Cables in troughs pose a particular problem as there tend to be few defined sizing methods. One common approach is to use the empirical method given in IEC 60287-2-1 "Calculation of the current rating - Calculation of thermal resistance". The approach is to calculate a temperature rise of the air in the trough above it's ambient, with the rating then being calculated as though it were in free air but with the increased temperature.
The required temperature adjustment, ΔΘtr is given by:
When calculating p, only the effective heat dissipation parts of the trough are included. Any side exposed to sunlight is not to be included. In practice this typically becomes the length of the base and two sides of the trough.
ΔΘtr - temperature rise above ambient adjustment, °C
WTOT - total power dissipated in trough per metre length, W/m
p - part of trough perimeter effective for heat dissipation, m