Geoscience Reference
In-Depth Information
Table 21.1 Empirical relationships between the Nusselt number and
Reynolds number determined for selected shapes from wind tunnel
studies (Data from Monteith and Unsworth, 1990).
Shapes
Range of Reynolds number (Re)
Nusselt number (Nu)
Flat pla tes
Streamline flow Re < 2 × 10 4
Nu = 0.60 Re
0.5
d
Turbulent flow Re > 2 × 10 4
Nu = 0.032 Re
0.8
d
d
Cylinders
1 to 4
Nu = 0.89 Re
0.33
4 to 40
40 to 4 × 10 3
4 × 10 3 to 4 × 10 4
4 × 10 4 to 4 × 10 5
Nu = 0.82 Re
d
0.39
Nu = 0.62 Re
0.47
Nu = 0.17 Re
0.62
Nu = 0.024 Re
0.81
The description of boundary-layer resistance to the transfer of other entities
such as water vapor and carbon dioxide is analogous to that for heat transfer, but
the boundary-layer resistances to such mass transfers are expressed in terms of
the Sherwood number. The Sherwood number is very similar in concept to the
Nusselt number and has also been expressed empirically in terms of Reynolds
number. However, the molecular diffusion coefficients differ for different
exchanged entities and all have a dependency on the temperature, T c , of the air in °C.
The molecular diffusion coefficients are: for momentum,
= 1.33 × 10 -5
(1+0.007 T c ) m 2 s -1 ; for heat, D H = 1.89 × 10 -5 (1+0.007 T c ) m 2 s -1 ; for water vapor,
D V = 2.12 × 10 -5 (1+0.007 T c ) m 2 s -1 ; and for carbon dioxide, D C = 1.29 × 10 -5
(1+0.007 T c ) m 2 s -1 .
The molecular diffusion coefficient for an entity influences not only its rate
of diffusion through a boundary layer but also the effective thickness of the
boundary layer relevant to each diffused entity. Experiments suggest that,
providing the exchange between the surface of a leaf and the canopy air stream
is dominated by forced convection, the ratio of the boundary-layer resistances
for two entities is inversely proportional to the ratio of the corresponding
molecular diffusion coefficients raised to the power 0.67 (Monteith and
Unsworth, 1990), e.g.
υ
0.67
R D
R D
(21.10)
V
=
H
0.9
H
V
 
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