In this article, a new mathematical model of magneto-thermoelasticity has been constructed to investigate the transient phenomena in the context of a new consideration of heat conduction with fractional order, where the anisotropic fibre-reinforced medium is rotating with an uniform angular velocity. The governing equations for Green-Naghdi theory have been formulated and solved analytically employing the normal mode analysis. Numerical results for the temperature, displacement and stresses are obtained and have been depicted graphically. According to the numerical results and corresponding graphical representations, conclusions about this new theory have been constructed. Finally, some comparisons have been shown to estimate the effect of magnetic field, reinforcement and the presence of non-local fractional parameter on all the studied fields.

A SUR

M KANORIA

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University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Procedia Engineering

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory responses which is defined in the form of convolution having kernels as power functions. Due to the shortcomings of power law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite porous material subjected to the presence of distributed time-dependent heat source acting over the plane area. The heat transport equation for this problem is involving the memory dependent derivative on a slipping interval in the context of three-phase-lag (3PL) model of generalized thermoelasticity. Employing the Laplace transform as a tool, the analytical results for the distributions of the change in volume fraction field, temperature, stress, and displacement are obtained on solving the vector-matrix differential equation using eigenvalue approach. The numerical inversion of the Laplace transform is performed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of memory dependent derivative and delay time also. © 2019, © 2019 Taylor & Francis Group, LLC.

Mechanics Based Design of Structures and Machines

Memory response on thermal wave propagation in an elastic solid with voids

Fractional derivative is a widely accepted theory to describe the physical phenomena and the processes with memory responses which are defined in the form of convolution having kernels as power functions. Due to the shortcomings of power-law distributions, some other forms of derivatives with few other kernel functions are proposed. This present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for an infinite solid with void under the action of an induced magnetic field due to the presence of a prescribed plane heat source. The heat transport equation for this problem is involving the memory-dependent derivative on a slipping interval in the context of Lord Shulman model of generalized thermoelasticity. Employing the Laplace transform as a tool, the analytical results for the distributions of the change in volume fraction field, temperature and deformations are obtained on solving the vector-matrix differential equation using eigenvalue approach. The numerical inversion of the Laplace transform is performed using the Zakian method. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of a magnetic field also. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Waves in Random and Complex Media

Memory response on thermal wave propagation in an elastic solid with voids due to influence of magnetic field

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. © 2019, Springer-Verlag GmbH Austria, part of Springer Nature.

Acta Mechanica

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 elasto-thermodiffusion to investigate the transient phenomena for a spherical shell in the context of two temperature theory based on Lord–Shulman model, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The inner and outer boundaries of the spherical shell are free of traction and are subjected to time-dependent thermal and chemical shocks. Employing Laplace transform as a tool, the problem has been solved analytically in the transformed domain. Numerical inversion of the Laplace transform is carried out incorporating the method of Bellman et al. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative, effect of delay time and thermodiffusion also. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Elasto-thermodiffusive response in a spherical shell subjected to memory-dependent heat transfer

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of heat transport in a functionally graded thick plate in the context of Taylor's series expansion involving memory-dependent derivative for the dual-phase-lag (DPL) heat conduction law, which is defined in an integral form of a common derivative with a kernel function on a slipping interval. The medium is considered as a thick plate, both the surfaces of which is taken to be traction free and the lower surface is subjected to different time-dependent thermal loadings (thermal shock, periodically varying thermal loading and ramp-type heating) while the upper surface is kept at zero temperature. Laplace transform technique is employed to find out the analytical solutions and the inversion of Laplace transform is carried out using a method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusion about the new theory is constructed due to the effect of nonhomogeneity. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and nonhomogeneity also. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.

Modeling of memory-dependent derivative in a functionally graded plate

This paper aims at studying the thermo-viscoelastic interaction in a functionally graded, infinite, Kelvin-Voigt-type viscoelastic, thermally conducting medium due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green-Naghdi model II (i.e. the model which predicts thermoelasticity without energy dissipation) and Green-Naghdi model III (i.e. the model which predicts thermoelasticity with energy dissipation) are employed to study thermomechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalised theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain and are solved in that domain. The inversion of the Fourier transform is carried out using residual calculus, where the poles of the integrand are obtained numerically in the complex domain by using Laguerres method and the inversion of the Laplace transform is done numerically using a method based on the Fourier series expansion technique. The numerical estimates of the thermal displacement, temperature, stress and strain are obtained for a hypothetical material. A comparison of the results for different theories is presented and the effect of viscosity is also shown and the effect of non-homogeneity is also seen for different values of the non-homogeneity parameter. © 2015 Taylor and Francis.

European Journal of Computational Mechanics

Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model

In this paper, a new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of heat conduction with fractional orders. The two-temperature Lord-Shulman (2TLS) model and two-temperature Green-Naghdi (2TGN) models of thermoelasticity are combined into a unified formulation using the unified parameters. The basic equations have been written in the form of a vector- matrix differential equation in the Laplace transform domain which is then solved by using a state-space approach. The inversions of Laplace transforms are computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter. © Springer-Verlag 2012.

Journal	Data powered by TypesetProcedia Engineering
Publisher	Data powered by TypesetElsevier Ltd
ISSN	1877-7058
Open Access	Yes