Thermal modeling of ice cores and boreholes via the finite element technique

An axisymmetric finite element computer program was developed to calculate heat transfer in cylindrical (r-z) geometry. The technique is applicable to steady-state and time-dependent problems and can handle convective, temperature-prescribed and heat-flux-prescribed boundary conditions. It employs the heat capacity method through the Dirac delta function to represent latent heat effect during freezing or thawing and computes movement of the phase front. A number of tests with different materials and boundary conditions were conducted to validate this code against heat transfer situations with and without phase change. The results showed good agreement with exact analytical and numerical solutions. The model was then applied to determine temperature profiles in ice cores. Subsequent investigations were made to determine the rate of freezing in a borehole and the movement of the freeze front with time. Furthermore, results were generated for predicting complete freeze-up of the ice test well maintained by the Polar Ice Coring Office for a number of boundary conditions.