This work deals with the study of transient responses in a two-temperature generalized thermoelastic infinite medium having a cylindrical cavity due to a time-dependent moving heat source where the conventional Fourier's law of heat conduction is modified by introducing a new Taylor's series expansion using memory-dependent derivative (MDD). The resulting non-dimensional equations are applied to a specific problem. A direct approach is introduced to obtain the analytical expressions of the physical quantities in the Laplace transform domain. The inversion of the Laplace transforms are carried out using the methods based on the Fourier series expansion technique. Numerical results for the dynamical and conductive temperatures, stress, strain, and displacement are presented graphically. The effects of time-delay and kernel function have been studied on the thermo-physical quantities. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

NANTU SARKAR

Applied Mathematics

S MONDAL

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

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Transient responses in a two-temperature thermoelastic infinite medium having cylindrical cavity due to moving heat source with memory-dependent derivative

In the application of pulsed laser heating, such as the laser hardening of metallic surfaces, the conduction limited process is the dominant mechanism during the laser-workpiece interaction. As a consequence, time unsteady analysis of this problem becomes necessary. The present study examines the effect of ultra-short-pulsed laser heating in the problem of coupled thermoelastic vibration of a microscale beam resonator. Due to the shortcomings of power law distributions in fractional derivatives, the usage of some other forms of derivatives with some other kernel functions is proposed. With this motivation, the heat transport equation is defined in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer. Finite sinusoidal Fourier and Laplace transform techniques are then employed to determine the lateral vibration of the beam and the temperature increment within the medium. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are drawn. An excellent predictive capability is demonstrated due to the presence of the energy absorption depth, memory dependent derivative, and delay time. © 2019, © 2019 Taylor & Francis Group, LLC.

Journal of Thermal Stresses

A memory response in the vibration of a microscale beam induced by laser pulse

We investigate the propagation of magneto-thermoelastic interaction in an isotropic homogeneous perfectly conducting two-dimensional semi-infinite medium using a new theory of two-temperature generalized thermoelasticity with memory-dependent derivative. The bounding surface of the medium is taken as stress free and subjected to a time dependent thermal shock. The combined Laplace–Fourier transform is applied to find the solutions in transform domain. Numerical results of the field variables are presented graphically to discuss the effect of time, space variable and the time-delay for some specific cases. The graphical representation shows that time-delay has significant effect on the distribution on the physical variables. © 2018, © 2018 Taylor & Francis Group, LLC.

Mechanics of Advanced Materials and Structures

A two-dimensional magneto-thermoelastic problem based on a new two-temperature generalized thermoelasticity model with memory-dependent derivative

A new nonlocal theory of generalized thermoelastic materials with voids based on Eringen’s nonlocal elasticity and Caputo fractional derivative is established. The one-dimensional form of the above theory is then applied to study transient wave propagation in an infinite thermoelastic materials with voids due to a time-dependent continuous heat sources distributed in a plane area. Laplace transform and eigenvalue approach techniques are used to obtain the closed form solution in the transform domain. Numerical inversions of the studied physical variables are carried out by Zakian algorithm in the space-time domain. Numerical results are plotted graphically in some cases and the results obtained are analyzed. Some comparisons for different cases are also noted. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

Journal	Data powered by TypesetZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Publisher	Data powered by TypesetWiley-VCH Verlag
ISSN	0044-2267
Open Access	No