Applied Continuum Mechanics for Thermo-Fluids presents the tensor notation rules and integral theorems before defining the preliminary concepts and applications of continuum mechanics. It bridges the gap between physical concepts and mathematical expressions with a rigorous mathematical treatment. After discussing fundamental concepts of continuum mechanics, the text explains basic subjects such as the Stokes hypothesis, the second coefficient of viscosity, non-Newtonian fluids, non-symmetric stress tensor, and the full Navier-Stokes equation. With coverage of interdisciplinary topics, the book highlights issues such as relativistic fluid mechanics, stochastic mechanics, fractional calculus, nanoscale fluid mechanics, polar fluids, electrodynamics, and traffic flows. It describes fundamental concepts of vorticity dynamics, including the definition of vorticity and circulation, with corresponding balance equations and related theorems. This text is intended for upper-level undergraduate and postgraduate mechanical, chemical, aerospace, civil engineering, and physics students taking continuum mechanics, advanced fluid mechanics, convective heat transfer, turbulence, or any other similar courses. In addition, this book can be an excellent resource for scientists who want to initiate research on topics related to thermo-fluids. Instructors will be able to utilize a Solutions Manual and Figure Slides for their courses. The eBook+ version includes the following enhancements: Videos placed throughout the text containing further explanation of key topics Multiple-choice quizzes to reinforce readers' understanding of physical concepts