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**Heat conduction within linear thermoelasticity.**
*(English)*
Zbl 0577.73009

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.

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) |