretical progress and practical aims. This updated version expands on the trusted content of its predecessor, making it more interesting and useful for a larger audience.

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1 Non-equilibrium Thermodynamics and Rheology.- 2 Non-equilibrium Temperature and Entropy in Flowing Ideal Gases: Maximum-Entrophy Approach.- 3 Kinetic Theory of Flowing Gases and Phonons. Phonon Hydrodynamics and Heat Transfer in Nanosystems.- 4 Non-ideal and Nuclear Collisions.- 5 Polymeric Solutions and Blends.- 6 Non-equilibrium Chemical Potential and Shear-Induced Effects in Polymer Solutions and Blends.- 7 Comparison of Thermodynamical and Dynamical Approaches.- 8 Shear-induced Migration and Flow Chromatography.- 9 Taylor Dispersion and Anomalous Diffusion.- 10 Chemical Reactions and Polymer Under Flow.- 11 Non-equilibrium Thermodynamics of Laminar and Turbulent Superfluids.- Appendices A Experimental Data on Polymer Solutions.- B Liquid Crystals.- C Summary of Vector and Tensor Notation.- D Useful Integrals in the Kinetic Theory of Gases.- E Some Physical Constant.- References.- Subject Index.

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