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<p>The transient process leading to a&#xa0;steady-state periodic thermal regime in the walls of a&#xa0;plate is investigated under the influence of a&#xa0;rapidly decaying periodic heat flux applied to one of its surfaces. This problem, in a&#xa0;first approximation, models the temperature field distribution in the walls of explosive chambers, which arises as a&#xa0;result of the detonation of combustible mixtures a&#xa0;process that typically exhibits a&#xa0;periodic nature in operational conditions. The problem also has practical significance in terms of identifying the time required to reach the “working regime” and determining the maximum value of the steady-state temperature field, depending on the type of boundary conditions applied to the opposite surface of the plate. An important factor is the presence of thermal protection in the form of a&#xa0;thin inner layer made of a&#xa0;material with high thermal conductivity on the surface exposed to the heat flux. The problem was solved numerically using a&#xa0;program based on the finite element method, and analytically using an asymptotic approach, under the assumption that the process is considered sufficiently far from the initial condition. A comparison of the two solutions showed very good agreement.</p>

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The transient process to a steady-state periodic temperature regime

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Purbo L. Abiduev,
  • Tumen G. Darmaev

摘要

The transient process leading to a steady-state periodic thermal regime in the walls of a plate is investigated under the influence of a rapidly decaying periodic heat flux applied to one of its surfaces. This problem, in a first approximation, models the temperature field distribution in the walls of explosive chambers, which arises as a result of the detonation of combustible mixtures a process that typically exhibits a periodic nature in operational conditions. The problem also has practical significance in terms of identifying the time required to reach the “working regime” and determining the maximum value of the steady-state temperature field, depending on the type of boundary conditions applied to the opposite surface of the plate. An important factor is the presence of thermal protection in the form of a thin inner layer made of a material with high thermal conductivity on the surface exposed to the heat flux. The problem was solved numerically using a program based on the finite element method, and analytically using an asymptotic approach, under the assumption that the process is considered sufficiently far from the initial condition. A comparison of the two solutions showed very good agreement.