Mathematical solution of steady-state temperature field of circular frozen wall by single-circle-piped freezing

Ground temperature distribution is one of the fundamental problems in the theory of artificial ground freezing. For the most widely applied freezing scheme, single-circle-piped freezing, there is only one analytical solution up to now, for the situation that the core is totally frozen. This paper gives a mathematical model to the steady-state temperature field of circular frozen wall by single-circle-piped freezing with unfrozen core. Then, the solutions are theoretical derived with some hypothesis, using conformal mapping and boundary separation method, as well, the same methods has been verified by the specific single-row-piped solution - Bakholdin's solution. After that, comparison between the analytical solutions and the numerical analysis is in good consistency. In addition, the methods to calculate the thickness and the average temperature of circular frozen wall are present.