Steady and Unsteady flow of non-newtonian fluid in curved pipe with triangular cross-section

A numerical study is presented for steady and unsteady slow flow of a viscous fluid of second order in a region bounded by a right-angled isosceles triangl~. The particular flow considered is the secondary flow generated in the plane of the cross-section by the primary axial flow, under action of the pressure gradient, through a slightly curved pipe of triangular cross-section. Two cases are considered; the first one is the steady case in which it is found that the motion equations, which are describing the fluid motion, are controlled by two parameters namely; Dean number and the nonNewtonian parameter. In the second case it is found that the motion equations are controlled, in addition to the parameters mentioned above, by third parameter namely; the frequency parameter. Solutions, of the first case, are expanded in tenns of [)ean number. While in the second case the solutions are firstly expanded in tenns of Dean number and secondly in terms of the frequency parameter. Perturbations equations are solved by Galerkin method after eliminating the dependency on ti,ne .In both cases, the effect of the parameters mentioned above on the secondary flow and the axial velocity is studied.