Melting of snow with a diffusion-controlled analytical model

An analytical study is reported of melting of a snow layer in an aqueous solution. A diffusion-controlled analytical model was proposed to the melting under an ideal condition that an aqueous solution was instantaneously filled up by a snow layer at the same temperature as the solution. The analytical results gave a qualitative prediction of the experimental results of the melting of snow layers suddenly immersed in a calcium chloride aqueous solution. The temperature in a melting system decreased rapidly during the melting process. The melting was complete within a few seconds, which denoted a thermodynamic equilibrium. When the initial temperatureT _i and the initial porosity of snow ? _i were the same, the initial concentrationC _mi in the solution strongly affected both the decrease in temperature in the melting system and the melting mass per unit volume of snowM. WhenC _mi andT _i were the same, the maximum melting mass per unit volume of snowM _max was not largely affected by snow particle diameters. A figure was presented for the relationM _max?T _i,C _mi, and ? _i , and also a relationship was presented to easily predict the non-dimensional maximum melting massM _max ^* .