Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity

Abbas, Ibrahim A.

doi:10.1016/j.apm.2015.01.065

Cited by 95 publications

(19 citation statements)

References 28 publications

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“…El-Sapa et al [32] studied the Moore-Gibsonompson model of an excited nonlocal semiconductor material when the stability investigations are taken into account. Abbas et al [33][34][35][36][37] used the eigenvalue approach to study the effect of fractional order on the wave propagations of elastic bodies under the impact of magnetic fields with some numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

Laser Short-Pulse Effect on Thermodiffusion Waves of Fractional Heat Order for Excited Nonlocal Semiconductor

Almoneef

El‐Sapa

Lotfy

et al. 2022

Advances in Condensed Matter Physics

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In this work, the thermal effect of a laser pulse is taken into account when mechanical-thermodiffusion (METD) waves are studied. The nonlocal semiconductor material is used when interference between holes and electrons occurs. The fractional technique is applied on the heat equation according to the photo-thermoelasticity theory. The governing equations describe the photo-excitation processes according to the overlapping between the thermoelasticity and photothermal theories. The thermoelastic deformation (TD) and the electronic deformation (ED) for the dimensionless fields are taken in one dimension (1D). The Laplace transforms are applied to obtain the analytical solutions when some initial and boundary conditions are applied at the nonlocal surface. The complete nondimensional solutions of the main quantities are obtained according to some numerical simulation approximate during the inversion processes of Laplace transforms and Fourier expansion. The time-fractional order, nonlocal, and thermal memories are used to compare the wave propagations of the main fields and are discussed graphically for nonlocal silicon material.

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Section: Introductionmentioning

confidence: 99%

Laser Short-Pulse Effect on Thermodiffusion Waves of Fractional Heat Order for Excited Nonlocal Semiconductor

Almoneef

El‐Sapa

Lotfy

et al. 2022

Advances in Condensed Matter Physics

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“…Some investigations related to heat transfer and Joule heating can be seen in the Refs. [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Flow Analysis of Hybridized Nanomaterial Liquid Flow in the Existence of Multiple Slips and Hall Current Effect over a Slendering Stretching Surface

et al. 2021

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Carbon nanotubes (CNTs) are favored materials in the manufacture of electrochemical devices because of their mechanical and chemical stability, good thermal and electrical conductivities, physiochemical consistency, and featherweight. With such intriguing carbon nanotubes properties in mind, the current research aims to investigate the flow of hybridized nano liquid containing MWCNTs (multi-wall carbon nanotubes) and SWCNTs (single-wall carbon nanotubes) across a slendering surface in the presence of a gyrotactic-microorganism. The temperature and solutal energy equation are modified with the impact of the modified Fourier and Fick’s law, binary chemical reaction, viscous dissipation, and joule heating. The slip conditions are imposed on the surface boundaries. The flow equations are converted into ODEs by applying similarity variables. The bvp4c approach is applied to tackle the coupled and extremely nonlinear boundary value problem. The outputs are compared with the PCM (Parametric continuation method) to ensure that the results are accurate. The influence of involved characteristics on energy distribution, velocity profiles, concentration, and microorganism field are presented graphically. It is noted that the stronger values of the wall thickness parameter and the Hartmann number produce a retardation effect; as a result, the fluid velocity declines for MWCNT and SWCNT hybrid nano liquid. Furthermore, the transport of the mass and heat rate improves with a higher amount of both the hybrid and simple nanofluids. The amount of local skin friction and the motile density of microorganisms are discussed and tabulated. Furthermore, the findings are validated by comparing them to the published literature, which is a notable feature of the present results. In this aspect, venerable stability has been accomplished.

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“…Also, Povstenko [9] solved analytically fractional heat conduction in a space with a source varying harmonically in time and calculated associated thermal stresses. Abbas [10] studied the fractional order theory with thermoelastic diffusion using the Laplace and Eigen value approach for an infinite elastic medium within a spherical cavity.…”

Section: Introductionmentioning

confidence: 99%

Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

Thakare¹,

Panke²,

Hadke³

2020

International Journal of Applied Mechanics and Engineering

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In this article, a time fractional-order theory of thermoelasticity is applied to an isotropic homogeneous elliptical disk. The lower and upper surfaces of the disk are maintained at zero temperature, whereas the sectional heat supply is applied on the outer curved surface. Thermal deflection and associated thermal stresses are obtained in terms of Mathieu function of the first kind of order 2n. Numerical evaluation is carried out for the temperature distribution, Thermal deflection and thermal stresses and results of the resulting quantities are depicted graphically.

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Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity

Cited by 95 publications

References 28 publications

Laser Short-Pulse Effect on Thermodiffusion Waves of Fractional Heat Order for Excited Nonlocal Semiconductor

Laser Short-Pulse Effect on Thermodiffusion Waves of Fractional Heat Order for Excited Nonlocal Semiconductor

Flow Analysis of Hybridized Nanomaterial Liquid Flow in the Existence of Multiple Slips and Hall Current Effect over a Slendering Stretching Surface

Application of Fractional Order Theory of Thermoelasticity in an Elliptical Disk and Associated Thermal Stresses

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