非Fourier效应对垂直槽道中磁流体热对流不稳定性的影响

孙艳军; 贾北楠; 长龙; 菅永军

doi:10.21656/1000-0887.460188

非Fourier效应对垂直槽道中磁流体热对流不稳定性的影响

doi: 10.21656/1000-0887.460188

1. 内蒙古财经大学统计与数学学院, 呼和浩特 010070;^{2. 东华大学数学与统计学院, 上海 201620}

基金项目:

内蒙古自治区自然科学基金(2025MS01028

2024LHMS01010)

内蒙古自治区高校创新团队计划(NMGIRT2323)

内蒙古自治区直属高校基本科研业务费(NCYWT25002)；内蒙古财经大学2024年度高质量科研成果培育基金(GZCG24248)

国家自然科学基金(12262026)

详细信息

作者简介:
孙艳军(1987—), 男, 副教授, 博士(E-mail: sunyanjun@imufe.edu.cn);菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).

通讯作者:
菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).

中图分类号: O361.3
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出版历程
- 收稿日期: 2025-10-16
- 修回日期: 2026-11-17
- 网络出版日期: 2026-10-31

Non-Fourier Effects on the Thermal Convection Instability of Magnetohydrodynamic Fluid in a Vertical Channel

1. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, P.R. China;^{2. School of Mathematics and Statistics, Donghua University, Shanghai 201620, P.R. China}

Funds:

The National Science Foundation of China(12262026)

摘要

摘要: 非Fourier热传导理论作为传热领域的重要修正理论，通过引入热松弛时间参数，突破了传统Fourier定律的抛物型方程限制，揭示了热量传递的波动特性.针对垂直槽道中磁流体热对流系统，重点研究了非Fourier效应对热对流不稳定性的影响机制.将各物理量分解为稳态解与小扰动叠加形式，导出扰动方程的广义特征值问题.基于线性稳定性理论，建立了考虑非Fourier效应与外加磁场的耦合控制方程组.采用Chebyshev配置法求解出时间增长率随波数的变化曲线以及中性稳定曲线，系统分析了不同参数下流动失稳的条件与模态特征.结果表明，Chandrasekhar数对热对流的不稳定性具有显著的抑制作用.当Grashof数较小时，磁场效应对热对流不稳定性的调控作用更明显.Cattaneo数和Prandtl数对热对流不稳定性都具有促进作用.特别地，增大Cattaneo数会使中性稳定曲线显示出显著的波动响应.
- 非Fourier热流模型 /
- 磁流体 /
- 热对流不稳定性 /
- 垂直槽道 /
- 线性稳定性分析
Abstract: The non-Fourier heat conduction theory, as an important modified theory in the field of heat transfer, breaks through the parabolic equation limitation of the traditional Fourier law through introduction of the thermal relaxation time parameter, to reveal the wave characteristics of heat transfer. Aimed at the magnetohydrodynamic thermal convection system in a vertical channel, the non-Fourier effect mechanism on the thermal convection instability was studied. Each physical quantity was decomposed into the form of a steady-state solution with a small perturbation, and the generalized eigenvalue problem of the perturbation equation was derived. Based on the linear stability theory, a coupled control equation set with the non-Fourier effect and the external magnetic field was established. The Chebyshev collocation method was used to solve the variation curves of the time growth rate with the wave numbers and the neutral stability curves, and the conditions and modal characteristics of flow instability under different parameters were systematically analyzed. The results show that, the Chandrasekhar number has a significant inhibitory effect on the instability of thermal convection. For a smaller Grashof number, the magnetic field effect on the thermal convection instability is more obvious. Both the Cattaneo number and the Prandtl number have a promoting effect on the thermal convection instability. Particularly, increasing the Cattaneo number will cause the neutral stability curve to give a significant wave response.
- non-Fourier heat flux model /
- magnetohydrodynamic fluid /
- thermal convection instability /
- vertical channel /
- linear stability analysis

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参考文献(32)

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非Fourier效应对垂直槽道中磁流体热对流不稳定性的影响

doi: 10.21656/1000-0887.460188

作者简介:
孙艳军(1987—), 男, 副教授, 博士(E-mail: sunyanjun@imufe.edu.cn);菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).

通讯作者:
菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).

计量

Non-Fourier Effects on the Thermal Convection Instability of Magnetohydrodynamic Fluid in a Vertical Channel

计量

目录

留言板

非Fourier效应对垂直槽道中磁流体热对流不稳定性的影响

doi: 10.21656/1000-0887.460188

作者简介: 孙艳军(1987—), 男, 副教授, 博士(E-mail: sunyanjun@imufe.edu.cn);菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).

通讯作者: 菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).

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出版历程

Non-Fourier Effects on the Thermal Convection Instability of Magnetohydrodynamic Fluid in a Vertical Channel

计量

出版历程

目录

作者简介:
孙艳军(1987—), 男, 副教授, 博士(E-mail: sunyanjun@imufe.edu.cn);菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).

通讯作者:
菅永军(1974—), 男, 教授, 博士, 博士生导师(通信作者. E-mail: jianyj@dhu.edu.cn).