RESEARCH PAPER
Heating a thermoelastic half space with a surface absorption pulsed laser using fractional order theory of thermoelasticity
 
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1
Department of Mathematics, College of Education, Majmaah University, Al-Majmaah, Saudi Arabia
2
Department of physics, Faculty of Science, Helewan University, Cairo, Egypt
Publish date: 2019-04-15
Submission date: 2018-05-03
Acceptance date: 2019-01-28
 
Journal of Theoretical and Applied Mechanics 2019;57(2):489–500
KEYWORDS
ABSTRACT
In this work, the problem of illuminating a thermoelastic half space by a laser beam is solved by utilizing the fractional order theory of thermoelasticity. The assumptions that the illuminated surface is exposed to a cooling effect and free from traction are considered. The problem is solved using Laplace transform techniques. The inverse Laplace transform has been calculated in numerical fashion. The obtained results are presented graphically.
 
REFERENCES (30)
1.
Allam M.N.M., Tayel I.M., 2017, Generalized thermoelastic functionally graded half space under surface absorption of laser radiation, Journal of Theoretical and Applied Mechanics, 55, 1, 155-165.
 
2.
Bagley R.L., Torvik P.J., 1983, A theoretical basis for the application of fractional calculus to viscoelasticity, Journal of Rheology, 27, 201-210.
 
3.
Biot M., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics, 27, 240-253.
 
4.
Caputo M., 1974, Vibrations of an infinite viscoelastic layer with a dissipative memory, The Journal of the Acoustical Society of America, 56, 3, 897-904.
 
5.
Caputo M., Mainardi F., 1971a, A new dissipation model based on memory mechanism, Pure and Applied Geophysics, 91, 134-147.
 
6.
Caputo M., Mainardi F., 1971b, Linear models of dissipation in anelastic solids, La Rivista del Nuovo Cimento, 1, 2, 161-198.
 
7.
Cattaneo C., 1948, Sulla conduzione del calore, Atti del Seminario Matematico e Fisico dell’Universita di Modena, 3, 83-101.
 
8.
Debnath L., Bhatta D., 2015, Integral Transforms and their Applications, Taylor and Francis.
 
9.
Ezzat M.A., El-Karamany A.S., Fayik M.A., 2012, Fractional ultrafast laser-induced thermo-elastic behavior in metal films, Journal of Thermal Stresses, 35, 7, 637-651.
 
10.
Hassan A., El-Nicklawy M.M., Nasr M.E., Hemida A.A., Abd El-Ghaffar A.O., 1996, Heating effects induced by a pulsed laser in a semi-infinite target in view of the theory of linear system, Journal of Optics and Laser Technology, 28, 337-343.
 
11.
Henain E.F., Hassan A.F., Megahed F., Tayel I.M., 2014, Thermoelastic half space under illumination of a laser beam using Lord and Shulman theory, Journal of Thermal Stresses, 37, 51-72.
 
12.
Ignaczak J., 1979, Uniqueness in generalized thermoelasticity, Journal of Thermal Stresses, 2, 2, 171-175.
 
13.
Ignaczak J., 1982, A note on uniqueness in thermoelasticity with one relaxation time, Journal of Thermal Stresses, 5, 257-263.
 
14.
Kothari S., Mukhopadhyay S., 2011, A problem on elastic half space under fractional order theory of thermoelasticity, Journal of Thermal Stresses, 34, 7, 724-739.
 
15.
Lord H., Shulman Y., 1967, A generalized dynamical theory of thermo elasticity, Journal of the Mechanics Physics of Solids, 15, 299-309.
 
16.
Machado J., Galhano A., Trujillo J., 2013, Science metrics on fractional calculus development since 1966, Fractional Calculus and Applied Analysis, 16, 479-500.
 
17.
McDonald F.A., 1990, On the precursor in laser-generated ultrasound waveforms in metals, Applied Physics Letters, 56, 3, 230-232.
 
18.
Povstenko Y.Z., 2005, Fractional heat conduction equation and associated thermal stress, Journal of Thermal Stresses, 28, 83-102.
 
19.
Povstenko Y.Z., 2009, Thermoelasticity that uses fractional heat conduction equation, Journal of Mathematical Sciences, 162, 2, 296-305.
 
20.
Raslan W., 2014, Application of fractional order theory of thermoelasticity to a 1D problem for a cylindrical cavity, Archives of Mechanics, 66, 4, 257-267.
 
21.
Raslan W., 2015, Application of fractional order theory of thermoelasticity in a thick plate under axisymmetric temperature distribution, Journal of Thermal Stresses, 38, 7, 733-734.
 
22.
Raslan W., 2016, Application of fractional order theory of thermoelasticity to 1D problem for spherical shell, Journal of Theoretical and Applied Mechanics, 54, 1, 295-304.
 
23.
Sherief H., 1986, Fundamental solution of the generalized thermoelastic problem for short times, Journal of Thermal Stresses, 9, 151-164.
 
24.
Sherief H., 1987, On uniqueness and stability in generalized thermoelasticity, Quarterly of Applied Mathematics, 45, 773-778.
 
25.
Sherief H., Abd El-Latief A.M., 2013, Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity, International Journal of Mechanical Sciences, 74, 185-189.
 
26.
Sherief H., Abd El-Latief A.M., 2014, Application of fractional order theory of thermoelasticity to a 1D problem for a half-space, ZAMM, 94, 6, 509-515.
 
27.
Sherief H., El-Sayed A.M.A., Abd El-Latief A.M., 2010, Fractional order theory of thermoelasticity, International Journal of Solids and Structures, 47, 269-275.
 
28.
Tzou D.Y., 1995, Experimental support for the lagging behavior in heat propagation, Journal of Thermophysics and Heat Transfer, 9, 686-693.
 
29.
Youssef H.M., 2010, Theory of fractional order generalized thermoelasticity, Journal of Heat Transfer, 132, 6, 061301, 1-7.
 
30.
Wang X., Xu X., 2001, Thermoelastic waves induced by pulsed laser heating, Applied Physics A, 73, 107-114.
 
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