Thermal Model and Design in Shaft Freezing

The equations of heat conduction are numerically solved for two kinds of artificial freezing- mechanical freezing and liquid nitrogen freezing. A two dimensional finite difference model simulating the freezing field is developed. The procedure introduces a way to simulate the effect of latent heat released when water transforms from liquid to solid. The procedure also produces a way to calculate the harmonic mean of heat conductivity used when dealing with heterogeneous material. The theoretically derived temperature distributions in frozen soil are given and compared with measured data. An analysis made on the thermal design in shaft freezing. The average temperature of frozen soil is calculated by using numerical integration. The regularity of development of frozen soil radius is revealed and given in an appropriate mathematical model.