Entrance and Temperature Dependent Viscosity Effects on Laminar Forced Convection in Straight Ducts With Uniform Wall Heat Flux

In this paper a parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously, i.e., hydro-dynamically and thermally, developing laminar flows of liquids in straight ducts of constant cross sections. Uniform heat flux boundary conditions are imposed on the heated walls of the ducts. Different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (rectangular and trapezoidal) ducts. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Pearson and Prandtl numbers. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions. Correlations are also provided for the local Nusselt number and the apparent Fanning friction factor in simultaneously developing flows in ducts of different cross sections.