JMAT_V4_N4_RP3 Samra Muhammad Raheel Mohyuddin Syed Mohammad Rizwan Journal on Mathematics 2277-5137 4 4 22 27 Grade-III Fluid, Perturbation Method, Unsteady Flow This is the study of the grade-III fluid having the unidirectional and unsteady flow. Differential equation is solved using perturbation method to get linear forms of the velocities. The velocity u(y,t) is perturbed in ε to get the two-linear Partial st iat Differential Equations (PDE's) in terms of u0(y,t) and u1(y,t). The solution of 1st linear is given in the exponent form f(y) eiat , that gives an ordinary differential equation that is easily solved to get the solution. This solution u0(y,t) is then utilized in Partial Differential Equation of 1st term velocity u1(y,t) and that gives linear Partial Differential Equation in the velocity u (y,t). The 3iat solution of u (y,t) is given in the exponent form F(y) e3iat , that gives an ordinary differential equation in F(y), that is solved to get the solution of F(y). This gives the perturbed solution for u1(y,t) in the form of F(y). First and zeroth solutions for the velocities give the solution for PDE. October - December 2015 Copyright © 2015 i-manager publications. All rights reserved. i-manager Publications http://www.imanagerpublications.com/Article.aspx?ArticleId=3697