APPROXIMATE ANALYTICAL SOLUTIONS OF THIN FILM FLOW OF A FOURTH GRADE FLUID ON AN INCLINED PLANE

In this paper, the steady uniform and unidirectional thin film flow of an incompressible fourth grade fluid on a plane inclined at an angle α ≠ 0 to the horizontal has been taken into consideration utilizing three methods, that is, Collocation Method (CM), Galerkin Method (GM), and Least Square Method (LSM). The results generated from CM, GM and LSM are compared employing a numerical method (NUM) for validation. The approximate results of LSM in compare to CM and GM, for greater regions of dimensionless non-Newtonian parameter B and for all possible boundary conditions were found to be in acceptable agreement with numerical solutions. It was observed that increasing the non-Newtonian parameter B for the boundary condition U’(1) > 0 caused velocity profiles to increase and for the boundary condition U’(1) = 0 caused velocity profiles to decrease.

کلیدواژه ها:

Fourth grade fluid ، Inclined plane ، Collocation Method (CM) ، Galerkin Method (GM) ، Least Square Method (LSM