A fluid with viscosity which depends on temperature and concentration is placed between two infinite parallel plates moving relative to each other with constant velocity. On the basis of certain simplifying assumptions, the fluid equations of continuity, momentum, energy and concentration are obtained and solved analytically. A non-linear integro-differential equation is derived which governs the fluid velocity component parallel to the walls and a parameter perturbation technique is suggested and utilized for its solution. Using the Padé approximants technique, the series summation and improvement is performed. The effect of viscosity variation due to variation in temperature and concentration on the fluid flow is discussed quantitatively.