Frost Protection - UTL Repository

MECHANISMS OF ENERGY TRANSFER
state from liquid to solid, but it drops as water sublimates from the ventilated
ice-covered thermometer bulb. Within a few minutes, the temperature will
stabilize at the frost-bulb (T f ) temperature. From the air and frost-bulb
temperatures, the vapour pressure of the air is then determined using:
e = − γ
where
e f
f
( − ) kPa Eq. 3.8
T a
T f
γ f
= 0.000582( 1 + 0.00115T f ) P b kPa °C -1 Eq. 3.9
is the psychrometric constant adjusted for the frost bulb temperature (T f ), and
the saturation vapour pressure at the frost-bulb temperature (e f ) is calculated by
substituting T f into Equation 3.4. Alternatively, one can find the value for e f
corresponding to the frost-bulb temperature in Table A3.3 in Appendix 3 of Volume I.
Relationships between temperature, vapour pressure and several measures of
humidity for a range of subzero temperatures are shown in Figure 3.10. The upper
curve represents the saturation vapour pressure over water (Equation 3.3) and the
lower curve represents the saturation vapour pressure over ice (Equation 3.4).
Therefore, at any given subzero temperature, the saturation vapour pressure
over ice is lower than over water. Given an air temperature of T a = -4°C
and a vapour pressure of e = 0.361 kPa, the corresponding temperatures are:
T d = -7.0, T i = -6.2, T w = -4.9 and T f = -4.7 °C for the dew-point, ice point,
wet-bulb and frost-bulb temperatures, respectively. The corresponding saturation
vapour pressures are: e d = 0.361, e i = 0.361, e w = 0.424 and e f = 0.411 kPa.
The saturation vapour pressure at air temperature is e s = 0.454 kPa.
Sometimes it is desirable to estimate the wet-bulb temperature from
temperature and other humidity expressions. However, because the vapour
pressure is a function of T w , e w , T a - T w and P b , it is difficult without complicated
programming. The same problem arises for estimating the frost-bulb
temperature (Equation 3.8) from other humidity expressions. However, an Excel
application (CalHum.xls) for estimating T w and T f from other parameters is
included as a computer application with this book.
For any given combination of subzero temperature and humidity level, the
actual and saturation vapour pressures at the dew-point and ice point are equal
(i.e. e d = e i = e). In addition, the dew-point is always less than or equal to the
wet-bulb, which is less than or equal to the air temperature (i.e. T d ≤ T w ≤ T a ).
A similar relationship exists for the ice point, frost-bulb and air temperature
(i.e. T i ≤ T f ≤ T a ). At any subzero temperature, e i ≤ e d .
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