Numerical Method For the Two-dimensional Freezing Problem Around a Horizontal Cylinder Encompassing a Density Inversion Point

Abstract

A numerical method for the two-dimensional freezing problem around a horizontal cylinder involving a maximum density point was presented. This problem offers a complex one involving the natural convection flow around the freezing front and the heat conduction inside it, and no exact analysis of it has been performed so far. The present numerical method utilizes the so-called boundary fixing method in which both the boundaries of body and freezing front are immobilized and it is applicable to general multi-dimensional moving boundary problems. Example calculations are made for steady freezing front shape, temperature distribution in solid phase, and also isotherms, streamlines, and Nusselt number distribution around the cylinder