The influence of Prandtl number on the thermohydraulic behaviour of laminar mixed convective flow through horizontal tubes heated at a constant heat flux

Abstract

The influence of Prandtl number on laminar mixed convective flow through a smooth, horizontal tube was investigated using ANSYS Fluent 22 to improve the understanding of the interaction between buoyancy and fluid viscosity on the thermohydraulic behaviour. Different propylene glycol concentrations (0%, 30%, 50%, 70%, 80%, and 90%) were considered for heat fluxes of 200-10 000 W/m2 and Reynolds numbers of 250-2000. The tube had an inner diameter of 5.1 mm and a length of 10 m. It was found that as the Prandtl number increased, the buoyancy force increased up to 74% for the 90% propylene glycol concentration compared to pure water, resulting in higher vorticity and circulation strength. However, this was confined near the tube wall and when quantifying the buoyancy effects using the secondary flow strength, viscosity-induced damping was found to decrease buoyancy effects by up to 95%. Conversely, for low-Prandtl number mixtures such as 0% and 30% propylene glycol concentrations, increased secondary flow thinned the thermal boundary layer and enhanced heat transfer by 40% and 28%, respectively, compared to forced convective flow, despite a lower buoyancy force. Furthermore, secondary flow strength was quantified and grouped into three distinct regions: (1) developing region, (2) suppression region, and (3) enhancement region. When viscous effects dominated at higher Prandtl numbers (70% and 90%), the velocity profile became skewed above the tube's centre, and the merging position of the hydrodynamic boundary layers shifted upwards, which is the opposite of the trend seen in fluids with lower Prandtl number (0%, and 30%). Furthermore, as the Prandtl number increased, the hydrodynamic boundary layers along the axis merge closer to the tube inlet, while the thermal boundary layers merge further downstream.

HIGHLIGHTS • An increase in Prandtl number increased the buoyancy force but decreased buoyancy effects due to higher viscosities. • The vorticity magnitude increased with Prandtl number but was confined near the tube wall. • At high Prandtl numbers, the mixed convective velocity profile was skewed upward, shifting the peak velocity above the tube centre, while the opposite occurred at low Prandtl numbers. • The mixed convective temperature profile was skewed downward, causing the upper thermal boundary layer thickness to be greater than the bottom. • The hydrodynamic boundary layer merged earlier along the tube for increasing Prandtl number.