Friction Factor and Nusselt Number Correlations for Laminar Convection of Liquid in Helical Tubes with Variable Properties

Abstract

Helical tubes are widely used in various industries with the advantages of compact structure, good thermal expansion and heat transfer performances. Characteristics of convection in helical tubes are more complicated than that in straight tubes due to the centrifugal forces. In the literature, (μ_w/μ_b)n is used to consider the property variation effects of liquid on laminar convection in straight tubes. However, investigations of property variation effects on laminar convection in helical tubes are few in the literature. In the current investigation, forced laminar convection with different kinds of liquid in helical tubes are simulated. Property variation effects on friction factor in helical tubes (ψ_f,hel) are compared with the property variation effects in straight tubes (ψ_f,str). Based on order magnitude analysis, the property variation effect ratio (ψ_f,hel/ψ_f,str)between convection in helical tubes and convection in straight tube is related to the Nusselt number ratio (Nu_hel,c/Nu_str,c) with constant properties. Then, the correlation form for friction factor is obtained and coefficients are determined by regression analysis of numerical results. Based on the friction factor correlation, the Nusselt number correlation is obtained. The new friction factor and Nusselt number correlations show good prediction of numerical results and can be used for different kinds of fluid.