The Generalized Lévèque Equation and its application to circular pipe flow

Abstract

This paper focuses on the application of the Generalized Lévèque Equation (GLE) to circular pipe flow with hydrodynamic and thermal developing flow describing the analogy between heat and momentum transfer. As shown theoretically by other authors, this analogy should be applicable to laminar and turbulent developing flow, in which the hydrodynamic exceeds the thermal boundary layer, i.e. for high Prandtl numbers. The question is, whether this fact can be proven experimentally, and above which Prandtl number is this applicable to a hydrodynamic and thermal developing circular pipe flow. Thus, this paper presents results of an experimental investigation on pressure drop and heat transfer for laminar, turbulent and transition flows in a circular pipe to check the applicability of the GLE for a wide range of Prandtl numbers. Experimental data for heat transfer coefficients are compared to heat transfer coefficients calculated from pressure drop data with the GLE. Reynolds numbers range between 500<Re<15000 and Prandtl numbers between 7<Pr<40. The test fluid is a water–glycol mixture with a mass fraction of water of xm=0.477. The results show that the GLE is applicable to hydrodynamic and thermal developing laminar and turbulent flow in a circular pipe for Pr>30. It is also shown that as soon as the hydrodynamic boundary layer thickness is triple the thermal one, the analogy between momentum and heat transfer according to the GLE is suitable for laminar circular pipe flow.