 solut free convect boundari layer equat electr conduct fluid solut free convect boundari layer equat electr conduct fluid author investig exist class solut free convect vertic flat plate free convect nonconduct fluid magnet field act transvers fluid motion assum remain constant direct perpendicular plate introduc momentum equat retard forc function distanc plate length similar magnet induct vari plate temperatur constant 0 magnet induct constant plate temperatur increas linearli 