Honam Mathematical Journal (호남수학학술지)

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EFFECTS OF PHASE-LAGS AND VARIABLE THERMAL CONDUCTIVITY IN A THERMOVISCOELASTIC SOLID WITH A CYLINDRICAL CAVITY

  • Zenkour, Ashraf M. (Department of Mathematics, Faculty of Science, King Abdulaziz University, Department of Mathematics, Faculty of Science, Kafrelsheikh University)
  • Received : 2015.03.18
  • Accepted : 2016.06.20
  • Published : 2016.09.25
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Abstract

This paper investigates the effect of dual-phase-lags on a thermoviscoelastic orthotropic solid with a cylindrical cavity. The cylindrical cavity is subjected to a thermal shock varying heat and its material is taken to be of Kelvin-Voigt type. The phase-lag thermoelastic model, Lord and Shulman's model and the coupled thermoelasticity model are employed to study the thermomechanical coupling, thermal and mechanical relaxation (viscous) effects. Numerical solutions for temperature, displacement and thermal stresses are obtained by using the method of Laplace transforms. Numerical results are plotted to illustrate the effect phase-lags, viscoelasticity, and the variability thermal conductivity parameter on the studied fields. The variations of all field quantities in the context of dual-phase-lags and coupled thermoelasticity models follow similar trends while the Lord and Shulman's model may be different. The influence of viscosity parameter and variability of thermal conductivity is very pronounced on temperature and thermal stresses of the thermoviscoelastic solids.

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References

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