A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system i...

Full description

Saved in:
Bibliographic Details
Published inResults in physics Vol. 9; pp. 787 - 792
Main Author Rawy, E.K.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2018
Elsevier
Subjects
Characteristics
Extended thermodynamics
Hyperbolic relaxation system
Nonlinear theory
Thermoelasticity
Thermoelasticity
Nonlinear theory
Extended thermodynamics
Characteristics
Hyperbolic relaxation system
Online AccessGet full text

Cover

More Information
Summary:We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.
ISSN:2211-3797
2211-3797
DOI:10.1016/j.rinp.2018.03.040