Approximate analytical solution for temperature fields in cold regions circular tunnels

According to the practical situation in permafrost regions, the governing differential equations of heat transfer in frozen zone and unfrozen zone are simplified. Then, using dimensionless and perturbative method, the approximate analytical solution for simplified heat transfer equation has been obtained. The research of the freezing process of circular tunnel with initial temperature near 0 °C has been made. Comparing the approximate analytical results with finite element results, it can be seen that the approximate analytical solution is of higher precision and this solution can meet the precision requirement of practical engineering. This solution can be used in both engineering computation and the examination of numerically calculated results.