e. Relative Humidity

a. Wind

b. Temperature

c. Precipitation

d. Diameter

c e lw sfvk

c elwsfv k

c elwsfv k

c e lw sfvk

c e lw sfvk

104

103

102

101

100

1

10

2

10

3

10

Cooling

Heating

Cooling

Heating

Cooling

Heating

Cooling

Heating

Cooling

Heating

Prandtl number *Pr *of the flow. In free convection,

where there is no external velocity scale, *Nu*L is

In the heat-balance model, the latent heat of

given in terms of the Rayleigh number *Ra*L, which

fusion given off by the fraction of precipitation

is the product of the Grashof and Prandtl numbers,

that freezes to the wire warms all the impinging

precipitation to 0C. Assuming the raindrops are

nondimensional parameters have been determined

at the air temperature *T*, *Q*w is the cooling flux

empirically for different cylinder roughnesses and

necessary to raise their temperature to 0C.

orientations.

To decide which empirical formula to use in

forced convection, we need to know the typical

One of the primary processes that cools the

range of Reynolds numbers for freezing rain

wireice accretion is the loss of heat from the cold

accreting to a wire. This geometry is idealized as

air blowing past the structure. When there is no

flow around an infinite cylinder with the wireice

wind, heat is removed at a slower rate by free

diameter (or icicle diameter) as the length scale.

convection controlled by the temperature differ-

The smallest diameter of interest is 0.5 cm for a

ence between the wireice accretion and the air.

new icicle, and the diameter of a moderately large

The Nusselt number *Nu*L is used to define the rate

wireice accretion is about 12 cm. Typical wind

of heat transfer in both forced and free convection

speeds during freezing rain range from 0.5 to 10

m/s, and the kinematic viscosity of air is νa = 0.132

in external flow:

cm2/s at 0C. Using these values, the Reynolds

number range of interest is 190 < *Re*D < 9.1 104,

(5)

where *D *is the diameter of either the icicle or the

where *h *is the heat transfer coefficient, *L *is the

wireice accretion.

appropriate length scale, and *k*a is the thermal

Achenbach (1977) determined the total Nusselt

conductivity of the air. In forced convection, *Nu*L

number for rough cylinders in subcritical flow, for

is given in terms of the Reynolds number *Re*L and

7