Interactions due to a moving heat source in a thin slim rod under memory-dependent dual-phase lag magneto-thermo-visco-elasticity

  • Sudip MondalEmail author
Original Research


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 magnetic field and moving heat source in a rod in the context of dual-phase lag (DPL) theory of thermo-visco-elasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and displacement is studied. It is found from the distributions that the temperature, thermally induced displacement, and stress of the rod decrease at large source speed.


Memory-dependent derivative Magneto-thermoelasticity Viscosity Moving heat source Laplace transform and numerical inversion of Laplace transform Dual-phase lag model 



The author would like to thank the Editor and the anonymous referees’ for their comments and suggestions on this paper. The author would also like to thank Mrs. Seuli Mondal for her continuous support during the preparation of this manuscript.

Funding The author received no financial support for the research.

Conflict of interest

The author declares that he has no conflict of interest.

Supplementary material

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsBasirhat CollegeNorth 24 ParganasIndia

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