On the flow of a class of viscoinelastic–viscoplastic fluids in tubes of non-circular contour

A unified analysis based on natural coordinates is presented for a class of viscoinelastic–viscoplastic fluids for the case of nearly viscometric flows driven by steady pressure gradients in straight ducts of arbitrary cross-sectional contour. General relationships which give phenomenological insight and which yield qualitative information, and some quantitative information as well, concerning the velocity and shear-stress fields of the family of fluids considered in this paper are derived for the case of flow in tubes of non-circular contour, and several applications are discussed.