Continuum thermodynamics
type: Item
instance of: scholarly article
title: Continuum thermodynamics
zbMATH Open document ID: 1426.80001
DOI: 10.1007/978-3-030-11157-1
author: Paolo Podio-Guidugli
published in: SISSA Springer Series
publication date: 2019-02-18T00:00:00Z
review text: The author presents a small text book on modern continuum thermodynamics that involves a large class of processes that typically are neither spatially homogeneous nor sequences of equilibrium states. Chapter 1 deals with the continuum theory of heat conduction, the constitutive laws furnish a mathematical characterization of the macroscopic manifestations of those fluctuations in position and velocity of microscopic matter constituents considering collectively by the statistically thermodynamics. A crucial assumption is based on the second law of thermodynamics in which the entropy inflow in a body part is equal to the ratio of the inflow of the internal energy and the reciprocal of the absolute temperature. Chapter 2 deals with thermomechanics wherein microscopic and macroscopic manifestations of motion are intertwined. The constitutive equations of thermoelasticity and thermoviscoelasticity are derived. Chapter 3 outlines the principle of virtual powers in modeling the problems of mechanical and thermal structures. The principle of virtual work is employed as a dimension reduction technique in 3D structural problems such as beam and plate theories. The same principle of virtual power is extended to thermomechanical problems in Chapter 4. The balance and imbalance laws of heat conduction are derived and axioms of conservation of internal action and dissipation are narrated. The final Chapter 5 includes a physical interpretation of the thermal displacement from the concept of Brownian motion as envisaged by Einstein and Langevin. Some basic notions of continuum mechanics are appended in the form of an appendix at the end of the book. The book is intended to the readers interested in mathematical modeling. It may find an appropriate place in the libraries of universities and research institutions.
Mathematics Subject Classification ID: 80-01
Mathematics Subject Classification ID: 80A05
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 00A79
zbMATH DE Number: 7024673
zbMATH Keywords: continuum thermodynamics
zbMATH Keywords: heat conduction
zbMATH Keywords: thermoelasticity
zbMATH Keywords: thermoviscoelasticity
zbMATH Keywords: virtual power
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-030-11157-1
OpenAlex ID: W4236116735
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description: scientific article; zbMATH DE number 7024673