## About this book

### Introduction

Modern continuum thermodynamics is a field theory devised to handle a large class of processes that typically are neither spatially homogeneous nor sequences of equilibrium states. The most basic chapter addresses the continuum theory of *heat conduction*, in which the constitutive laws furnish a mathematical characterization of the macroscopic manifestations of those fluctuations in position and velocity of the microscopic matter constituents that statistical thermodynamics considers collectively. In addition to a nonstandard exposition of the conceptual steps leading to the classical heat equation, the crucial assumption that energy and entropy inflows should be proportional is discussed and a hyperbolic version of that prototypical parabolic PDE is presented. *Thermomechanics* comes next, a slightly more complex paradigmatic example of a field theory where microscopic and macroscopic manifestations of motion become intertwined. Finally, a *virtual power format for thermomechanics* is proposed, whose formulation requires that temperature is regarded formally as the time derivative of *thermal displacement*. It is shown that this format permits an alternative formulation of the theory of heat conduction, and a physical interpretation of the notion of thermal displacement is given.

It is addressed to mathematical modelers – or mathematical modelers to be – of continuous material bodies, be they mathematicians, physicists, or mathematically versed engineers.

### Keywords

### Bibliographic information

- DOI https://doi.org/10.1007/978-3-030-11157-1
- Copyright Information Springer Nature Switzerland AG 2019
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-030-11156-4
- Online ISBN 978-3-030-11157-1
- Series Print ISSN 2524-857X
- Series Online ISSN 2524-8588
- Buy this book on publisher's site