Mathematics Today Vol.31 (June & December 2015) 39-53 ISSN 0976-3228 Group Theoretic Analysis of Quasi Three Dimensional Non-Newtonian Sutterby fluids Nita Jain 1 and M.G. Timol 2 1 Department of Humanities & sciences , Thakur College of Engineering and Technology, Mumbai -101, Maharashtra, INDIA. Email: nita.jain109@gmail.com 2 Department of Mathematics, Veer Narmad South Gujarat University, Surat-7, Gujarat, INDIA Email: mgtimol@gmail.com (Acceptance Date: December 19, 2015) Abstract The deductive group-theoretic method is employed to derive the similarity transformations of steady, laminar, incompressible quasi three dimensional boundary layer flow governing non-Newtonian Sutterby fluid. The purpose of similarity transformations is to transform the governing highly non-linear partial differential equations along with auxiliary conditions to a similarity variable η, functions of η and their derivatives. The main stream flow conditions are then derived for which the transformed equations reduce to ordinary differential equations. Effects of all emerging physical parameters are demonstrated with the help of graphs for both velocity and temperature distribution. The numerical solution of the considered Sutterby fluid is also discussed. Keywords Deductive group–theoretic method, quasi three dimensional flow, Sutterby fluid, Similarity equations, Similarity solution. AMS Classification: 54H15, 65L05, 76A05, 76M55 1. Introduction Most of the fluids in industry unable to meet commonly accepted assumption of a linear relationship between the stress and the rate of strain and thus are characterized as non- Newtonian fluids. Due to complex rehology of biological fluids, different non-Newtonian fluids have been investigated and become more and more important due to their industrial applications. Polymer melts, certain oils and greases, clay coating and other suspensions, drilling mud are few examples of non-Newtonian fluids. Academic curiosity and practical applications have generated considerable interest in finding the solutions of differential