Flow and Heat Transfer in Convectively Cooled Underground Electric Cable Systems: Part 2—Temperature Distributions and Heat Transfer Correlations

Abstract

Temperature distributions and heat transfer correlations have been obtained experimentally for a wide range of physical, flow and thermal parameters in three models of oil-cooled underground electric cable systems. The results show that in the laminar range, with the oils used, the thermal boundary layer thickness around the heated cables is only of the order of 2–3 mm over the entire length of the test section. Consequently, the best correlation of the heat transfer results is obtained if the Nusselt number, based on the cable diameter, is plotted against Re·Pr0.4, where the Reynolds number is based on the overall hydraulic diameter of the cross section of the flow. For laminar flows, the oil temperatures in the restricted flow channels between three cables or two cables and the pipe wall are about 11°C higher than corresponding bulk temperatures. As the flow becomes turbulent, the thermal boundary layer tends to vanish and the oil temperature becomes uniform over the entire flow cross section. Laminar Nusselt numbers are independent of the skid wire roughness ratio and the flow Reynolds number, but increase with increasing Rayleigh number and axial distance from the inlet, indicating significant natural convection effect. The range of laminar Nusselt numbers was 5–16. Turbulent Nusselt numbers increase with increasing roughness ratios. The Nusselt numbers at Re = 3000 are 30 and 60 for roughness ratios of 0.0216 and 0.0293, respectively.