Heating a thermoelastic half space with a surface absorption pulsed laser using fractional order theory of thermoelasticity

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.

Thermoelastic Response Induced by Volumetric Absorption of Uniform Laser Radiation in a Half-Space

“…Since the maximum temperature occurs as the absorbed energy is equal to the consumed one, the LS and DPL maximum must occur more near the maximum of the laser profile g(t) than that of the CTE, which consumes more energy in penetrating more into the medium. According to [30], the maximum values of θ(0, z) for the models of CTE and LS induced by the surface absorption is greater than the case of the volumetric absorption by approximately 20% and its shift towards t-values is less.…”

“…To demonstrate the consistency of the obtained results, an illustrative example is given for a copper half-space whose surface is illuminated by a pulsed laser assuming that τ 2 = 75 × 10 −5 and ξ = 10 5 m −1 . In order to compare the results of the present paper with those considered the surface absorption, the optical and physical parameters have to be used as [30]:…”

“…Abbas and Marin [29] studied the thermoelastic interaction induced by laser pulse in a 2D half-space and introduced an analytical solution in the context of the generalized theory with one relaxation time. Tayel and Hassan [30] employed the fractional order theory of thermoelasticity to study the effect of the fractional parameter in the existence and absence of heat losses in a thermoelastic half-space heated uniformly by surface absorption of laser radiation.…”

“…The aims of this work are to investigate the thermoelastic interactions in a half-space induced by volumetric absorption of laser radiation in the existence and absence of heat losses by employing three different theories of thermoelasticity, namely, DPL, LS, and CTE, and to study the influences of the phase lag of the temperature gradient of the dual-phase-lag theory. Moreover, the response of LS and CTE models will be compared with the response induced by surface absorption technique in a previously published paper [30].…”

Heating a 2D Thermoelastic Half-Space Induced by Volumetric Absorption of a Laser Radiation

“…Abouelregal and Zenkour [29] employed the generalized two-temperature thermoelastic theory to discuss thermoelastic responses in a half-space, whose pounding plane was exposed to a laser pulse. Tayel and Hassan [30] and Tayel [31] studied the thermoelastic interaction induced by both surface and volumetric absorption techniques, respectively, in a one-dimensional semi-infinite medium, considering the absence and existence of cooling, by employing various thermoelasticity theories.…”