Magnetohydrodynamic free convection in a strong cross field

The problem of magnetohydrodynamic free convection of an electrically conducting fluid in a strong cross field is investigated. It is solved by using a singular perturbation technique. The solutions presented cover the range of Prandtl numbers from zero to order one. This includes both the important cases of liquid metals and ionized gases. A general examination is given of the role of the important parameters: Hartmann, Grashof and Prandtl numbers of the problem. This provides clear insight into its singular character and yields the correct expansion parameters. The boundary-layer approximations are derived from the complete Navier-Stokes and energy equations. The conditions for these approximations to be valid will be explicitly stated. Attention is given to ‘power law’ wall-temperatures and magnetic fields, and an assessment is given of the range of application.