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Temperature increase of air

This is the temperature rise of the air inside an air-filled trough or channel.

Symbol
$\Delta \theta_{air}$
Unit
K
Formulae
$T_{tr} W_{sum}$in trough
$\left(T_e+T_{at}\right) W_{sum}$in channel (Heinhold)
$\left(\frac{1}{2} T_{4pi}+T_{4pii}+T_{4piii}\right) W_{sum}+\Delta \theta_p$in air-filled pipe with objects
Related
$\Delta \theta_p$
Temperature rise by other buried objects [K]
$T_{4pi}$
Thermal resistance of medium in the air-filled pipe with objects [K.m/W]
$T_{4pii}$
Thermal resistance of the pipe wall [K.m/W]
$T_{4piii}$
Thermal resistance of the pipe to ambient [K.m/W]
$T_{at}$
Thermal resistance by convection, air to tunnel [K.m/W]
$T_e$
External thermal resistance of tunnel [K.m/W]
$T_{tr}$
Thermal resistance of trough [K.m/W]
$W_{sum}$
Sum of total losses of all systems [W/m]
Used in
$\theta_{at}$
Air temperature under load [°C]
$\theta_t$
Temperature of inner tunnel wall [°C]