The problem of three-dimensional thermal instability over a horizontal ice cylinder which occurs in a minimum heat transfer region has been solved. A fully numerical method was applied to the governing equations in the transverse and longitudinal planes, which were simplified to two-dimensional. The perturbation method was employed to obtain the wave number. The appearance of a convexo-concave melting front, which was predicted by a previous experiment, was clearly explained by the convection pattern along the cylinder. The transient process of onset of stable vortices around a cylinder was clarified by streamlines and isotherms. Comparing the wave numbers obtained by the numerical and the small perturbation methods, it is concluded that the perturbation method cannot be effectively applied to problems involving density inversion.

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