Melting of a Vertical Ice Wall by Free Convection into Fresh Water

A steady-state two-dimensional finite difference analysis is presented for the heat and momentum transfer resulting when the leading portion of a semi-infinite vertical ice sheet at 0°C melts into fresh water by natural convection. Fluid properties are assumed to be constant and are evaluated beyond the edges of the boundary layers with the exception of fluid density which varies with the local temperature. Results of the analysis are presented for free stream temperatures from 0 to 24.0°C. They include streamlines, velocity profiles, melt velocities, and average Nusselt numbers for the leading 0.7632 m portion of a semi-infinite ice sheet. Overall, the results show three distinct flow regimes: steady upward flow for T_∞ ≤ 4.50°C, steady downward flow for T_∞ ≥ 6.0°C and steady dual or bi-directional flow for 5.70 ≤ T_∞ ≤ 6.0°C. In the range 4.50°C < T_∞ < 5.70°C the solution failed to converge and since the method is capable of accounting for local recirculations, it is suggested that this flow regime may be transitory in nature.