One of the most successful, fascinating and useful applications of mathematics has been in the study of motions of fluids (gases and liquids).The perfect or ideal fluids are characterized by the assumptions that for then the stress tensor is a linear function of the rate of strain tensor and the stress vector on a plane surface in contact with a fluid is normal to the surface. About seven decades ago phenomena were observed which could not be explained on the assumptions of this theory. When the assumptions of this theory were examined, it was considered feasible to relax the assumption of linearity between stress and rate of strain tensors. More general nonlinear relations between stress and rate of strain tensors were postulated. It immediately led to the development of theory of non-Newtonian fluids flows. #To extend the results of the flow and heat transfer behavior of Newtonian fluids to Non-Newtonian Reiner-Rivlin fluid. #To study the flow and heat transfer behaviour of Reiner-Rivlin fluid as it occur in industry under conditions, which arise there. The solution of each of the problems given in the book is an intellectual challenge.