An Investigation into the Effect of Prandtl Number on Heat Transfer in a Liquid Metal Flow in a Round Tube at a Constant Peclet Number

Abstract

The effect of dimensionless operating parameters (Reynolds (Re) and Prandtl (Pr) numbers) on the dimensionless heat-transfer coefficient (Nusselt (Nu) number) is examined in a liquid metal flow in a round tube. The Nu number dependences at Pr \( \ll \) 1 (liquid metals) are often presented as Nu = f (Pe), where Pe = Re Pr is the Peclet number. The simplified dependence for Nu relies very much on the fact that determination of the dependence Nu = f (Re, Pr) from the experiments with liquid metal coolants is a challenging matter since such experiments involve great difficulties. Moreover, the measurement error in in such experiments is 10–20% or higher, which is comparable with the deviation of the Nusselt number under the effect of the Prandtl number. In addition, when making experiments under earthly environment conditions, the effect of natural convection on the experimental results cannot be eliminated. In this work, to study the dependence of the Nusselt number on the Prandtl number, a series of calculations of a liquid metal flow in a round tube at a constant Peclet number was performed using the direct numerical simulation (DNS) technique. The predictions demonstrate an increase in the Nusselt number by approximately 10% as the Prandtl number drops from Pr = 0.025 (mercury) to Pr = 0.005 (liquid sodium) at Pe = 125. The influence of the Pr number on the Nu number decreases (in percentage terms) as the Pe number increases.