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Dynamic Problem of Fractional Thermoelasticity in Bounded Cylindrical Domain with Relaxation Time

  • Gaurav MittalEmail author
  • V. S. Kulkarni
Conference paper
  • 17 Downloads
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

A fractional heat conduction model of a solid heat conductor is designed in the bounded cylindrical domain. The solid heat conductor under consideration is assumed to be in the form of a thick circular plate. The boundaries of the thick circular plate are traction free and subjected to externally applied axisymmetric heat source. Governing heat conduction equation of this model has been designed in the context of time fractional derivative with one-relaxation time. The solution of fractional heat conduction equation in association with Caputo time fractional derivative has been found by transforming the original boundary value problem into eigenvalue problem through the integral transforms. The inversion of Laplace transforms in terms of infinite series approximations has been achieved numerically using Gaver–Stehfest algorithm. The convergence of infinite series solutions has been discussed. Illustratively, the numerical scheme has been employed to partially distributed heat flux and thermal behavior of a heat conductor has been discussed numerically and studied graphically. Results obtained are compared with coupled thermoelasticity, fractional thermoelasticity, and generalized thermoelasticity.

Keywords

Dynamic problem Fractional thermoelasticity Finite wave speed Relaxation time Integral transforms 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Applied MathematicsThadomal Shahani Engineering CollegeMumbaiIndia
  2. 2.Department of MathematicsUniversity of MumbaiMumbaiIndia

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