Instability of an upward mixed convection flow in a vertical heated pipe under a transverse magnetic field
Phys. Rev. Fluids 10, 103901 – Published 14 October, 2025
DOI: https://doi.org/10.1103/twsp-czgg
Abstract
Instability of an upward flow in a vertical heated pipe under a unidirectional transverse magnetic field is investigated through both linear global stability analysis and direct numerical simulations. The magnetic effect on the dominant thermal-buoyant instability for the moderate Prandtl number, for water, and the dominant thermal-shear instability for the small Prandtl number, for liquid metal, is revealed. The two plane symmetric spiral modes for both the thermal-buoyant and thermal-shear instabilities are broken into two asymmetric branches with different critical values for the Rayleigh number and wave number. For the thermal-buoyant instability with , as the Hartmann number increases, the critical Rayleigh number on one branch changes significantly faster than that on the other branch. The flow can become unstable at much smaller Rayleigh numbers under the action of the magnetic field with a moderate Hartmann number. For the thermal-shear instability with , the critical Rayleigh numbers on the two asymmetric branches also show significant differences in changes. The critical Rayleigh number of one branch increases monotonically as the Hartmann number increases from zero, while that of the other branch first decreases and then increases, showing a nonmonotonic change. Energy budget analyses at the critical values are also performed to validate the increasing stabilization effect of the magnetic field with the increase of the Hartmann number. Direct numerical simulations are used to compute the linear growth rate and validate our linear global stability analysis. Furthermore, fully developed nonlinear flow states of the MHD mixed convection are investigated near the critical curves of linear stability. It is found that for water with , the thermal-buoyant instability is supercritical and large-scale spatiotemporal structures are maintained within a large range of the Rayleigh number. In comparison, for liquid metal with , the thermal-shear instability can be subcritical because nonlinear sustained states are found below the critical Rayleigh number for linear instability. The flow exhibits turbulent behaviors when the Hartmann number is small but turns to nonturbulent regular structures as the Hartmann number increases due to the suppression of small-scale turbulent structures by the magnetic field.
