New friction factor and Nusselt number equations for turbulent convection of liquids with variable properties in circular tubes

Abstract

Large temperature differences between the wall and bulk fluid in heat exchangers will result in significant property variations in the cross section. Most existing equations use correction factors such as (μw/μb)n or (Prw/Prb)m to take account of property variation effects on heat transfer coefficients and friction factors. The exponents, n or m obtained by regression analysis of experimental data are not consistent in the literature. They are also different for heating and cooling conditions. In the current investigation, velocity and temperature distributions of turbulent convection with variable properties in circular tubes are analyzed using classical turbulent boundary layer theory. The viscosity variation effects on velocity and temperature fields are simplified to the effects on the critical point between the linear and the logarithmic distribution regions. New friction factor and Nusselt number equations for turbulent convection of liquids with variable properties are obtained. The new equations show accurate predictions of experimental data for both heating and cooling conditions and for different kinds of liquids. The new equations show that viscosity variation effects on friction factor decrease with the increasing of Reynolds number, while its effects on Nusselt number almost keep constant with the increasing of Reynolds number.