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Thermoelastic Interactions in an Infinite Orthotropic Continuum of a Variable Thermal Conductivity with a Cylindrical Hole

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Abstract

In this work, the generalized thermoelasticity theory with phase lags is used to solve a thermoelastic problem for an orthotropic infinite unbounded body containing a cylindrical cavity by approximate techniques. The thermal conductivity of the present body is assumed to vary linearly with the temperature. The surface of the cylinder is traction free and subjected to a uniform step temperature. The general solutions for the temperature, displacement, and thermal stresses are obtained by the method of Laplace transforms. The effects of dual phase lags and the variable thermal conductivity parameter on the studied fields for a cobalt material are discussed.

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Abbreviations

C ij :

Isothermal elastic constants

\( C_{\text{E}} \) :

Specific heat at constant strain

\( K_{r} \) :

Thermal conductivity

\( Q \) :

Internal heat supplied per volume and unit time

\( q_{i} \) :

Heat flows vector

T :

Temperature

\( T_{0} \) :

Reference temperature

\( u_{i} \) :

Displacement vector

\( \beta_{ij} \) :

Thermal elastic coupling components

\( \varepsilon_{kk} \) :

Strain dilatation

\( \varepsilon_{rr} \), \( \varepsilon_{\xi \xi } \) :

Radial and hoop strains

\( \rho \) :

Material density

\( \sigma_{rr} \), \( \sigma_{\xi \xi } \) :

Radial and hoop stresses

\( \theta \) :

Thermodynamical temperature

\( \theta_{0} \) :

Reference thermodynamical temperature

\( \tau_{\theta } \), \( \tau_{\text{q}} \) :

Finite times required for thermal equilibrium

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    A. M. Zenkour

  2. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh, 33516, Egypt

    A. M. Zenkour

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    A. E. Abouelregal

  4. Department of Mathematics, College of Science and Arts, University of Aljouf, Al-Qurayyat, Saudi Arabia

    A. E. Abouelregal

Authors
  1. A. M. Zenkour
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  2. A. E. Abouelregal
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Correspondence to A. M. Zenkour.

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Zenkour, A.M., Abouelregal, A.E. Thermoelastic Interactions in an Infinite Orthotropic Continuum of a Variable Thermal Conductivity with a Cylindrical Hole. Iran J Sci Technol Trans Mech Eng 43, 281–290 (2019). https://doi.org/10.1007/s40997-017-0117-x

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  • DOI: https://doi.org/10.1007/s40997-017-0117-x

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