Simulation of the process of water freezing in a round pipe

The problem of freezing of pure water in a round pipe is treated with due regard for convection under asymmetric thermal boundary conditions in the absence of motion along the pipe. The problem is solved numerically using the control volume approach, SIMPLER algorithm, and the enthalpy method. Results are obtained for three Grashof ($\mathrm{Gr}$) and six Biot ($\mathrm{Bi}$) numbers: $\mathrm{Gr}=1.55\times10^6$, $\mathrm{Bi}=0.305$ $(0\le\varphi<\pi)$, $\mathrm{Bi}=0.044$ $(\pi\le\varphi<2\pi)$; $\mathrm{Gr}=1.24\times10^7$, $\mathrm{Bi}=0.610$ $(0\le\varphi<\pi)$, $\mathrm{Bi}=0.087$ $(\pi\le\varphi<2\pi)$; $\mathrm{Gr}=9.89\times10^7$, $\mathrm{Bi}=1.220$ $(0\le\varphi<\pi)$, $\mathrm{Bi}=0.174$ $(\pi\le\varphi<2\pi)$. The correctness of calculation of the problem disregarding free-convection flows is analyzed.