This work is related to flow of an electro conducting fluid presented thermoelectric figure-of-merit effect, in the presence of magnetic field. The electro conducting thermofluid equation heat transfer with one relaxation time is derived. The flow of electro conducting fluid over a suddenly moved plate is considered. The governing coupled equations in the frame of the boundary layer model are applied to Stokes' first problem with heat sources. Laplace transforms and Fourier transforms techniques are used to get the solution. The inverses of Fourier transforms are obtained analytically. Laplace transforms are obtained using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature distribution and the velocity component are represented graphically. Thermoelectric figure-of-merit effect on the fluid flow is studied.