Forced Convection in Non-Circular Tubes with Non-Linear Viscoelastic Fluids Including Viscous Dissipation

The steady, laminar, non-isothermal fully developed flow of a class of non-linear viscoelastic fluids in tubes of arbitrary contour is analyzed under constant wall heat flux including viscous dissipation. Equations of motion and energy are solved analytically and velocity and temperature fields are determined through an asymptotic approach in terms of the Weissenberg number coupled with the shape factor method a one-to-one and continuous mapping taking the circular boundary into a large, continuous spectrum of non-circular tube contours. The analysis developed is general and covers all members of the family of constitutive models considered as well as a large array of non-circular tubes. The case of tubes with circular and triangular contours are discussed as specific examples for various numerical combinations of the Weissenberg, Reynolds, Péclet and Brinkman numbers and the Nusselt number variation is computed for fluids abiding by the Modified Phan-Thien-Tanner (MPTT) and Simplified Phan-Thien-Tanner (SPTT) models. Newtonian velocity and temperature fields in a large spectrum of non-circular tubes are recovered at the lowest order of the asymptotic analysis. Through a matching procedure we also extend the computation of the Nusselt number in round tubes to any desired value of the Weissenberg number. © 2019 Elsevier Masson SAS