Numerical simulation of the Graetz problem in ducts with viscoelastic FENE-P fluids

• A numerical study of fully developed Nusselt number in circular, rectangular, square and triangular section ducts.
• Fluid rheology model used is FENE-P type.
• New values for Nusselt number for FENE-P viscoelastic fluids are obtained.
• A parametric study of the influence of elasticity and extensibility parameter is conducted.
• Axisymmetric case contrasted against analytical solutions.

A numerical investigation of heat transfer with viscoelastic fluid based on the FENE-P model in straight pipes of circular and some non-circular cross-sections is carried out to analyze the influence of the rheological parameters on heat transfer enhancement with negligible axial heat conduction and viscous dissipation by assuming temperature-independent model parameters. Numerical simulation is conducted using the finite element based software Polyflow and results are compared with analytical and semi-analytical solutions available in the literature for the 2D axisymmetric pipes. The analysis considers a constant wall heat flux boundary condition and shows that an increase in fluid elasticity raised the normalized heat transfer coefficient due to the increased level of shear-thinning behavior. But increasing the extensibility parameter L2 leads to a decrease in Nusselt number. Nusselt number distribution in the entrance region of tubes of equilateral triangular, square and rectangular cross-sections is reported for the first time for non-linear viscoelastic fluids of the FENE-P type.