Cableizer

Rayleigh number riser/tray—air

Rayleigh number $c_{Nu}$ gas/duct

Symbol
$\mathrm{Ra}_{ext}$
Formulas
$\mathrm{Gr}_{ext} \mathrm{Pr}_{gas}$riser: duct to ambient
$\frac{g \mathrm{Pr}_{gas} \beta_{gas} \left(\theta_{de}-\theta_{air}\right) {L_{d}}^3}{{\nu_{gas}}^2}$riser: Chippendale, IEC
$\frac{g \mathrm{Pr}_{gas} \beta_{gas} \left(\theta_{tw,ot}-\theta_{air}\right) \left(w_{t}+2t_{t}\right)^3}{{\nu_{gas}}^2}$tray top—air (TA)
$\frac{g \mathrm{Pr}_{gas} \beta_{gas} \left(\theta_{tw,ob}-\theta_{air}\right) \left(w_{t}+2t_{t}\right)^3}{{\nu_{gas}}^2}$tray bottom—air (BA)
$\frac{g \mathrm{Pr}_{gas} \beta_{gas} \left(\theta_{tw,os}-\theta_{air}\right) \left(h_{t}+2t_{t}\right)^3}{{\nu_{gas}}^2}$tray side—air (SA)
$\frac{g \mathrm{Pr}_{gas} \beta_{gas} \left(\theta_{e}-\theta_{air}\right) {w_{c}}^3}{{\nu_{gas}}^2}$tray cable pack—air (CA)
Related
$\beta_{gas}$
Volumetric thermal expansion coefficient gas [1/K]
$g$
Standard acceleration of gravity [m/s$^2$]
$\mathrm{Gr}_{ext}$
Grashof number riser/tray—air
$h_{t}$
Height (inner) [m]
$L_{d}$
Length duct [m]
$\nu_{gas}$
Kinematic viscosity gas [m$^2$/s]
$\mathrm{Pr}_{gas}$
Prandtl number gas
$t_{t}$
Thickness wall [m]
$\theta_{air}$
Ambient air temperature [°C]
$\theta_{de}$
Temperature duct outer surface [°C]
$\theta_{e}$
External temperature object [°C]
$\theta_{tw,ob}$
Temperature tray wall (outer) bottom [°C]
$\theta_{tw,os}$
Temperature tray wall (outer) sides [°C]
$\theta_{tw,ot}$
Temperature tray wall (outer) top cover [°C]
$w_{t}$
Width (inner) [m]
Used in
$h_{conv,ext}$
Heat transfer coefficient convection riser/tray—air [W/(K.m$^2$)]
$\mathrm{Nu}_{tray}$
Nusselt number tray—air