Heat Conduction Within Linear Thermoelasticity
J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth o...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1985, 1985
|
| Edition: | 1st ed. 1985 |
| Series: | Springer Tracts in Natural Philosophy
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Preliminaries
- §1.1 One-dimensional linear thermoelasticity
- §1.2 An energy integral
- 2 The Coupled and Quasi-static Approximation
- §2.1 An integro-differential equation
- §2.2 Construction of solutions
- §2.3 Failure of the Maximum Principle
- §2.4 Behaviour of the kernel
- §2.5 Initial sensitivity to the boundary
- §2.6 A monotone property of the entropy
- 3 Trigonometric Solutions of the Integro-differential Equation
- §3.1 Maximum Principles for the pointwise mean total energy density and the pointwise mean square heat flux
- §3.2 The effect of coupling on trigonometric solutions
- 4 Approximation by Way of the Heat Equation or the Integro-differential Equation
- §4.1 Status of the heat equation
- §4.2 Comments on Theorem 13
- §4.3 Proof of Theorem 13
- §4.4 Mean and recurrence properties of the temperature
- §4.5 Status of the integro-differential equation
- 5 Maximum and Minimum Properties of the Temperature Within the Dynamic Theory
- §5.1 Maximum and minimum properties with prescribed heat fluxes
- §5.2 Maximum and minimum properties with prescribed temperatures
- References