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The effect of two-temperature on thermoelastic medium with diffusion due to three phase-lag model

Sarhan Y. Atwa

Sarhan Y. Atwa

Dep. of Eng. Math. And Physics, Higher Institute of Engineer, Shorouk AcademyCairo, Egypt
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Atwa, Sarhan Y.
, 
M. K. Ammar

M. K. Ammar

Department of Mathematics, Faculty of Science, Helwan UniversityCairo, Egypt
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Ammar, M. K.
 and 
Eman Ibrahim

Eman Ibrahim

Department of Mathematics, Faculty of Science, Helwan UniversityCairo, Egypt
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Ibrahim, Eman
  
Jun 27, 2017
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Published Online: Jun 27, 2017
Page range: 259 - 270
Received: Mar 09, 2017
Accepted: Jun 27, 2017
DOI: https://doi.org/10.21042/AMNS.2017.1.00022
Keywords
© 2017 Sarhan Y. Atwa, M. K. Ammar, Eman Ibrahim, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Distribution the displacement component u with and without diffusion.
Distribution the displacement component u with and without diffusion.

Fig. 2

Distribution the temperature function φ with and without diffusion.
Distribution the temperature function φ with and without diffusion.

Fig. 3

Distribution the stress function σyy with and without diffusion.
Distribution the stress function σyy with and without diffusion.

Fig. 4

Distribution the stress function σxy with and without diffusion.
Distribution the stress function σxy with and without diffusion.

Fig. 5

Distribution the chemical potential p with and without diffusion.
Distribution the chemical potential p with and without diffusion.

Fig. 6

Distribution the concentration C with and without diffusion.
Distribution the concentration C with and without diffusion.

Fig. 7

Distribution the displacement component u against both components of distance in the TPL model with diffusion.
Distribution the displacement component u against both components of distance in the TPL model with diffusion.

Fig. 8

Distribution the temperature component fagainst both components of distance in the TPL model with diffusion.
Distribution the temperature component fagainst both components of distance in the TPL model with diffusion.

Nomenclature

σijComponents of stress tensor
e = ekkCubic dilatation
u,vDisplacement vectors
ToReference Temperature
PChemical potential
λ, μLame’s constants
αtCoefficient of linear thermal expansion
αcCoefficient of diffusion thermal expansion
CESpecific heat at constant strain
K*Material characteristic of the theory
τqPhase lag of Heat flux
dThermoplastic diffusion constant
∇2∂2∂x2+∂2∂y2+∂2∂z2$\begin{array}{} \displaystyle \frac{{{\partial ^2}}}{{\partial {x^2}}} + \frac{{{\partial ^2}}}{{\partial {y^2}}} + \frac{{{\partial ^2}}}{{\partial {z^2}}} \end{array}$
eijComponents of strain tensor
δijKronecker’s delta
TThermodynamic Temperature
φConductive temperature
CConcentration distribution
γ(3λ + 2μ)αt
β1(3λ + 2μ)αc
ρDensity
KCoefficient of thermal conductivity
τvPhase lag of thermal displacement gradient
τTPhase lag of temperature gradient
τDiffusion relaxation time
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