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Heat propagation in a nonuniform rod of variable cross section

机译：变截面非均匀棒中的热传播

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摘要

An integral formula is used to average a coupled problem of thermoelasticity for a nonuniform rod of variable cross section. Effective characteristics are found. It is shown that, in addition to the expected effective coefficients, there appear five independent coefficients characterizing the temperature change rate effect on the stresses in the rod, on the longitudinal heat flux, and on the entropy distribution along the length of the rod. A feature of these new coefficients is that they become equal to zero in the case of a uniform rod. The homogenization of the thermoelasticity equations for nonuniform rods allows one to propose a new theory of heat conduction in rods. This new theory differs from the classical one by the fact that some new terms are added to the Duhamel-Neumann law, to the Fourier heat conduction law, and to the entropy expression. These new terms are proportional to the temperature change rate with time. It is also shown that, in the new theory of heat conduction, the propagation velocity of harmonic heat perturbations is dependent on the oscillation frequency and is finite when the frequency tends to infinity.
机译：积分公式用于求变截面非均匀杆的热弹性耦合问题的平均值。找到有效的特征。结果表明，除了预期的有效系数外，还出现了五个独立的系数，这些系数表征了温度变化率对杆中应力，纵向热通量以及沿杆长度的熵分布的影响。这些新系数的特征在于，在均匀棒的情况下，它们变为等于零。非均匀棒的热弹性方程的均质化允许提出一种新的棒中热传导理论。这一新理论与经典理论的不同之处在于，在Duhamel-Neumann定律，傅立叶热传导定律和熵表达式中增加了一些新的术语。这些新项与温度随时间的变化率成正比。还表明，在新的热传导理论中，谐波热扰动的传播速度取决于振荡频率，并且在频率趋于无穷大时是有限的。

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  • 来源
    《Moscow university mechanics bulletin》 |2017年第2期|48-53|共6页
  • 作者

    Gorbachev V. I.;

  • 作者单位

    Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, Russian Federation;

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