General solutions for MHD motions of ordinary and fractional Oldroyd‐B fluids through a porous medium over a moving plate

The motion problem of the electrically conducting incompressible fluids, both conventional and fractional Oldroyd‐B, over an infinite horizontal flat plate moving within its plane in the presence of a transverse magnetic field and porous medium, has been thoroughly resolved. Exact general expressions are established for the dimensionless velocity and non‐trivial shear stress fields and the Darcy's resistance by means of the integral transforms. These expressions, which are validated through graphical representations or comparisons with established results in the literature, are capable of generating exact solutions for any motion pertaining to incompressible ordinary or fractional Oldroyd‐B fluids of this nature. For illustration, solutions corresponding to Stokes problems are presented, and the time required to attain a steady state is graphically evaluated for both models. Our findings indicate that the steady state is achieved earlier in the presence of a magnetic field or porous medium. Simultaneously, it is observed that the attainment of the steady state occurs later for motions involving fractional fluids compared to ordinary fluids. Furthermore, as anticipated, the fluid flow is decelerated in the presence of a magnetic field or porous medium. Notably, it is to highlight that the first problem of Stokes converges to a steady state over time for both ordinary and fractional fluids, and the corresponding steady states velocities are same.