Generalized analytical solution to steady-state temperature field of double-circle-piped freezing

Temperature field distribution is the basis theory of artificial ground freezing, which is essential for mastering the temperature development of frozen soil wall. In practice, the double-circle-piped arrangements of freezing pipes are mostly applied. Concerning to all analytical solutions to the steady-state temperature field, there is no result of the double-circle-piped freezing. This paper establishes a model for the steady-state temperature field of double-circle-piped freezing. Then, according to conformal mapping and the boundary separation method, this model of the double-row-piped freezing is transformed into two special single-row-piped freezing models. Thereby, the solution to double-circle-piped freezing model is obtained by solving the single-row-piped freezing problem. And the analytical results for some typical double-circle-piped problems show good consistent with the numerical thermal results. Furthermore, the applications for calculating the thickness and average temperature under double-circle-piped condition are derived.