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<p>This study presents a mathematical framework to examine the thermoelastic response of an unbounded isotropic medium with a cylindrical cavity exposed to a continuous line heat source. The analysis employs the dual-phase-lag (DPL) heat conduction model under traction-free and ramp-type thermal conditions within generalized thermoelasticity. Building upon earlier eigenvalue-based formulations in Cartesian coordinates, this work extends the analytical methodology to cylindrical geometry, enabling a more realistic representation of thermal and elastic interactions induced by line heat sources. The governing equations are transformed into the Laplace domain and reduced to a vector–matrix system of coupled differential equations. Analytical expressions for field variables are obtained in the transformed domain and numerically inverted into the time domain using Stehfest’s algorithm implemented in MATLAB. The results graphically demonstrate how ramp-type heat, phase-lag, and time parameters influence the propagation of field variables, emphasizing the analytical significance of the adopted methodology. The novelty of this study lies in the combined analytical and numerical formulation of a DPL-based thermoelastic model for cylindrical geometry under ramp-type heating, offering a realistic representation of finite-speed thermal and elastic wave propagation pertinent to advanced engineering and biomedical systems.</p>

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Eigenvalue approach to study generalized thermoelastic interaction in an infinite medium with cylindrical cavity

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Prajjwal Parmar,
  • Abhijit Lahiri,
  • Smita Pal Sarkar

摘要

This study presents a mathematical framework to examine the thermoelastic response of an unbounded isotropic medium with a cylindrical cavity exposed to a continuous line heat source. The analysis employs the dual-phase-lag (DPL) heat conduction model under traction-free and ramp-type thermal conditions within generalized thermoelasticity. Building upon earlier eigenvalue-based formulations in Cartesian coordinates, this work extends the analytical methodology to cylindrical geometry, enabling a more realistic representation of thermal and elastic interactions induced by line heat sources. The governing equations are transformed into the Laplace domain and reduced to a vector–matrix system of coupled differential equations. Analytical expressions for field variables are obtained in the transformed domain and numerically inverted into the time domain using Stehfest’s algorithm implemented in MATLAB. The results graphically demonstrate how ramp-type heat, phase-lag, and time parameters influence the propagation of field variables, emphasizing the analytical significance of the adopted methodology. The novelty of this study lies in the combined analytical and numerical formulation of a DPL-based thermoelastic model for cylindrical geometry under ramp-type heating, offering a realistic representation of finite-speed thermal and elastic wave propagation pertinent to advanced engineering and biomedical systems.