The linear stability of Hunt-Rayleigh-Bénard flow

The stability of a pressure driven flow in a duct heated from below and subjected to a vertical magnetic field (Hunt-Rayleigh-Benard flow) is studied. We use the Chebyshev collocation approach to solve the eigenvalue problem for the small-amplitude perturbations. It is demonstrated that the magnetic field can stabilize the flow, while the temperature field can disturb the flow. There exists a threshold for the Hartmann number below which the growth rate changes with the Prandtl number non-monotonously (first increases and then decreases) with a critical Prandtl number for the maximum growth rate. By comparing the R e – α neutral curves at different Rayleigh numbers, we find that the critical Reynolds number decreases with the increase in the Rayleigh number, which has an obvious influence on the long-wave instability and a little influence on the short-wave instability. The dominant mode of the long-wave instability changes from the boundary layer instability to the inflectional instability with the incre...