Heat conduction within linear thermoelasticity. (English) Zbl 0577.73009

Day, William Alan

Springer Tracts in Natural Philosophy, Vol. 30. New York etc.: Springer- Verlag. VIII, 82 p. DM 98.00 (1985).

(From author’s introduction.) The arguments upon which the derivation of the heat equation is based presume the conducting body to be rigid, and, thus, they ignore any possible interaction between thermal effects and mechanical effects. It is the purpose of this tract to suggest that insight into the nature of thermomechanical interaction can be obtained by studying what is a very restricted subject indeed, namely heat conduction according to the one-dimensional version of the equations of linear thermoelasticity for a homogeneous and isotropic body. These equations constitute the simplest generalization of the heat equation which incorporates the effect of thermomechanical coupling and the effect of inertia. At all points we shall attempt to point out both the contrasts and the similarities between the heat equation and the thermoelastic equations.
In Chapter 1 the system of thermoelastic equations is deduced. Further two chapters are dedicated to the careful analysis of the integro- differential equation, which represents the coupled and quasistatic approximation of the system. The title of Chapter 4 is: Approximation by way of the heat equation or integro-differential equation. The last chapter deals with maximum and minimum properties of the temperature within the dynamic theory.

Reviewer: O.John

MSC:

74F05	Thermal effects in solid mechanics
35K55	Nonlinear parabolic equations
74-02	Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74A15	Thermodynamics in solid mechanics
35K05	Heat equation
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

one-dimensional version of the equations of linear; thermoelasticity; homogeneous and isotropic body; thermomechanical coupling; effect of inertia; system of thermoelastic equations; integro-differential equation; coupled and quasistatic approximation of the system; Approximation by way of the heat equation or integro-differential; equation; maximum and minimum properties; one-dimensional version of the equations of linear thermoelasticity; Approximation by way of the heat equation or integro-differential equation