In this paper, the unsteady of magnetohydrodynamics (MHD) second grade fluid in a porous medium due to non–coaxial rotation is investigated. The effects of heat and mass transfers (double diffusion) through an oscillating disk are considered. The non–dimensional governing momentum, energy and mass equations are obtained by using the suitable non–dimensional variables. The Laplace transform method is used to obtain the
exact solutions of non–dimensional velocity, temperature and concentration profiles. The expressions of skin friction, Nusselt number and Sherwood number are also presented. The numerical result for all fluid flow profiles are plotted in graphs for the different parameters studied. The results also show that, velocity for present solution (with heat and mass transfers) has a significant impact on the velocity profiles in non-coaxial rotation due to exhibits high thermal diffusivity and thermal conductivity. The obtained exact solutions are found to be identical to the Guria [10]. It is worth mentioning that, the exact solutions are in excellent agreement with the numerical solutions of Inverse Laplace transform obtained by Gaver-Stehfest algorithm.