Energy transfer by turbulent dissipation in glacial conduits

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.