On exact solutions of Stokes second problem for MHD Oldroyd-B fluid

The present study is an attempt to look at the exact solutions of Stokes second problem. Constitutive equations for an Oldroyd-B fluid have been taken into consideration. The fluid is electrically conducting under the influence of a uniform transverse magnetic field. The hydromagnetic flow is generated by the oscillations of an infinite flat plate. Employing the Laplace transform, the expressions for the velocity field and the associated tangential stress are obtained. These solutions are presented as a sum of steady state and transient solutions. The results are graphically displayed and the influence of various parameters is discussed. Further, the results under the limiting conditions are found to be in good agreement with the existing ones.

► Establishment of the starting solutions for Stokes second problem of an Oldroyd-B fluid.
► The fluid is electrically conducting under the influence of a uniform transverse magnetic field.
► The exact solutions for the velocity field and the associated tangential stress are obtained by using Laplace transform.
► The solutions for Newtonian and Stokes first problem is obtained as a limiting cases.