A brief survey of secondary flows of complex fluids in straight tubes is given including recent work by Professor Rajagopal pointing at striking analogies with transversal deformations associated with the simple shearing of nonlinear solid materials. The importance and implications of secondary flows of viscoelastic fluids in heat transfer enhancement in tubes are explored. Steady and unsteady pressure gradient driven secondary flows of constitutively nonlinear simple fluids in straight pipes of non-circular shape are discussed. Specifically the steady secondary flow of Phan-Thien-Tanner fluids in pipes of unconventional contours together with work which explores for the first time the structure of the secondary flow field in the pulsating flow in straight tubes of arbitrary cross-sections is summarized. Arbitrary conduit contours are obtained through a novel domain mapping/perturbation technique. The secondary flow structure in the steady flow of Phan-Thien-Tanner fluids in several unconvential cross-sections is described. In the case of the pulsating pressure gradient driven flows time averaged, mean secondary flow streamline contours are presented for triangular, square and hexagonal pipes. Heat transfer enhancement in the flow of complex fluids in tubes of any shape is primarily due to the existence and strength of the secondary flows. Heat transfer enhancement increases as the strength of secondary flows increases without any significant additional energy input to drive the secondary flows. Results of related work by the author and colleagues in the case of Phan-Thien-Tanner fluids driven by a steady pressure gradient in straight tubes of arbitrary shape will be briefly discussed.
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