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Nonhomogeneous Dual-Phase-Lag Heat Conduction Problem: Analytical Solution and Select Case Studies

机译：非均相双相滞后热传导问题：解析解和精选案例研究

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摘要

Finite integral transform techniques are applied to solve the one-dimensional (1D) dual-phase heat conduction problem, and a comprehensive analysis is provided for general time-dependent heat generation and arbitrary combinations of various boundary conditions (Dirichlet, Neumann, and Robin). Through the dependence on the relative differences in heat flux and temperature relaxation times, this analytical solution effectively models both parabolic and hyperbolic heat conduction. In order to demonstrate several exemplary physical phenomena, four distinct cases that illustrate the wavelike heat conduction behavior are presented. In the first model, following an initial temperature spike in a slab, the thermal evolution portrays immediate dissipation in parabolic systems, whereas the dual-phase solution depicts wavelike temperature propagation—the intensity of which depends on the relaxation times. Next, the analysis of periodic surface heat flux at the slab boundaries provides evidence of interference patterns formed by temperature waves. In following, the study of Joule heating driven periodic generation inside the slab demonstrates that the steady-periodic parabolic temperature response depends on the ratio of pulsatile electrical excitation and the electrical resistivity of the slab. As for the dual-phase model, thermal resonance conditions are observed at distinct excitation frequencies. Building on findings of the other models, the case of moving constant-amplitude heat generation is considered, and the occurrences of thermal shock and thermal expansion waves are demonstrated at particular conditions.
机译：应用有限积分变换技术来解决一维（1D）双相热传导问题，并对常规的随时间变化的热量生成和各种边界条件（Dirichlet，Neumann和Robin）的任意组合提供了全面的分析。 。通过依赖于热通量和温度松弛时间的相对差异，此分析解决方案有效地模拟了抛物线和双曲线的热传导。为了证明几种示例性的物理现象，提出了四种不同的情况，这些情况说明了波状热传导行为。在第一个模型中，在平板中出现初始温度峰值之后，热演化刻画了抛物线形系统中的即时耗散，而双相解则描述了波状温度传播，其强度取决于弛豫时间。接下来，对板坯边界处的周期性表面热通量的分析提供了由温度波形成的干涉图样的证据。接下来，对平板内部焦耳加热驱动的周期性发电的研究表明，稳态周期抛物线温度响应取决于平板的脉动电激发比和电阻率。对于双相模型，在不同的激发频率下观察到热共振条件。在其他模型的发现的基础上，考虑了移动恒定振幅发热的情况，并证明了在特定条件下热冲击和热膨胀波的发生。

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  • 来源
    《Journal of Heat Transfer》 |2018年第3期|031301.1-031301.22|共22页
  • 作者

    Simon Julius; Boris Leizeronok; Beni Cukurel;

  • 作者单位

    Turbomachinery and Heat Transfer Laboratory,Faculty of Aerospace Engineering,Technion—Israel Institute of Technology,Haifa 3200003, Israel;

    Turbomachinery and Heat Transfer Laboratory,Faculty of Aerospace Engineering,Technion—Israel Institute of Technology,Haifa 3200003, Israel;

    Turbomachinery and Heat Transfer Laboratory,Faculty of Aerospace Engineering,Technion—Israel Institute of Technology,Haifa 3200003, Israel;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Temperature; Heat conduction; Slabs; Boundary-value problems; Heat flux; Heat;

    机译：温度;热传导;平板;边值问题;热通量;热;

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