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Convection heat transfer, gas to duct

Radiation heat transfer from gas in duct to inner wall of the duct used for riser/J-tube.

Symbol
$W_{conv,gd}$
Unit
W/m
Formulae
$0$Riser closed at both ends (Hartlein & Black)
$0$Riser open at both ends (Hartlein & Black IIa)
$\frac{\mathrm{Nu}_{gd} \pi D_{di} \left(\theta_{air}-\theta_{di}\right) k_{gas}}{\frac{D_{di}}{2}}$Riser open at both ends, 0.1 ≤ $Ra$ < 10^5 (Hartlein & Black IIb)
$\frac{\mathrm{Nu}_{gd} \pi D_{di} \left(\theta_{air}-\theta_{di}\right) k_{gas}}{\frac{D_{di}}{2}}$Riser open at top and closed at bottom (Hartlein & Black)
$h_{conv,gd} \pi D_{di} \left(\theta_{gas}-\theta_{di}\right)$Anders
Related
$D_{di}$
Inner diameter of duct [m]
$h_{conv,gd}$
Convection heat transfer coefficient, gas to duct [W/(K.m$^2$)]
$k_{gas}$
Thermal conductivity for gas [W/(m.K)]
$\mathrm{Nu}_{gd}$
Nusselt number, gas to duct
$\pi$
Archimedes' constant $\pi$
$\theta_{air}$
Ambient air temperature [°C]
$\theta_{di}$
Temperature of duct inner wall [°C]
$\theta_{gas}$
Gas temperature [°C]
Used in
$T_{4i}$
Thermal resistance of medium in the duct [K.m/W]