Entrance and temperature dependent property effects in the laminar forced convection in straight ducts with uniform wall temperature

The paper reports the results of a parametric investigation on the effects of temperature dependent viscosity and thermal conductivity on forced convection in simultaneously developing laminar flows of liquids in straight ducts of constant cross-sections. Uniform temperature boundary conditions are specified at the duct walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries, namely circular and flat ducts, are considered. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number are presented for different values of the entrance Prandtl number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain an approximate value of the local Nusselt number by separately considering the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity.