ON THE STEADY FLOW OF THIRD GRADE FLUIDS IN A POROUS HALF SPACE

The steady unidirectional flow induced by a uniformly moving plane surface adjacent to a porous half-space filled by a viscoelastic third grade fluid has attracted considerable attention in recent years. The present paper revisits this topic and shows that the governing equation admits a first integral. As a consequence the corresponding boundary value problem can be reduced to an initial value problem. This finding simplifies the general approach substantially. For special values of the involved parameters several exact solutions are given in terms of elementary functions. These solutions also suggest an improved choice of the linear operator and of the initial guess required for an efficient application of the homotopy methods. A scaling transformation of the transverse coordinate leads to a further reduction of the complexity of the problem.