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A novel model of fractional thermal and plasma transfer within a non-metallic plate

  • Ezzat, Magdy A. (Department of Mathematics, College of Science and Arts, Qassim University)
  • Received : 2020.03.06
  • Accepted : 2020.09.16
  • Published : 2021.01.25
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Abstract

While in several publications the thermo-viscoelastic properties of solids have been documented, no attempt has been made to examine the action of coupled thermal and plasma wave in viscoelastic materials. In this paper, a new mathematical model for thermal and plasma transfer in an organic semiconductor was constructed with a time-fractional derivative of order α(0 < α ≤ 1) and a time-fractional integral of order β(0 < β ≤ 2), respectively. A two-dimensional problem is viewed for a half-space of viscoelastic thin-walled semiconductor whose surface is traction free and subjected to a heat flux with an exponentially decaying pulse. Laplace and Fourier's integral transforms are utilized. The carrier density, temperature, thermal stress, and viscoelastic displacement distributions have been obtained through the use of the theoretical model together with plasma and thermo-viscoelastic effects. The inversion technique for Fourier and Laplace transforms is carried out using a numerical technique based on Fourier series expansions. Comparisons are made with the results anticipated thru the coupled idea and generalized theory. The influence of the fractional-order parameter on all the regarded fields is examined.

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