Modified Fractional Photo-Thermoelastic Model for a Rotating Semiconductor Half-Space Subjected to a Magnetic Field
- PDF / 3,516,322 Bytes
- 14 Pages / 595.276 x 790.866 pts Page_size
- 27 Downloads / 188 Views
ORIGINAL PAPER
Modified Fractional Photo-Thermoelastic Model for a Rotating Semiconductor Half-Space Subjected to a Magnetic Field Ahmed E. Abouelregal 1,2 Received: 26 August 2019 / Accepted: 2 January 2020 # Springer Nature B.V. 2020
Abstract The purpose of this work is to introduce a new modified model for photo-thermoelasticity with regard to a new consideration of generalized heat conduction equations with time-fractional order. We consider an isotropic semiconductor half-space which rotating with uniform angular velocity and subjected to a magnetic field. By applying the technique of normal mode analysis, the analytical expressions for the distribution of the displacement components, temperature, carrier density, the thermal stresses, and Lorentz force are obtained and represented graphically. Comparisons are made between the results expected by the modified new fractional model and the classical one. Also, the effects of rotation, the lifetime of the photo-generated, magnetic field and fractional parameter on all the field variables are investigated. Keywords Thermoelasticity . Time-fractional derivative . Magnetic field . Photothermal . Rotation
1 Introduction Fractional order differential equations of had been the focal point of many studies because of their common look in numerous applications in viscoelasticity, biology, fluid mechanics, engineering and physics. The most significant improvement by using the usage of differential equations of fractional order in several applications is their nonlocal property. Fractional calculus is a natural extension of classical mathematics. In fact, since the foundation of the differential calculus, the generalization of the concept of derivative and integral to a non-integer order has been the subject of distinct approaches. Due to this reason, there are several definitions [1–3] which are proved to be equivalent. Fractional calculus has been applied in many fields, ranging from statistical physics, chemistry, biological sciences, and economics. In recent years, there has been a great deal of interest in fractional differential equations. Several definitions of the fractional derivative have been proposed. The history and classic transform
* Ahmed E. Abouelregal [email protected] 1
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2
Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat, Saudi Arabia
rules on this subject are well covered in the monograph by Podlubny [4]. During recent years, fractional calculus has also been introduced in the field of thermoelasticity. Povstenko [5] has constructed a quasi-static uncoupled thermoelasticity model based on the heat conduction equation with a fractionalorder time derivative. He used the Caputo fractional derivative [6] and obtained the stress components corresponding to the fundamental solution of a Cauchy problem for the fractionalorder heat conduction equation in both the one-dimensional and two-dimensional cases. In 2010, a new theory of
Data Loading...
