Air temperature without load

The meaning of this parameter depends on the calculation method:

For ventilated tunnels, this is the temperature of the air at the inlet.
For troughs, unventilated tunnels and channels, this is the temperature of the air inside the trough with no load.

The temperature of the air with no load depends on the object:

For troughs, it is equal to the ambient air temperature above ground plus an increase caused by solar radiation acting directly on the through cover.
For unventilated tunnels and channels, it is equal to the ambient soil temperature plus an increase proportional to the inner surfaces.
Explanations: The temperature of the soil depends on the laying depth. The temperature at a depth of about 10 m is constant and equal to the average annual temperature of the air (e.g. in Germany about 9°C). In less deep layers, the temperature follows the fluctuations in the air temperature with a certain time delay. Seasonal fluctuations can be observed at medium depths. In addition, fluctuations in the time of day can be detected in the vicinity of the earth's surface. Their mean value is higher in the summer months than the temperature in lower layers. With no load, the air in an unventilated tunnel or channel assumes an average temperature, which results from the temperatures of the inner surfaces and the proportion of the inner surfaces on the circumference of the object. The bottom and walls take on the temperature of the ground at the depth of the object's center. Under the influence of air temperature and solar radiation, the inside surface of the ceiling reaches in the summer months a temperature that is at most increased by $\Delta\theta_{sun}$. The mean temperature of the air in the duct with unloaded cables is the ambient air temperature above ground plus the increase through solar radiation divided by a geometric factor depending on height and width of the channel.

Symbol

$\theta_{init}$

Unit

°C

Formulas

$input$	in tunnel
$\theta_a+\frac{\Delta \theta_{sun}}{2\left(\frac{h_t}{w_t}+1\right)}$	in channel (Heinhold)
$\theta_{air}+\Delta \theta_{sun}$	in air-filled trough
$\theta_{air}$	in air-filled pipe with objects

Related

$\Delta \theta_{sun}$

Temperature difference conductor—enclosure [K]

$h_t$

Height (inner) [m]

$\theta_a$

Ambient temperature [°C]

$\theta_{air}$

Ambient air temperature [°C]

$w_t$

Width (inner) [m]

Used in