Linear stability of buoyant convective flow in a vertical channel with internal heat sources and a transverse magnetic field

Linear stability of buoyant convective flow of an electrically conducting fluid in a vertical channel owing to internal heat sources has been studied. The flow takes place in a transverse, horizontal magnetic field. The results show that up to four different local minima may be present in the neural stability curve. Up to two of these modes may be the most unstable depending, critically, on the value of the Hartmann number. Over a wide range of moderate to high Hartmann numbers thermal waves dominate the instability. As the Hartmann number increases, however, this mode is strongly damped. Then the so-called Hartmann mode takes over, which involves the characteristic Hartmann layers at the walls appearing due to modification of the basic velocity profile by the magnetic field. Overall, for liquid metals at high magnetic fields the basic flow is very stable. Variation of the Prandtl number in a wide range has also been performed as, depending on the type of an electrically conducting fluid (liquid metal or various kind of electrolytes), the Prandtl number varies over several orders of magnitude. As may be expected, the increase of the Prandtl number lowers the instability threshold for the thermal waves.