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<p>A&#xa0;nonlinear parabolic equation with state-dependent coefficients arising in the high-temperature heat conduction of nanoparticles under pulsed volumetric heating is considered. The temperature dependence of heat capacity and thermal conductivity introduces competing nonlinearities in the time derivative and the diffusion flux, respectively. For a&#xa0;spherically symmetric domain with convective and radiative boundary conditions, an initial-boundary value problem is formulated and solved numerically. A&#xa0;conservative finite-difference discretization in the radial direction, combined with the method of lines, preserves the divergence form of the nonlinear flux and provides second-order spatial accuracy. The resulting system of ordinary differential equations is integrated using implicit BDF schemes with adaptive time stepping. Numerical experiments demonstrate the efficiency and robustness of the proposed approach. The computational framework is applicable to a&#xa0;broader class of parabolic problems with coefficients depending on the unknown function.</p>

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Numerical modeling of nonlinear heat conduction in nanoparticles under pulsed heating: a parabolic equation with state-Dependent coefficients

  • 期刊论文

  • 发表日期：

    2026年4月13日

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  • S. Rekhviashvili,
  • R. Berezgova

摘要

A nonlinear parabolic equation with state-dependent coefficients arising in the high-temperature heat conduction of nanoparticles under pulsed volumetric heating is considered. The temperature dependence of heat capacity and thermal conductivity introduces competing nonlinearities in the time derivative and the diffusion flux, respectively. For a spherically symmetric domain with convective and radiative boundary conditions, an initial-boundary value problem is formulated and solved numerically. A conservative finite-difference discretization in the radial direction, combined with the method of lines, preserves the divergence form of the nonlinear flux and provides second-order spatial accuracy. The resulting system of ordinary differential equations is integrated using implicit BDF schemes with adaptive time stepping. Numerical experiments demonstrate the efficiency and robustness of the proposed approach. The computational framework is applicable to a broader class of parabolic problems with coefficients depending on the unknown function.