Heat transfer regimes in fully developed plane-channel flows

Abstract

This paper investigates heat transfer regimes in fully developed plane channel flows without considering the buoyancy effect. Analyzing the governing thermal energy equation, aided by direct numerical simulation (DNS) data, six heat transfer regimes are identified including (i) laminar flow and laminar heat transfer (LamF-LamH), (ii) transitional flow and laminar-like heat transfer (TraF-LamH), (iii) transitional flow and transitional heat transfer (TraF-TraH), (iv) turbulent flow but laminar-like heat transfer (TurF-LamH), (v) turbulent flow and transitional heat transfer (TurF-TraH), and (vi) turbulent flow and turbulent heat transfer (TurF-TurH). One key result is the clarification of a TurF-LamH regime which exists only for low Prandtl number fluid (Pr≪1). A critical non-dimensional number is determined as ReτPr1/2≲50 where Reτ is the Reynolds number defined by the channel half-height δ and the frictional velocity uτ. In the TurF-LamH regime, the simplified thermal energy equation yields a prediction of Nusselt number as Nu≈6.0. The clarification of the TurF-LamH regime provides valuable insight into the understanding of the Nusselt number data for liquid metals, which have very low Prandtl number. Another major finding is that, in the TurF-TurH regime, the Kader-Yaglom-style equation is shown to be better than the traditional power law correlations at predicting Nusselt number, for either low or high Prandtl numbers. No separate correlations are needed for the prediction of Nusselt number at low Prandtl numbers and high Prandtl numbers. Another advantage of the Kader-Yaglom-style equation is that the equation can be theoretically connected to the log-law for the mean velocity and the mean temperature. More importantly, in the TurF-TurH regime the prediction of Kader-Yaglom-style equation can be reliably extended to ultra high Reynolds numbers, for either low or high Prandtl numbers.