MHD natural convection in a laterally and volumetrically heated square cavity.

*(English)*Zbl 1189.76790Summary: A numerical study is presented of unsteady two-dimensional natural convection of an electrically conducting fluid in a laterally and volumetrically heated square cavity under the influence of a magnetic field. The flow is characterized by the external Rayleigh number, \(Ra_{E}\), determined from the temperature difference of the side walls, the internal Rayleigh number, \(Ra_{I}\), determined from the volumetric heat rate, and the Hartmann number, \(Ha\), determined from the strength of the imposed magnetic field. Starting from given values of \(Ra_{E}\) and \(Ha\), for which the flow has a steady unicellular pattern, and gradually increasing the ratio \(S = Ra_{I}/Ra_{E}\), oscillatory convective flow may occur. The initial steady unicellular flow for \(S = 0\) may undergo transition to steady or unsteady multicellular flow up to a threshold value, \(Ra_{I,cr}\), of the internal Rayleigh number depending on \(Ha\). Oscillatory multicellular flow fields were observed for \(S\) values up to 100 for the range \(10^{5}-10^{6}\) of \(Ra_{E}\) studied. The increase of the ratio \(S\) results usually in a transition from steady to unsteady flow but there have also been cases where the increase of \(S\) results in an inverse transition from unsteady to steady flow. Moreover, the usual damping effect of increasing Hartmann number is not found to be straightforward connected with the resulting flow patterns in the present flow configuration.