Fully developed forced convection of the Phan-Thien–Tanner fluid in ducts with a constant wall temperature

Two problems of laminar-forced convection in pipes and channels, under fully developed conditions, are solved for an imposed constant temperature at the wall, with fluids obeying the simplified Phan-Thien–Tanner (SPTT) model. The fluid properties are taken as constants and axial conduction is negligible. The first case represents the asymptotic behaviour of the Graetz problem for the SPTT fluid, i.e., equilibrium between axial convection and radial conduction of thermal energy with negligible viscous dissipation. The solution is given by an analytical expression but it is only approximate (within 0.3%) as it was obtained with an algebraic method based on successive approximations. The second problem has an exact analytical solution representing the equilibrium between viscous dissipation and radial heat conduction, with negligible axial convection and a constant wall temperature.