Page 220 - Geothermal Energy Renewable Energy and The Environment

208 Geothermal Energy: Renewable Energy and the Environment

Table 11.3
selected convection heat Transfer coefficients, h
2
condition J/m -s-k
static environment with T 1 − T 2 = 30 k
Vertical plate in air (0.3 m high) 4.5
Horizontal cylinder in air, 5 cm dia. 6.5
Horizontal cylinder in water, 2 cm dia. 890

Flowing air and water
2 m/s airflow over 0.2 m square plate 12
35 m/s airflow over 0.75 m square plate 75
10 m/s airflow in 2.5 cm tube at 0.2 MPa 65
0.5 kg/s water flow in 2.5 cm dia. pipe 3500
50 m/s airflow across 5 cm dia. pipe 180
Source: Holman, J. P., Heat Transfer, 7th ed., New York: McGraw-Hill, 1990.

properties of the interface, the geometry of the flow path, and the orientation of the surface with
respect to the gravitational field. As a result, h is highly variable and specific to a given situation.
Table 11.3 lists values for h for some geometries and conditions.
Determining values for h requires geometry-specific experiments, or access to functional rela-
tionships that have been developed for situations that are closely analogous to those of a given
application. For example, convective heat loss from a small pond over which air is flowing at a low
velocity can be reasonably well represented by (Rafferty 2006; Wolf 1983):

Q = (9.045 × v) × A × dT,
cv
3
where v is the velocity of the air and the effective units of the factor 9.045 are kJ-s/m -h- °C. For a
5 m by 5 m external pool of water that is at 30°C (303 K), with a 3 m/s wind and an external tem-
perature of the air at 0°C (273 K), the heat loss would amount to

Q = (9.045 × 3.0 m/s) × 25 m × 30°C = 20,351.25 kJ/h.
2
cv
For this and many other situations in which heat is transferred from one medium to another and
the possibility of fluid movement is significant, heat transfer via this mechanism must be accounted
for to realistically represent heat transfer processes.

heaT Transfer by radiaTion
In the ideal case, heat transfer via radiation can be represented by considering a so-called ideal
black body. In this instance, heat transfer occurs by emission of heat that can be described by

Q = σ × A × T , (11.3)
4
rd
where Q is the emitted or radiated energy and σ is the Stefan–Boltzmann constant, which equals
rd
−8
5.669 10 W/m K . An ideal black body emits radiation that is strictly and absolutely dependent only
4
2
on temperature. As a result, the wavelength of the emitted radiation is strictly inversely proportional
to the temperature. At room temperature, for example, an ideal black body would emit primarily
infrared radiation while at very high temperatures the radiation would be primarily ultraviolet. Real