A Supplementary Note on the Problem of Ice Formation

Abstract

In this paper, the author deals theoretically with the problem of ice formation, in view of extending his previous study, and the formula which approximately represents the speed of the growth of ice layer is derived as
where ε₀: thickness of ice layer,
t: time measured from the beginning of ice formation,
U( ): air temperature, at a point sufficiently far from the ice surface,
k: coefficient of heat condution of ice, ρi; density of ice,
L: melting heat of ice, α: heat transfer coefficient.
Although this formula is derived as an approximate solution of the differential equation of heat conduction in an ice layer, it is also made clear that the accuracy of this approximation is very satisfactory. The good agreement between this theoretical result and the experimental data recently obtained by K. Neumann verifies also the validity of this formula.
In the latter part of this paper, the relation between α and wind velocity is discussed and it is shown that the transfer from the surface of ice into the air can be reasonably explained, provided that we take the existence of a turbulent boundary layer near the surface into consideration.