Flow of non-Newtonian fluid in a helical pipe with an elliptical cross-section

A theoretical analysis has been carried out of the flow of an incompressible non-Newtonian viscous fluid in a helical pipe; this type of pipes is characterized by non-zero pitch. The motion equations are derived, and it is shown that they are depend on Dean number L, the non-Newtonian parameter beta and the parameter lambda/Re where lambda is the ratio of the torsion tau to the curvature kappa of the pipe axis and Re is Reynolds number. The solutions of motion equations are expanded in term of Dean number. Analytical solutions of perturbation equations are derived for small values of Reynolds number by using Galerkin variation method. The effect of the parameters mentioned above are studied upon the secondary flow and the axial velocity. Also we improve and recover many subcases, which have been studied before, such as, the flow of Newtonian fluid in a helical pipe with elliptical cross-section, the flow of Newtonian and non-Newtonian fluid in a curved pipe with elliptical cross-section and the flow in a straight pipe.