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Impact of Variable Thermal Conductivity of Thermal-Plasma-Mechanical Waves on Rotational Microelongated Excited Semiconductor

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Abstract

In the presented work, the propagation of thermal-plasma-mechanical waves of an elastic microelongated semiconductor medium is studied. A novel model describes the interference between waves under the influence of a rotational field when the medium’s thermal conductivity is variable. Thermal conductivity is selected based on the temperature when the microelongated semiconductor medium is in an excited state. The microelongation parameters of the medium are taken into account according to the microelement transport processes for the micropolar-photo-thermoelasticity theory. The governing equations are investigated in two dimensions (2D) when the main quantities are taken dimensionless. To add, harmonic wave analysis is employed to obtain complete analytical solutions of the main physical fields when some boundary conditions are chosen at the medium surface. The influence of physical fields variables is analyzed and illustrated graphically for silicon (Si) material in different values of variable thermal conductivity, thermal relaxation times and rotation parameters.

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Abbreviations

\(\lambda ,\,\,\mu \quad \quad \;\) :

Lame’s elastic semiconductor parameters.

\(\delta_{n} = (3\lambda + 2\mu )d_{n}\) :

The deformation potential difference

\(\underline{n}\) :

Unit vector in the direction of y-axis

\(T_{0} \;\) :

Reference temperature in its natural state

\(\hat{\gamma } = (3\lambda + 2\mu )\alpha_{{t_{1} }}\) :

The volume thermal expansion

\(\sigma_{ij}\) :

The microelongational stress tensor

\(\rho \quad \quad\) :

The density of the microelongated sample

\(\alpha_{{t_{1} }}\) :

Coefficients of linear thermal expansion

\({\text{e}}\) :

Cubical dilatation

\(C_{e}\) :

Specific heat of the microelongated material

\(K\) :

The thermal conductivity

\(D_{E}\) :

The carrier diffusion coefficient

\(\tau\) :

The photogenerated carrier lifetime

\(E_{g}\) :

The energy gap

\(e_{ij}\) :

Components of strain tensor

\(\Pi ,\Psi\) :

Two scalar functions

\(j_{0}\) :

The microinertia of microelement

\(a_{0} ,\,\alpha_{0} ,\lambda_{0} ,\lambda_{1}\) :

Microelongational material parameters

\(\tau_{0} ,\nu_{0}\) :

Thermal relaxation times

\(\varphi\) :

The scalar microelongational function

\(m_{k}\) :

Components of the microstretch vector

\(s = s_{kk}\) :

Stress tensor component

\(\delta_{ik}\) :

Kronecker delta

\(\underline{\Omega } = \Omega \underline{n}\) :

Angular velocity

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Acknowledgments

The authors extend their appreciation to Princess Nourah bint Abdulrahman University for fund this research under Researchers Supporting Project number (PNURSP2022R154) Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. Acknowledgment 2: The authors are thankful to Taif University. This paper was funded by Taif University Researchers Supporting Project number (TURSP-2020/16), Taif University, Taif, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P. O. Box 84428, Riyadh, 11671, Saudi Arabia

    Shreen El-Sapa

  2. Department of Mathematics and Statistics College of Science, Taif University, P. O. Box 11099, Taif, 21944, Saudi Arabia

    K. A. Gepreel & A. M. S. Mahdy

  3. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box44519, Zagazig, Egypt

    Kh. Lotfy

  4. Department of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia

    Kh. Lotfy

  5. Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt

    A. El-Bary

  6. Council of Futuristic Studies and Risk Management, Academy of Scientific Research and Technology, Cairo, Egypt

    A. El-Bary

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  1. Shreen El-Sapa
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  3. Kh. Lotfy
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Correspondence to Kh. Lotfy.

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El-Sapa, S., Gepreel, K.A., Lotfy, K. et al. Impact of Variable Thermal Conductivity of Thermal-Plasma-Mechanical Waves on Rotational Microelongated Excited Semiconductor. J Low Temp Phys 209, 144–165 (2022). https://doi.org/10.1007/s10909-022-02766-0

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