VII. COMPARISON OF SENSIBLE HEAT FLUX
Based on boundary layer integral analysis in conjunction with a study of heat flux over Arctic
leads, Andreas (1977) presented a dimensionless relation relating the Nusselt number Nu to the
products of the Stanton number St, the Reynolds number Re, and the Prandtl number Pr, as
Nu = St Re Pr,
(86)
in which the dimensionless groups are chosen to be defined as
u0.5 x
Hx
H
Re =
Nu =
, St =
and
,
,
k (Tw - T0.5 )
ρ cp u0.5 (Tw - T0.5 )
v
where Tw is the surface water temperature, and u0.5 and T0.5 are the mean wind speed and air
temperature measured at 0.5 m above the lead at fetch x, respectively. All the other properties, i.e.,
v, ρ, cp, and k, are evaluated at Tw. Andreas's results were finally expressed either by
Nu = 0.18 Re0.71
(87)
or in linear form as
Nu = 2.24 10-3 Re + 1120 ,
(88)
which was compared with the theoretical expression presented by Kays (1966) for flow over a
constant-temperature flat plate, i.e.,
St = 0.0295 Re0.2 Pr0.4,
(89)
which is not in good agreement with the expression resulting by equating eq 87 and 86, i.e.,
St Re Pr = 0.18 Re0.71
(90)
or
St = 0.18 Re0.29 Pr1.
(91)
For Pr = 0.714, eq 91 becomes
St = 0.2521 Re0.29,
(92)
which is quite different from Kay's theoretical expression (eq 89). By substituting Pr = 0.714, eq 89
becomes
St = 0.0338 Re0.2,
(93)
Assuming eq 92 and 93 have a same exponent to Re, eq 92 gives about seven times larger values
than Kay's theoretical expression (eq 93). Andreas also compared his findings with the theoretical
expression developed by Schlichting (1968) for flow over a heated plate by assuming a drag
coefficient of 1.76 103 and Pr = 1.0, i.e.,
Nu = 1.76 103 Re
(94)
For a value of Re = 2.94 105, we have a flux value H of 36 W/m2 from eq 83. For the same
value of Re and a ∆T of 20C, eq 88 gives an H value of ~400 W/m2, which is approximately 10
times higher than the value obtained from this study. But for the same values of Re and ∆T, eq 94
predicts a value of ~125 W/m2, which is about one third of the 400 W/m2 given by eq 88 and about
three times larger than the 36 W/m2 given by eq 83. However, it should be noted that in Andreas's
field test not only is the temperature difference (Tw T0.5) always about 20C, but the measurement
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