An Apparent Free Surface Method for Determining the Transient Freezing Around a Buried Pipe in a Semi-Infinite Region

A new quasi-steady analytic solution procedure is introduced for determining the noncircular growth of the freeze/thaw boundary around a buried pipe in a half space for the case where the pipe wall temperature is a slowly varying function of time and the freezing/thawing commences at the surface of the pipe. All previous approximate analytic solutions have been based on the critical assumption that all isotherms including the thaw boundary at each instant were eccentric circles belonging to the bicircular coordinate transformation containing the tube wall and the free surface. It is first shown that this assumption is a poor approximation, except as the asymptotic steady state is reached, and that the curvatures of the upper and lower portions of the thaw boundary will grow at vastly different rates except at very early times. A new solution methodology is proposed based on the concept of a virtual free surface. This solution permits the lower portion of the thaw front (i) to develop at a different rate than the upper region and (ii) to undergo a continuous transition in behavior from the infinite burial depth solution at early times to the asymptotic bicircular steady state solution at large times.