Heat transfer in steady viscoelastic flow in pipes of complex shapes

An analysis of heat transfer in pipe-flow is presented for the cases in which viscoelastic properties of the fluid induce secondary flows in no-circular tubes, thus enhancing the tranversal transport capacity of the flow. It is used the Phan-Thien-Tanner (PTT) viscoelastic model, and the flow is assumed steady and laminar. The velocity field is first determined through a technique previously developed by the authors, and the energy equation is solved afterward for the temperature field for conditions of constant wall temperature and constant longitudinal temperature gradient. Perturbation analysis is applied around the relaxation time as parameter, where from all orders of velocity and temperature are analytically found up to third order. Plots of results for triangular and square tubes are presented, followed by a discussion of the relevant findings related to interactions among the main variables generated by viscoelastic fluid behaviour.