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Steel and Composite Structures
  Volume 38, Number 4, February25 2021, pages 447-462
DOI: http://dx.doi.org/10.12989/scs.2021.38.4.447
 


Transient memory response of a thermoelectric half-space with temperature-dependent thermal conductivity and exponentially graded modulii
Magdy A. Ezzat

 
Abstract
    In this work, we consider a problem in the context of thermoelectric materials with memory-dependent derivative for a half space which is assumed to have variable thermal conductivity depending on the temperature. The Lame's modulii of the half space material is taken as a function of the vertical distance from the surface of the medium. The surface is traction free and subjected to a time dependent thermal shock. The problem was solved by using the Laplace transform method together with the perturbation technique. The obtained results are discussed and compared with the solution when Lame's modulii are constants. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions. Affectability investigation is performed to explore the thermal impacts of a kernel function and a time-delay parameter that are characteristic of memory dependent derivative heat transfer in the behavior of tissue temperature. The correlations are made with the results obtained in the case of the absence of memory-dependent derivative parameters.
 
Key Words
    thermoelectric materials; fractional order theory; variable of thermal conductivity; variable Lame's moduli; perturbation method; numerical results
 
Address
Magdy A. Ezzat: Department of Mathematics, College of Science and Arts, Qassim University, Al Bukairiyah, Saudi Arabia;
Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
 

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