Nu ¼
h c D
k
ð6:30Þ
From Eq. (6.25), we can derive
Nu ¼
D
d t
ð6:31Þ
where the Nusselt number becomes the ratio between the characteristic dimension
of the object and the thickness of the thermal boundary layer. Equation (6.30)
allows interpreting N u as the ratio between convective heat transfer from a surface
and the conductive flow through a fluid plane, per unit of the characteristic
dimension.
Equation (6.24) can also be written as
H ¼ h c T s À T a
ð
Þ¼
kNu
D
T s À T a
ð
Þ
ð 6:32Þ
From the knowledge of the Nusselt number (Eq. 6.30) in conjunction with
Eq. (6.32), it is possible to determine the convection coefficient and the sensitive
heat transfer, under conditions of forced convection.
Based on the heat transfer by convection theory, the following general relationship can be determined (Gates 1980):
Nu ¼ f ðRe; PrÞ
ð 6:33Þ
Physical properties of water and air, the most important fluids in environmental
physics, allow to obtain their dimensionless flow parameters. For air at 20 °C,
thermal conductivity k, is 25.7 Â 10
–3 Wm
−1 K
−1 , kinematic viscosity m is
15.3 Â 10
−5 m
2 s
−1 , dynamic viscosity l, equals 18.2 Â 10
–6 Nsm
−2 , the specific
heat at constant pressure c p , is 1.01 Â 10
3 JKg
−1 K
−1 , gravity acceleration is
9.8 ms
−2 , and the volumetric expansion coefficient, b, is 3.67 Â 10
−3 K
−1 . Using
Fig. 6.4 Aerodynamic and thermal boundary layers on a flat plate under laminar flow (after
Mimoso 1987)
6.2 Convection
173
h c D
k
ð6:30Þ
From Eq. (6.25), we can derive
Nu ¼
D
d t
ð6:31Þ
where the Nusselt number becomes the ratio between the characteristic dimension
of the object and the thickness of the thermal boundary layer. Equation (6.30)
allows interpreting N u as the ratio between convective heat transfer from a surface
and the conductive flow through a fluid plane, per unit of the characteristic
dimension.
Equation (6.24) can also be written as
H ¼ h c T s À T a
ð
Þ¼
kNu
D
T s À T a
ð
Þ
ð 6:32Þ
From the knowledge of the Nusselt number (Eq. 6.30) in conjunction with
Eq. (6.32), it is possible to determine the convection coefficient and the sensitive
heat transfer, under conditions of forced convection.
Based on the heat transfer by convection theory, the following general relationship can be determined (Gates 1980):
Nu ¼ f ðRe; PrÞ
ð 6:33Þ
Physical properties of water and air, the most important fluids in environmental
physics, allow to obtain their dimensionless flow parameters. For air at 20 °C,
thermal conductivity k, is 25.7 Â 10
–3 Wm
−1 K
−1 , kinematic viscosity m is
15.3 Â 10
−5 m
2 s
−1 , dynamic viscosity l, equals 18.2 Â 10
–6 Nsm
−2 , the specific
heat at constant pressure c p , is 1.01 Â 10
3 JKg
−1 K
−1 , gravity acceleration is
9.8 ms
−2 , and the volumetric expansion coefficient, b, is 3.67 Â 10
−3 K
−1 . Using
Fig. 6.4 Aerodynamic and thermal boundary layers on a flat plate under laminar flow (after
Mimoso 1987)
6.2 Convection
173