Transient Heat Conduction Analysis on Subsea Single-Layer Pipes Under Internal Heat Sources With the Integral Transform Method

The pipeline for marine transportation of high-temperature oil and gas is affected by the convective heat transfer of the fluid inside the pipe and the internal heat source. With the rise of the pipe body temperature, the heat will also transfer from the pipe wall surface to the external low-temperature seawater, to form a temperature gradient in the pipeline radial and axial direction. The 2D transient heat transfer in an axisymmetric single-layer pipe with non-homogeneous boundary conditions and an internal heat source was analyzed with the integral transform technique. First, the 2D transient temperature was expressed as a combination of axisymmetric 1D steady-state temperature with a heat source, a filtered 2D steady-state temperature, and a filtered homogeneous 2D transient temperature, and was non-dimensionalized. Next, based on the method of separating variables to determine the integral transform pairs in radial and axial directions, the heat conduction control equations and boundary conditions plus initial conditions were subjected to the integral transform process to separate the time and space dependence of transient temperatures, and the 1st-order linear ordinary differential equations with respect to time were obtained. Finally, the theoretical solution of the 2D transient temperature distribution was obtained through the inverse transformation of the integral transform pair, and the 2D transient temperature distribution was verified through comparison of the results with the steady-state temperature distribution. On this basis, the effects of different combinations of inner and outer Biot numbers and different heat source strengths G on the temperature distributions of pipes were investigated. The results show that, the temperature gradients and temperature values in the spatial and temporal dimensions of the pipe are larger for the same combination of internal and external Biot numbers and for the high intensity of the heat source. There are differences in the temperature gradient and overall temperature distribution in the spatial and temporal dimensions when the intensity of the heat source is the same but the combinations of the internal and external Biot numbers are different. In the radial direction and the temporal dimension, the temperature distribution curves of different combinations of inner and outer Biot numbers have an intersection point where the temperature gradient and the relative magnitude of the temperature values change, but this phenomenon does not occur in the axial direction.