 magnetohydrodynam free-convect pipe flow magnetohydrodynam free-convect pipe flow transvers magnet field practic strength exert consider influenc liquid-metal free-convect vertic flat-plate parallel-plate flow field extent influenc determin magnitud nondimension paramet ratio hartmann number fourth root grashof number measur rel influenc magnet buoyant forc note steadi fulli develop laminar free-convect flow fluid electr conduct fulli submerg open-end constant-temperatur vertic pipe locat transvers magnet field strength analyz term paramet magnitud influenc veloc temperatur profil surfac shear heat transfer volumetr flow rate determin 