Numerical simulation of the laminar flow and heat transfer of the viscoelastic duct flows with the entrance effects

In this study, the three dimensional flow and heat transfer of viscoelastic fluid has been modeled with the Giesekus constitutive equation. In the most previous research, they focused on the fully developed region of flow which is due to the lack of comprehensive research in this field, the studding of the viscoelastic flow in the developing region seems be essential. The governing equation that should be solved are: mass, momentum and energy conservation with the Giesekus constitutive equation that are descried with the finite difference method and solved by the artificial compressibility method on the staggered grid. It should be noted that, with this constitutive equation, the second normal stress difference is non-zero and therefore the secondary flow in the cross section are formed and will be visible. The dependency of the fluid property to temperature is one of the advantages of this research. Due to the dominant group of the viscoelastic fluid are melt polymers and in this situation, the variation of the temperature is high, therefore this assumption seems be necessary. The results in the fully developed zone are in good agreement with the other reported results.