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The present review is intended to encompass the applications of symmetry based approaches for solving non-Newtonian fluid flow problems in various physical situations. Works which deal with the fundamental science of non-Newtonian fluids that are analyzed using the Lie group method and conditional symmetries are reviewed. We provide the mathematical modelling, the symmetries deduced, and the solutions obtained for all the models considered. This survey includes, as far as possible, all thedoi:10.1155/2017/6847647 fatcat:aejxzn5uuzafdkzof7lymehn7q