A class of exact solutions of the unsteady magnetohydrodynamic free-convection flows

The unsteady free-convection flow of an electrically-conducting fluid near a moving vertical plate of infinite extent is investigated in the presence of uniform transverse magnetic field fixed to the fluid or to the plate. Exact solution of this problem is obtained with the aid of the Laplace transform technique, when the plate is moving with a velocity which is an arbitrary functiuon of time. The solution is exemplified for three particular cases of physical interest; the non-magnetic case is also discussed.