Fully developed forced convection of the Phan-Thien-Tanner fluid in ducts with a constant wall temperature
The authors present analytical solutions for the problem of laminar forced convection in pipes and channels, under fully developed constant temperature at the wall, for fluids obeying the simplified Phan-Thien-Tanner (SPTT) model. The fluid properties are taken as constants, and the axial conduction is negligible. The solution for the pipe flow represents the asymptotic behaviour of solutions for the Graetz problem for SPTT fluids, i.e. describes the equilibrium between axial convection and radial conduction of thermal energy with negligible viscous dissipation. The channel problem has also an exact analytical solution which represents the equilibrium between viscous dissipation and radial heat conduction, with negligible axial convection and at constant wall temperature. Results are presented for radial/transverse profile of normalized temperature, and for Nusselt number as a function of relevant non-dimensional Brinkman number and Weissenberg number \(W\). It is found that an increase in fluid elasticity (as measured by \(\sqrt W\)) raises the normalized heat transfer coefficient by at most \(14\%\) due to the increase level of shearing-thinning behaviour. On the other hand, the authors show that the viscous dissipation is responsible for the increase in Nusselt number, which is more pronounced for more elastic fluids.
scientific article; zbMATH DE number 1741819