Abstract
A new mathematical model of thermoelectric MHD theory has been constructed in the context of a new consideration of heat conduction law with time-delay and kernel function. The memory-dependent differential equation of heat transfer is established. This model is applied to Stokes' flow of unsteady incompressible fluid due to a moving flat plate in the presence of both heat sources and a transverse magnetic field. Laplace transforms and state-space techniques will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. The predictions of the theory are discussed and compared with dynamic coupled theory for different forms of kernel functions. The thermoelectric effects with time-delay parameter on the temperature and velocity fields are analyzed and discussed in detail with the aid of graphical illustrations.