A Solution of the Graetz Problem in Tubes of Arbitrary Cross-Section Shape for Viscoelastic Fluids

The Graetz problem is addressed for the case of steady laminar flow of non-Newtonian fluids obeying the Modified Phan-Thien-Tanner Model (MPTT) in tubes of arbitrary cross-section. The method herein presented models the velocity and temperature fields so that the corresponding non-slip and thermal boundary conditions are met at the walls of the tube for a wide range of different shapes. The main results are the general temperature distribution for different duct geometries that include the triangular and square cases as particular examples. Copyright © 2014 by ASME.