Analytical formulation of temperature field of single freezing pipe with constant outer surface temperature

TLDR: In this paper, the phase transition of thermal conduction in the outer wall temperature constant condition for a single freezing pipe, frozen field and non-frozen field were separated by the freezing frontal edge, the temperature field was analyzed using the method of variable substitution.

Abstract: Aiming at the phase transition of thermal conduction in the outer wall temperature constant condition for a single freezing pipe,frozen field and non-frozen field were separated by the freezing frontal edge,the temperature field was analyzed using the method of variable substitution.The results was obtained,such as:the relation between the radius of freezing frontal edge and freezing time follows the square root equation,the temperature distribution of frozen field and non-frozen field and the corresponding formula for calculating the dimensionless temperature are expressed by an exponential integral function.For the easiness of numerical calculation,the higher precision and lower derivative polynomial expression of exponential integral function were given.And the analytical formula about the heat flux of freezing pipe’s wall was obtained.The distribution laws of temperature field for a single freezing pipe in the outer wall temperature constant condition were explained by example in the end.The result shows that the temperature field for a single freezing pipe is similar to a logarithmic function,its curvatures decrease with the increment of the freezing days,and unfrozen surface area is longer about 4 times than the radius of the freezing frontal edge.