This book deals with an important topic in rational continuum physics, thermodynamics.Although slim, it is fairly well self-contained; some basic notions in continuum mechanics, which a well-intentioned reader should but may not be familiar with, are collected in a final appendix.
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.