Fractional Differential Equations

Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

Integral transforms and their applications

Thank you very much for downloading thermal stresses advanced theory and applications. As you may know, people have look hundreds times for their chosen novels like this thermal stresses advanced theory and applications, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some malicious virus inside their desktop computer.

Thermal Stresses Advanced Theory And Applications

This article highlights on the study of coupled plasma, thermal and elastic waves within an orthotropic infinite semiconducting medium in context of photothermal transport process having a spherica...

Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of a non-Gaussian pulsed laser type heat source in a stress free isothermal half-space in the context of Lord–Shulman (LS), dual-phase lag (DPL), and three-phase lag (TPL) theories of thermoelasticity simultaneously. The memory-dependent derivative is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. Employing Laplace transform as a tool, the problem has been transformed to the space-domain, and it is then solved analytically. To get back all the thermophysical quantities as a function of real time, we use two Laplace inversion formulas, viz. Fourier series expansion technique (Honig in J Comput Appl Math10(1):113–132, 1984) and Zakian method (Electron Lett 6(21):677–679, 1970). According to the graphical representations corresponding to the numerical results, a comparison among LS, DPL, and TPL model has been studied in the presence and absence of a memory effect simultaneously. Moreover, the effects of a laser pulse have been studied in all the thermophysical quantities for different kernels (randomly chosen) and different delay times. Then, the results are depicted graphically. Finally, a comparison of results, deriving from the two numerical inversion formulas, has been made.

Transient response in a thermoelastic half-space solid due to a laser pulse under three theories with memory-dependent derivative

Enlightened by the Caputo fractional derivative, the present study treats with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a fiber-reinforced hollow cylinder due to the influence of thermal shock and magnetic field in the context of a three-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. Employing Laplace transform as a tool, the problem has been transformed to the space domain, where the Galerkin finite element technique is incorporated to solve the resulting equations in the transformed domain. The inversion of the Laplace transform is carried out numerically on applying a method of Bellman et al. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of reinforcement, memory-dependent derivative, and magnetic field also.

Finite element analysis in a fiber-reinforced cylinder due to memory-dependent heat transfer

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a fiber-reinforced thick plate due to the gravitational effects having a heat source, in the context of three-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The upper surface of the plate is free of traction having a prescribed surface temperature while the lower surface rests in a rigid foundation and is thermally insulated. Employing Laplace and Fourier transforms as tools, the problem has been solved analytically in the transformed domain. The inversion of the Fourier transform is carried out using suitable numerical techniques while the numerical inversion of Laplace transform is done incorporating a method on Fourier series expansion technique. According to the graphical represent...

Modeling of memory-dependent derivative in a fiber-reinforced plate under gravitational effect

This paper deals with the problem of magneto-thermoelastic interactions in a functionally graded isotropic, unbounded, rotating medium due to a periodically varying heat source in the context of the linear theory of generalized thermoelasticity without energy dissipation and with energy dissipation. The governing equations of generalized thermoelasticity (GN model) for a functionally graded material under the influence of a magnetic field are established. The Laplace–Fourier double transform technique has been used to get the solution. The inversion of Fourier transform is done by using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerre’s method, and the inversion of the Laplace transformation is done numerically using a method based on Fourier series expansion technique. The numerical estimates for displacements, temperature and stress are obtained for a hypothetical material. The solution to the analogous problem is obtained by taking a suitable non-homogeneous parameter. Finally, the results obtained are presented graphically to show the effect of rotation, non-homogeneity, damping coefficient and magnetic field on displacements, temperature and stress.

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

The aim of this article is to study the gravitational response in an infinite, homogeneous, transversely isotropic thick plate. The upper surface of the plate is free from traction, and the surface temperature distribution is imposed on it. The lower surface of the plate is kept on a rigid base and is thermally insulated. The heat conduction equations in the presence of heat source are of hyperbolic types among them (i) without energy dissipation (GN-II model) and (ii) with energy dissipation (GN-III model). The Laplace–Fourier double-transform technique has been developed to solve the nondimensional coupled field equations. The physical quantities are obtained in the space–time domain using a numerical inversion method. Numerical calculations are performed for a thick plate made of magnesium (Mg) metal and have been depicted graphically to estimate the effect of gravity. The results for the isotropic material (Cu) and that of the transversely isotropic material (Mg) have been compared for both th...

P. K. Pal

Papers

Transient response in a thermoelastic half-space solid due to a laser pulse under three theories with memory-dependent derivative

Finite element analysis in a fiber-reinforced cylinder due to memory-dependent heat transfer

Modeling of memory-dependent derivative in a fiber-reinforced plate under gravitational effect

Magneto-thermoelastic response in a functionally graded rotating medium due to a periodically varying heat source

Thermoelastic wave propagation in a transversely isotropic thick plate under Green–Naghdi theory due to gravitational field