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Transient responses in a two‐temperature thermoelastic infinite medium having cylindrical cavity due to moving heat source with memory‐dependent derivative
Author(s) -
Sarkar Nantu,
Mondal Sudip
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800343
Subject(s) - thermoelastic damping , laplace transform , heat kernel , mathematical analysis , displacement (psychology) , thermal conduction , fourier transform , integral transform , time derivative , mechanics , transient (computer programming) , heat equation , materials science , mathematics , physics , thermal , thermodynamics , computer science , psychology , psychotherapist , operating system
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.