https://doi.org/10.1140/epjp/i2019-12631-1
Regular Article
Effects of variable thermal conductivity of a small semiconductor cavity through the fractional order heat-magneto-photothermal theory
1
Department of Mathematics, Faculty of Science, P.O. Box 44519, Zagazig University, Zagazig, Egypt
2
Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt
* e-mail: khlotfy_1@yahoo.com
Received:
26
September
2018
Accepted:
12
March
2019
Published online:
24
June
2019
In this investigation, a theoretical discussion of a fractional model of a heat order equation of a semiconductor medium in form of a spherical small cavity is studied. The model is taken as one dimensional under the effect of magnetic field and initial stress. The variable thermal conductivity is considered as a linear function of temperature (which depends on temperature). The medium has been studied in the context of photothermal transport processes (excited by light). The model presents the interaction between the waves of plasma (carrier density of free electric charge), namely the elastic and the thermal waves. The Laplace transform method is used to solve the main equations in cylindrical coordinates. The numerical technique (which depends on the Fourier series expansion) is used to get the complete solutions of the main variables under investigation. The thermal and mechanical loads such as the ramp heat type and free traction are applied to the inner surface of the cavity to obtain the main physical fields. The numerical computations of some main physical fields are discussed and plotted graphically.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019
