Some dynamical problems of thermoelastic dielectrics

Nowacki, J.; Glöckner, P.G.

doi:10.1016/0020-7683(79)90029-5

Cited by 24 publications

(29 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We consider the quasi-static problem in the linear thermoelastic diffusion theory [7][8][9][10]20]. Thus, the displacement u i , the temperature θ and the concentration C satisfy the governing equations:…”

Section: Formulation Of the Problemmentioning

confidence: 99%

See 1 more Smart Citation

Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

Aouadi

2008

Acta Appl Math

View full text Add to dashboard Cite

In this paper we derive some spatial stability results for the quasi-static problem in thermoelastic diffusion theory for anisotropic media. The coupled system of equations of thermoelasticity with diffusion is a coupling of an elliptic equation with two parabolic equations. It poses some new mathematical difficulties. Here we study the exponential spatial decay of solutions. An upper bound for the amplitude in terms of the boundary and initial conditions is obtained. The extension of the spatial stability results is also treated.

show abstract

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Nowacki [7][8][9][10] developed the theory of thermoelastic diffusion in the context of the coupled thermoelastic model. Recently Sherief et al [11] derived the theory of thermoelastic diffusion in the context of Lord-Shulman's model with one relaxation time.…”

Section: Introductionmentioning

confidence: 99%

Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

Aouadi

2008

Acta Appl Math

View full text Add to dashboard Cite

show abstract

“…Using the entropy equation [8][9][10][11] ρTṠ = q i,i − P η i,i + ρQ, (2.12) and the conservation of mass, namelyĊ…”

Section: Derivations Of the Governing Equationsmentioning

confidence: 99%

“…Nowacki [8][9][10][11] developed the theory of thermoelastic diffusion. In this theory, the coupled thermoelastic model is used.…”

Section: Introductionmentioning

confidence: 99%

A theory of thermoelastic diffusion materials with voids

Aouadi

2009

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

In the first part of this paper, we derive the equations of the linear theory of thermoelastic diffusion in porous media based on the concept of volume fraction. Then, we establish a reciprocal relation which leads to reciprocity, uniqueness and continuous dependence theorems for anisotropic materials. Finally, we prove the existence of a generalized solution by means of the semigroup of linear operators theory. (2000). 74F05 · 74H20 · 74H25 · 74H30. Mathematics Subject Classification

show abstract

“…The coupling of temperature, mass diffusion and strain fields is known as thermodiffusion in an elastic solid. Nowacki [11,12] developed the coupled theory of thermoelastic diffusion in solids. Sherief et al [14] developed the generalized theory of thermoelastic diffusion, which permits finite speed of thermal signals.…”

mentioning

confidence: 99%

Propagation of Rayleigh Surface Wave in a Two-Temperature Thermoelastic Solid Half-Space with Diffusion

Kumari¹,

Singh²

2016

JAAM

View full text Add to dashboard Cite

Lord and Shulman theory of generalized thermoelasticity is applied to formulate the field equations governing a two-temperature thermoelastic medium with diffusion. The equations are reduced for an isotropic case in x-z plane. These equations are solved for general surface wave solutions. Particular solutions satisfying the required radiations conditions are obtained in a half-space. Applying suitable boundary conditions at free surface, a secular equation for wave speed of Rayleigh surface wave is obtained. The wave speed of Rayleigh wave is computed by using Fortran Program of iteration method for a particular example of the half-space. The effects of two-temperature parameter, frequency, thermodiffusion parameter and diffusion relaxation time are observed graphically on the wave speed of Rayleigh wave.

show abstract

Some dynamical problems of thermoelastic dielectrics

Cited by 24 publications

References 6 publications

Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

Spatial Stability for the Quasi-Static Problem in Thermoelastic Diffusion Theory

A theory of thermoelastic diffusion materials with voids

Propagation of Rayleigh Surface Wave in a Two-Temperature Thermoelastic Solid Half-Space with Diffusion

Contact Info

Product

Resources

About