Journal ArticleDOI
On Thermoelastic Transients in a General Theory of Heat Conduction with Finite Wave Speeds
R. P. Sawatzky,T. B. Moodie +1 more
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In this paper, the linear Chen-Gurtin-Pipkin theory of heat conduction in a deformable material is employed to study the one dimensional problem of a homogeneous thermoelastic half space subjected to thermal and mechanical disturbances at its boundary.Abstract:
The linear Chen-Gurtin-Pipkin theory of heat conduction in a deformable material is employed to study the one dimensional problem of a homogeneous thermoelastic half space subjected to thermal and mechanical disturbances at its boundary. A ray series approach is used to generate asymptotic wavefront expansions for the temperature, strain, and stress response of the medium to the disturbances. General properties of the propagation process are obtained simply and directly. We specialize the solution to the case for which this theory reduces to that of Lord and Shulman and demonstrate that our results for this example agree with asymptotic results obtained previously by other investigators.read more
Citations
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Heat-pulse propagation in thermoelastic systems: application to graphene
TL;DR: In this article, the consequences of thermoelastic coupling on heat and stress pulse propagation along equilibrium and nonequilibrium reference states were studied and a generalized heat-transport equation accounting for relaxational and nonlinear effects was used.
Journal ArticleDOI
Finite speed thermal transients generated by nonuniform sources applied to circular boundaries in inhomogeneous conductors
T.S. Öncü,T. B. Moodie +1 more
TL;DR: In this paper, the Gurtin-Pipkin theory of heat conduction is adopted for the analysis of thermal transients generated by nonuniform sources applied to circular cavities in inhomogeneous conductors.
Journal ArticleDOI
Propagation of waves in nonlinear uniaxial coupled thermoelastic solids
Maninderjeet Singh,D. V. D. Tran +1 more
Journal ArticleDOI
Nonlinear Propagation of Coupled First- and Second-Sound Waves in Thermoelastic Solids
TL;DR: In this article, coupled nonlinear first and second-sound propagation along equilibrium and nonequilibrium states of a thermoelastic system undergoing small perturbations is studied, and the speeds of thermomechanical waves are obtained, and they depend on whether the waves are travelling along, or against, a superimposed constant heat flux.
Journal ArticleDOI
Boundary-initiated wave phenomena in thermoelastic materials
T. S. Öncü,T. B. Moodie +1 more
TL;DR: In this article, a ray-series approach is employed to generate asymptotic wavefront expansions for the field variables, and numerical results for various values of material parameters obtained from the ray series solution in conjunction with the use of Pade approximants are displayed graphically.
References
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Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Methods of Mathematical Physics
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
A generalized dynamical theory of thermoelasticity
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Journal ArticleDOI
A general theory of heat conduction with finite wave speeds
TL;DR: In this article, the authors developed a general theory of heat conduction for nonlinear materials with memory, a theory which has associated with it finite propagation speeds, i.e., a thermal disturbance at any point in the body is felt instantly at every other point; or in terms more suggestive than precise, the speed of propagation of disturbances is infinite.
Journal ArticleDOI
Solution of the Linearized Phonon Boltzmann Equation.
Robert A. Guyer,J. A. Krumhansl +1 more
TL;DR: In this article, the linearized Boltzmann equation for the pure phonon field may be solved formally in terms of the eigenvectors of the normal-process collision operator, since in the isotropic dispersionless case the temperature deviation and the heat current Q are related to zero-eigenvalue eigenfunctions of this operator.