Paper 28: Turbulent Heat Transfer to Air in the Vicinity of the Entry of an Internally Heated Annulus

Abstract

A new theoretical analysis has been made of turbulent heat transfer in the region of simultaneously developing hydrodynamic and thermal boundary layers in annular flow. A boundary layer-potential stream model has been used to describe the flow, heat transfer being predicted through the use of a modified Reynolds analogy. Skin friction data for the inner heated wall have been obtained from correlations pertaining to boundary layers on immersed bodies. Experiments have been made with air in the entry region of internally heated annuli with radius ratios 2·1 and 4·0. Satisfactory agreement between theory and experiment has been achieved.

A Review of Forced Convective Heat Transfer in Stationary and Rotating Annuli

“…(1) is also valid for turbulent flow in a stationary annulus and much theoretical and experimental work exists on this case of annulus flow. For the concentric annulus, these can be broadly divided into: (a) fully hydrodynamically and thermally developed flow (7), (b) fully developed hydrodynamic flow with developing thermal flow (7,18,19) and (c) simultaneously developing thermal and hydrodynamic flow (20,21). These cases, for axisymmetric heating, along with others reporting on the effect of asymmetric heating and eccentricity considerations, are reviewed below.…”

Resistor-Network Formulation of Multitemperature Forced-Convection Problems

“…Note that 12 Nu and 21 Nu are not equal due to the difference between the respective areas; 12 Nu / 21 Nu =φ=0.5.…”

“…The baseline CFD solutions were validated against the experimental results of Roberts and Barrow [12] for simultaneously-developing flow of air (Pr=0.7) at Re=55000 in an annulus with φ=0.476, while the inner wall was heated with a uniform heat flux and the outer wall was insulated. As shown in Figure 9, the present numerical solution is in better agreement with the measurements of Roberts and Barrow than the results of an earlier numerical study by Malik [13].…”

“…Away from the inlet (x>5D h ) the present numerical results are less than 10% higher than the experimental data. Unfortunately, the turbulence intensity at the inlet and the uncertainty in the measurements of the wall Nusselt number are not reported by Roberts and Barrow [12]. It is stated that the flow is ensured to be fully turbulent by the use of tripping devices at the annulus entrance [12], but the inlet turbulence was not quantified, merely reported to be "small."…”

“…Unfortunately, the turbulence intensity at the inlet and the uncertainty in the measurements of the wall Nusselt number are not reported by Roberts and Barrow [12]. It is stated that the flow is ensured to be fully turbulent by the use of tripping devices at the annulus entrance [12], but the inlet turbulence was not quantified, merely reported to be "small." In reference [13] an inlet turbulence intensity of 0.02% has been used.…”