Comparison of Carslaw and Jaeger method and finite element method to estimate temperature of soil in Antarctica

초록

We examined the Carslaw and Jaeger (C-J) method to compute the temperature profile of inner soil in a region of Antarctica. The solution of the C-J method is expressed as an integral of the convolution of surface temperature and a transfer function, and can be used to determine the thermal diffusivity of soil. The obtained solution, however, is only an approximation of the integral because the field measured temperature data used as the surface temperature are usually obtained at a specific time interval, causing some error in the C-J method This error is identified in the present study through mathematical examples which graphically compare the results obtained from finite element analysis and the C-J method The error increases as the surface temperature changes abruptly or with a larger thermal diffusivity. As the time interval increases, the error tends to increase for the C-J method, implying that the time interval needs to be small enough to ensure that the analysis is accurate. This study, therefore, recommends a finite element method to solve heat conduction problems related to estimating the temperature of inner soil, because this method is not dependent on the measurement time interval.

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