Energy Transfer by Turbulent Dissipation in Glacial Conduits

Water flow within and beneath glaciers and ice sheets influences ice dynamics and is relevant for practical applications such as modeling outburst floods from mountain glaciers. The most general models for glacial hydrologic conduits include an energy equation, wherein a heat transfer coefficient controls the rate at which heat generated by mechanical energy dissipation is transferred to conduit walls, producing melt. Previous models employ heat transfer coefficients derived for engineering heat transfer problems, where heat is transferred between the walls of a conduit and a flowing fluid that enters the conduit at a temperature different from the wall temperature. These heat transfer coefficients may not be appropriate for glacial hydrologic conduits in temperate ice, where the water and conduit walls (ice) are at almost the same temperature. We revisit the energy transport equations that provide a basis for the derivation of heat transfer coefficients and highlight the distinctions between the heated walls and dissipated energy heat transfer cases. We present computational results for both cases across a wide range of Reynolds numbers in circular conduit and sheet geometries. We show that the heat transfer coefficients for transfer of heat generated by mechanical energy dissipation to circular conduit walls are smaller than calculated using the Dittus‐Boelter correlation by approximately a factor of 2. However, heat transfer coefficients are higher for flow through a wide sheet at R e = 1 0 6 , highlighting the influence of noncircular geometries on heat transfer in englacial conduits and subglacial drainage systems.