The unsteady free convection flow of an electrically conducting fluid past an accelerated infinite vertical plate with constant heat flux is investigated under the influence of uniform transverse magnetic field fixed relative to the fluid or to the plate in the presence of heat generation or absorption. Two important cases, (i) exponentially accelerated plate (EAP) and (ii) uniformly accelerated plate (UAP), have been considered. The governing partial differential equations have been solved analytically using the Laplace transform technique and closed form solutions are obtained for the velocity and temperature fields without any restriction. The effects of system parameters such as the Prandtl number, heat generation or absorption, Grashof number, and magnetic field parameter on the flow fields are analyzed through graphs and tables. Further, the solution of the problem involves inverse Laplace transforms of some new exponential forms and these formulas are provided. The unsteady free convection flow of an electrically conducting fluid past an accelerated infinite vertical plate with constant heat flux is investigated under the influence of uniform transverse magnetic field fixed relative to the fluid or to the plate in the presence of heat generation or absorption. Two important cases, (i) exponentially accelerated plate (EAP) and (ii) uniformly accelerated plate (UAP), have been considered. The solution of the problem involves inverse Laplace transforms of some new exponential forms and these formulas are provided. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.