Viscoelastic Fluid Dynamics: An exact solution for second grade fluid for MHD in porous cylinder

Viscoelastic fluid dynamics of second-grade fluid in porous cylindrical containers have been studied. Laplace and Hankel transformations are employed simultaneously on the partial differential equations governing the motion of a second-grade fluid. An exact solution has been obtained to study magnetohydrodynamics (MHD) and porous effects. The exact solution has four parts corresponding to velocity, shear stress, temperature, and concentration of a second-grade fluid moving in a cylindrical container. One of the important characteristics of these solutions is its variable boundary conditions, i. e. the boundary conditions are the function of time. Hence, elastic response and viscous effect can be studied for various functions of time. The results can be applied in industrial applications such as polymer solutions and characteristics of oil. The solutions for velocity, shear stress, temperature, and concentration have also been discussed graphically, the limiting case of Newtonian fluid where the elastic effect of viscoelastic fluid vanishes is also discussed.