Influences of magnetic field in viscoelastic fluid

This communication in fluences on magnetohydrodynamic ow of viscoelastic fluid with magnetic field induced by oscillating plate. General solutions have been found out for velocity and shear stress proles using mathematical transformations (integral transforms). The governing partial differential equations have been solved analytically under boundary conditions u(0; t) = A0H(t)sin( t) and u(0; t) = A0H(t)cos( t) with t ≥ 0. For the sake of simplicity of boundary conditions are veried on the analytical general solutions and similar solutions have been particularized under three limited cases namely (i) Maxwell fluid without magnetic field if 6= 0;M = 0 (ii) Newtonian fluid with magnetic field if = 0;M 6= 0 and (iii) Newtonian fluid with out magnetic field if = 0;M = 0. Finally various physical parameters with variations of fluid behaviors are analyzed and depicted graphical illustrations.