New friction factor and Nusselt number equations for laminar forced convection of liquid with variable properties

Abstract

Friction factor and heat transfer coefficient of liquid flow with variable properties can significantly differ from that with constant properties. Existing equations obtained by regression analysis of experimental data use correction factors to account for variable property effect. They are limited to specific kind of fluid and low or medium temperature differences. The correction factors of the equations for heating and cooling conditions are different. New explicit friction factor and Nusselt number equations for laminar forced convection of liquid with variable properties are derived with a first order approximation of dynamic viscosity-temperature variation. The new equations are applicable to all kinds of liquids and can be used for large temperature differences. Governing equations of laminar forced convection of water and ethanol are numerically solved using computational fluid dynamics (CFD) method and the results are used to verify the derived equations. The derived equations show good predictions of friction factors and Nusselt numbers for both heating and cooling conditions and show more accurate predictions than the existing equations. A dimensionless number is also introduced based on theoretical analysis to evaluate property variation effects on friction factors and heat transfer coefficients.