Free convection flow near an infinite vertical plate of 

an electrically conducting fluid of Prandtl number unity 

has been considered when the flow takes place 

under the combined influence of heat flux 

at the boundary and an externally applied magnetic field. 

For the impulsive and accelerated motions of the boundary, 

unified closed form analytical solutions have been obtained 

for the fluid velocity and the skin friction corresponding 

to the cases of magnetic field fixed relative to the fluid 

or to the boundary. As a special case, 

an approximation of the solution in terms of exponential 

functions is also discussed.