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孙艳军, 王嘉璐, 贾北楠, 菅永军. 非傅里叶效应对Maxwell流体在垂直槽道中热对流不稳定性的影响. 力学学报, 2024, 56(6): 1-9. DOI: 10.6052/0459-1879-24-042
引用本文: 孙艳军, 王嘉璐, 贾北楠, 菅永军. 非傅里叶效应对Maxwell流体在垂直槽道中热对流不稳定性的影响. 力学学报, 2024, 56(6): 1-9. DOI: 10.6052/0459-1879-24-042
Sun Yanjun, Wang Jialu, Jia Beinan, Jian Yongjun. Effect of non-fourier on thermal convection instability of maxwell fluids in a vertical channel. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1-9. DOI: 10.6052/0459-1879-24-042
Citation: Sun Yanjun, Wang Jialu, Jia Beinan, Jian Yongjun. Effect of non-fourier on thermal convection instability of maxwell fluids in a vertical channel. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(6): 1-9. DOI: 10.6052/0459-1879-24-042

非傅里叶效应对Maxwell流体在垂直槽道中热对流不稳定性的影响

EFFECT OF NON-FOURIER ON THERMAL CONVECTION INSTABILITY OF MAXWELL FLUIDS IN A VERTICAL CHANNEL

  • 摘要: 基于Maxwell流体在科学、工程和技术等各个领域的重要性, 并且结合非傅里叶热传导效应在许多不同研究领域的广泛关注, 文章研究了非傅里叶效应对Maxwell流体在垂直槽道中热对流不稳定性的影响. 将传统傅里叶热传导模型加入一个包含热松弛时间的新瞬态项, 得到了非傅里叶热传导方程. 使用切比雪夫配置法数值求解了一个广义特征值问题, 得到了时间增长率和中性稳定曲线随各参数的变化情况. 结果表明, 时间增长率会随着松弛时间参数Λ增加而增加. 中性稳定曲线表明, 在波数相对较小的范围内, 松弛时间的影响几乎可以忽略. 但是当波数较大时, 松弛时间对热对流不稳定性的影响逐渐加剧. 这表明Maxwell流体的弹性效应增强了垂直管道内的热对流不稳定性. 对于傅里叶流体, 中性稳定性曲线不会随着Prandtl数变化. 另一方面, 非傅里叶效应增强了热对流不稳定性, 并且新的双曲型热传导方程使得中性稳定曲线产生了波动现象. 进一步研究表明, 这种波动会随着Prandtl数的增加而增强. 当Prandtl数超过一定临界值时, 中性稳定曲线同时出现稳态分支和振荡分支, 而且在振荡分支中, 不稳定性显著增强.

     

    Abstract: Based on the importance of Maxwell fluids in various fields such as science, engineering and technology, and combined with the wide interest of non-Fourier heat conduction effects in many different research fields, the influence of non-Fourier effects on the thermal convection instability of Maxwell fluids in vertical channels is investigated in this paper. The non-Fourier heat transfer equation is obtained by adding a new transient term including the thermal relaxation time to the traditional Fourier heat transfer model. A generalized eigenvalue problem is numerically solved using the Chebyshev configuration method, and the temporal growth rate and neutral stability curve for each parameter are obtained. The results show that the temporal growth rate increases with the increase of the relaxation time parameter Λ. The neutral stability curve shows that the effect of relaxation time is almost negligible in the relatively small range of wave number. However, when the wave number increases, the effect of relaxation time on the convective instability is gradually intensified. This indicates that the elastic effect of Maxwell fluids enhances the thermal convection instability in vertical pipes. For Fourier fluids, the neutral stability curve does not vary with the Prandtl number. On the other hand, the non-Fourier effect enhances the convective instability, and the new hyperbolic heat transfer equation causes the neutral stability curve to fluctuate. Further studies show that this fluctuation is enhanced with the increase of Prandtl number. When the Prandtl number surpasses a specific critical value, the neutral stability curve splits into stationary and oscillatory branches. Furthermore, in the oscillatory branches, the instability is greatly increased.

     

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