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Abstract <p>The paper formulates and analytically solves a nonlinear unsteady heat conduction problem in a three-phase domain with two nonstationary moving phase boundaries. The linear and mass velocities of these boundaries are determined from the heat flux balance at the phase interfaces. To determine the velocities and positions of the moving boundaries at each moment in time, a system of two transcendental equations is derived and solved numerically using an iterative method, with the initial approximation of the boundary positions specified. Temperature distributions are continuous across the moving boundaries, while temperature gradients and heat fluxes exhibit discontinuities. Such problems are nonlinear not only in the case of two, but even with a single nonstationary moving phase transition boundary, since the coordinates and velocities of the moving boundaries are determined by the balance of incoming and outgoing heat fluxes at these boundaries, which, in turn, depend on the temperature distributions in the vicinity of the boundaries. Numerical results are obtained and analyzed.</p>

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Mathematical Modeling of Heat Transfer in Three-Phase Domains with Two Moving Phase Boundaries

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Ek. L. Kuznetsova,
  • A. A. Orekhov,
  • L. N. Rabinskiy

摘要

Abstract

The paper formulates and analytically solves a nonlinear unsteady heat conduction problem in a three-phase domain with two nonstationary moving phase boundaries. The linear and mass velocities of these boundaries are determined from the heat flux balance at the phase interfaces. To determine the velocities and positions of the moving boundaries at each moment in time, a system of two transcendental equations is derived and solved numerically using an iterative method, with the initial approximation of the boundary positions specified. Temperature distributions are continuous across the moving boundaries, while temperature gradients and heat fluxes exhibit discontinuities. Such problems are nonlinear not only in the case of two, but even with a single nonstationary moving phase transition boundary, since the coordinates and velocities of the moving boundaries are determined by the balance of incoming and outgoing heat fluxes at these boundaries, which, in turn, depend on the temperature distributions in the vicinity of the boundaries. Numerical results are obtained and analyzed.