Here the constant C is equal to 1.0 for brazed foams, the Reynolds number will be
replaced with our Reynolds number based on the hydraulic diameter, and 6 is the
porosity of the metallic foam. The friction factor will then be used to calculate the
pressure drop. This pressure drop uses the normal horizontal cylinder calculation.
LV2
Ap = p f (46)
2Dh
The Nusselt number is calculated as shown below.
Nud = 0.606Pe056 E52 (47)
The Nusselt number here is based on the diameter and for our purposes it will be based
on the hydraulic diameter. Pe is the Peclet number, which is equivalent to the Reynolds
number times the Prandtl number. Again we will use the Reynolds number based on the
hydraulic diameter to determine the Peclet number. In order to calculate the porosity it
either had to be provided to me from the manufacturer, or it can be calculated with a few
known parameters. A study done by Zhao et al. [8] shows the particular details needed
for my foam purchased from Porvair Fuel Cell Company. Their study shows an average
cell size and the ligament size of a copper foam from Porvair. Their average cell size is
.104 in and the ligament size is .0104 in. Then it explains how to use these two
parameters to calculate the porosity of the foam. Shown below are the steps in order to
calculate the porosity.
df 1 1 (48)
= 1.18 C
-dp 3;r 1 exp( 1 (48)
Sexp^ U/0.04jJ
Here df is the ligament diameter and dp is the pore size diameter or cell size diameter.
From here the porosity can be calculated and used to solve for the Nusselt number as well