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Abstract <p>The increasing demand for accurate modeling of heat transport in micro/nano-scale devices and ultrafast laser applications reveals the limitations of classical heat conduction theories like Fourier’s law. To address this, a novel framework for generalized thermoelasticity is proposed, incorporating a non-Fourier heat conduction law grounded in thermomass theory—where heat is modeled as the motion of an equivalent mass of phonon gas. The model also integrates a nonlocal formulation for stress and incorporates memory effects via the memory-dependent derivative (MDD), allowing for the influence of past thermal states.</p> <p>The study considers a one-dimensional thermoelastic rod subjected to ramp-type thermal loading at one boundary, with the other end maintained at zero temperature. Both ends are mechanically fixed. The governing equations are solved in the Laplace domain, and numerical inversion using Zakian’s technique is applied to obtain time-space domain results. Different types of kernel functions are introduced to capture memory effects, and nonlocality is embedded in the stress field.</p> <p>The results demonstrate that kernel choice, nonlocal length scale, ramp duration, and delay-time parameters significantly influence temperature, stress, and displacement distributions. Comparisons with the classical Lord–Shulman model reveal the proposed theory’s superior capability in capturing wave-like thermal and mechanical behavior, especially under conditions involving finite speed heat propagation and size-dependent effects.</p>

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A Novel General Generalized Model Based on Thermomass Theory due to Ramp-Type Heating

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Sudip Mondal,
  • Abhik Sur

摘要

Abstract

The increasing demand for accurate modeling of heat transport in micro/nano-scale devices and ultrafast laser applications reveals the limitations of classical heat conduction theories like Fourier’s law. To address this, a novel framework for generalized thermoelasticity is proposed, incorporating a non-Fourier heat conduction law grounded in thermomass theory—where heat is modeled as the motion of an equivalent mass of phonon gas. The model also integrates a nonlocal formulation for stress and incorporates memory effects via the memory-dependent derivative (MDD), allowing for the influence of past thermal states.

The study considers a one-dimensional thermoelastic rod subjected to ramp-type thermal loading at one boundary, with the other end maintained at zero temperature. Both ends are mechanically fixed. The governing equations are solved in the Laplace domain, and numerical inversion using Zakian’s technique is applied to obtain time-space domain results. Different types of kernel functions are introduced to capture memory effects, and nonlocality is embedded in the stress field.

The results demonstrate that kernel choice, nonlocal length scale, ramp duration, and delay-time parameters significantly influence temperature, stress, and displacement distributions. Comparisons with the classical Lord–Shulman model reveal the proposed theory’s superior capability in capturing wave-like thermal and mechanical behavior, especially under conditions involving finite speed heat propagation and size-dependent effects.