I've been trying to find a Nusselt number correlation for a sphere cooling in a forced gas cross flow where the sphere temperature is much higher than the free stream temperature.
I want something like this: $ Nu = F(Re, Pr, …)$ that is applicable for a hot spherical body cooling in a forced crossflow of air at roughly $ 10< Re < 1000 $ and $ .5< Pr < .8 $. I'm interested in cases where the temperature differences are quite large (~$1000^oC$). The closest I've found (DOI 10.1002/aic.690180219) is correlations of the form:
$$ Nu = F\left(Re, Pr, \frac{\mu_\text{free stream}}{\mu_\text{surface}} \right)$$ but in these correlations the viscosity ratio must be $>1$ which is consistent with a sphere being heated not cooled (for air the viscosity increases with temperature).
Other details:
- I'm not interested in radiation for this (I'm keeping track of it separately)
- I'm aware you can use a "film temperature" but this is typically for much smaller temperature differences.
- It can be theoretically or empirically based – as long as it is applicable!
- If there is a way to show that the effect of large temperature differences shouldn't matter that is equally useful.
Best Answer
Here is an equation that you can use: