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Temperature difference solar radiation

Temperature rise by solar radiation.

Symbol
$\Delta \theta_{sun}$
Unit
K
Formulas
$\sigma_{sun} D_{o} H_{sun} T_{4iii}$in air
$\operatorname{Min}\left(30, \operatorname{Max}\left(0.037H_{sun}-26.3, 0\right)\right)$in air-filled trough
$\operatorname{Min}\left(30, \operatorname{Max}\left(28.751e^{-9.8d_{t}}, 0\right)\right)$in channel (Heinhold)
$\frac{0.29H_{sun}}{{V_{air}}^{0.89} {L_{cm}}^{0.07}}$in filled trough
Related
$D_{o}$
Outer diameter [m]
$d_{t}$
Channel covering [m]
$H_{sun}$
Intensity of solar radiation [W/m$^2$]
$L_{cm}$
Depth of laying [m]
$\sigma_{sun}$
Absorption coefficient solar radiation
$T_{4iii}$
Thermal resistance ambient [K.m/W]
$V_{air}$
Air velocity [m/s]
Used in
$\Delta \theta_{s}$
Temperature difference surface—ambient [K]
$I_{c}$
Conductor current [A]
$T_{tr}$
Thermal resistance trough [K.m/W]
$\theta_{c}$
Temperature conductor [°C]
$\theta_{init}$
Air temperature without load [°C]
Image

Kabel und Leitungen für Starkstrom by Heinhold (1999) Bild 18.53

Equation derived from ECRC/R219 (1968) & 'Ampacity Calculations for Cables in Shallow Troughs' by Anders (2010)