| Snow is very popular in many cities all over the world. With the development of times, expansion of cities' scale and booming of cities' competence, communications and transportation and in addition cities' life is seriously affected by snow in winter. The railroad and highway are blocked by bulk snow, furthermore, road covered with ice and snow is a very important reason to the traffic accidents in winter. So it is a primary task of many cities to eliminate snow with a safety method thus to relieve people of snow harm.In recent years, snow-melting agent is a favorite method in all snow-eliminating methods over cities because of its simple operating, low prices and excellent snow -melting effects. The principle of snow-melting agent melting snow is that the melting point of snow-melting agent is lower than that of water, so the snow mixed with snow-melting agent is able to melt at lower temperature. NaCl solution is a traditional snow-melting agent used by people in previously times, however, because NaCl solution after melting snow has brought lots of abuse to the environment and ecology, it is gradually replaced by other more friendly environmental and more safety new snow-melting agent.The "amicable to environment and nutritious to crops" snow-melting agent is a kind of new environmental products. Its main ingredient is KCl-MgCl2-Lux series . It is tested that when the proportion of KCl:MgCl2:Lux is 40:50:10, 20:70:10 and 10:80:10, the ability of melting snow in the series achieves 90% of NaCl in the same conditions, it contains K,Ca,Mg,N and so on nutrition which the crops need to grow. The first is eliminated because of its expensive costs, the third is more harmful to crops thus it is also eliminated; the second is a more ideal environmental products via a series of toxicity tests.In order to evaluate the ability and velocity of melting snow in snow-melting agent, this research discusses dynamics model in snow melting process on the basis of Shaun Sellar's article " Theory of water transport in melting snow with a moving surface".Colbeck's theory treats the snow cover as a porous medium consisting of three phases: ice crystals, water, and air. The ice crystals form a rigid porous matrix through which the water and air can flow. At time t = 0 , heat (q(t)) is supplied to the surface z = H, resulting in surface melting of the ice crystals. The meltwater percolates downwards due to gravity and capillary effects, producing a percolation or wetting front zp(t), which separates the wet snow region from the dry snow region. Additionally, due to the surface melting, the snow surface itself will move downwards as a melt front zm(t). The water volume flux( uw) and effective saturation (S*) as functions of depth and time mirror the transportation of water. The governing equations for this problem are developed. They are based on Darcy's law and the mass balance of the water phase, supplemented with appropriate boundary conditions.The water mass balance and Darcy's law in conjunction with the constitutive relation yield an evolution equation for the effective saturation S*, the nonlinear Fokker-Plank equationThis equation is uncoupled from the equations governing the other phases. Thus to determine the effective water saturation S* in the bulk region, it is only necessary to solve the Fokker-Plank equation (1) . The corresponding water flux uw is then determined by Darcy's law and the constitutive relations.Equation (1) for the bulk region must be supplemented by boundary conditions. These conditions will be obtained from the balance laws by treating the boundaries as singular surfaces, across which relevant quantities may be discontinuous.The boundary conditions of equation (1) is:In this process, the melt front velocity zm is:The equations governing the evolution of the singular percolation surface is developed from two cases:1) Discontinuous saturation2) Continuous saturationAlthough the interface position zm(t) can be explicitly determined through once the heating is specified, the proble...
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