8.5.2 More realistic case

Typically, the mean atmosphere temperature is lower than the ambient temperature near the ground by about 40 K: $T_{atm} \simeq T_{gr} - 40~{\mathrm K}$; then, the formula above still holds if we replace T_cal by:

  

$$({T_{load}- T_{emi}})e^\tau$$ T_cal = (8.33)

$$T_{sky} \eta_f+ (1-\eta_f) T_{gr}$$ with  T_emi =

$$\frac{(T_{load}+ T_{rec})\times M_{atm}}{M_{load}}-T_{rec}$$ = (8.34)

$$\T_{sky} (1-e^{-\tau})(T_{gr}-40)$$ =

T_rec, the receiver effective temperature is usually calculated by the Yfactor method using a cold load (usually cooled in liquid nitrogen, i.e. at 77 K) and an ambient load (e.g. at 290 K).

 

$$\frac{M_{hot\_load}}{M_{cold\_load}}$$ Y =

$$\frac{T_{hot\_load}-Y T_{cold\_load}}{Y-1}$$ T_rec = (8.35)