Magnetophotothermal interaction in a rotating solid cylinder of semiconductor silicone material with time dependent heat
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-021-2682-6
Magneto-photothermal interaction in a rotating solid cylinder of semiconductor silicone material with time dependent heat flow∗ A. E. ABOUELREGAL1,2,† 1. Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 77423, Saudi Arabia; 2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt (Received Jun. 20, 2020 / Revised Aug. 29, 2020)
Abstract A mathematical model linking thermoelasticity to photothermal experiments is proposed with the consideration of the photothermal effect. The system equations for coupled plasma, heat conduction with phase-lags (PLs), and motion equations are introduced and solved by using the Laplace transform technique. The photothermal, thermal, and elastic waves in a rotating solid cylinder of semiconductor material are analyzed with the proposed model. The cylinder surface is constrained and subjected to a time-dependent pulse heat flux. The sensitivity of the physical fields for the angular velocity, PLs, and thermal vibration parameters is investigated. In addition, the effects of the effective parameters on the physical quantities are graphically illustrated and discussed in detail. Key words photothermal, phase-lag (PL), solid cylinder, rotation, semiconductor, carrier concentration Chinese Library Classification O343 2010 Mathematics Subject Classification
74B10
Nomenclature λ, µ, αt , Ce , γ, T0 , θ, T, u, e, σij , eij , δij ,
Lam´e constants; thermal expansion coefficient; specific heat; thermal coupling parameter; environmental temperature; temperature increment; absolute temperature; displacement vector; cubical dilatation; stress tensor; strain tensor; Kronecker’s delta function;
n0 , H, h, dn , K, ρ, Ω, t, E, N, τq , τθ ,
equilibrium carrier concentration; magnetic field; induced magnetic field; diffusion coupling parameter; thermal conductivity; material density; angular velocity vector; time; induced electric field; carrier density; phase-lag (PL) of heat flux; PL of temperature;
∗ Citation: ABOUELREGAL, A. E. Magneto-photothermalinteraction in arotating solid cylinder of semiconductor silicone material with time dependent heat flow. Applied Mathematics and Mechanics (English Edition) (2021) https://doi.org/10.1007/s10483-021-2682-6 † Corresponding author, E-mail: [email protected] ©Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2021
2 Eg , δn , DE , q,
1
A. E. ABOUELREGAL semiconducting energy gap; electronic deformation coefficient; diffusion coefficient; heat flux;
κ, τ1 , J, µ0 ,
thermal activation coupling parameter; lifetime of photogenerated electron; current density; magnetic permeability.
Introduction
When material is exposed to electromagnetic radiation, some energy will be absorbed, while some energy will be released as heat. This occurrence is called the photothermal effect. Heating material through radiation leads to various photothermal effects, which may cau
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