Fractional Green-Naghdi theory for thermoelectric MHD

In this work, we use the Green-Naghdi theory of thermomechanics of continua to derive a linear theory of MHD thermoelectric fluid with fractional order of heat transfer. This theory permits propagation of thermal waves at finite speed. The one-dimensional model of the theory 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. The problem was solved using the Laplace transform technique. The solution in the transformed domain is obtained by a direct approach. A numerical method based on a Fourier-series expansion is used for the inversion process. The thermoelectric effects with fractional parameter on the temperature and velocity fields are analyzed and discussed in detail with the aid of graphical illustrations.