Effects of second-order slip on the flow of a fractional Maxwell MHD fluid

The magnetohydrodynamic (MHD) flow of a generalized Maxwell fluid induced by a moving plate has been investigated, where the second-order slip between the wall and the fluid in the wall is considered. The fractional calculus approach is used to establish the constitutive relationship model of the non-Newtonian fluid model. Exact analytical solutions for the velocity field and shear stress in terms of Fox H-function are obtained by means of the Laplace transform. The solutions for the generalized Maxwell second-order slip model without magnetic field, the MHD flow of generalized Maxwell flow without slip effects or first-order slip model can be derived as the special cases. Furthermore, the influence of the order of fractional derivative, the magnetic body force, the slip coefficients and power index on the velocity and shear stress are analyzed and discussed in detail. The results show that the velocity corresponding to flows with slip condition is lower than that for flow with non-slip conditions, and the velocity with second-slip condition is lower than that with first-order slip condition.