MHD Flows of Second Grade Fluid Through the Moving Porous Cylindrical Domain

Abstract

The flows of Magnetohydrodynamics(MHD) second grade fluid between two infinite porous coaxial circular cylinders are studied. At time t=0^+, the inner cylinder begins to rotate around its axis and to slide along the same axis due to torsional and longitudinal time dependent shear stresses and the outer cylinder is also rotate around its axis and to slide along the same axis with acceleration. The exact solutions obtained with the help of discrete Laplace and finite Hankel transform, satisfy all imposed initial and boundary conditions. The solution presented in convolution product of Laplace transform . The corresponding solutions for second grade and Newtonian fluids are also obtained as limiting cases with and without MHD effect. Finally, the influence of pertinent parameters on the velocity components and shear stresses, as well as a comparison among, second grade and Newtonian fluids with and without MHD  is also analyzed by graphical illustrations.