Reynolds Number Calculations for Duct Flow with Obstructions

[gomerpyle]

I'm trying to calculate the reynolds number for flow inside an air duct with an obstruction. Basically the set up involves cooling electronics by placing aerodynamic "shrouds" over the device to improve the heat transfer. So far a cube is being used to approximate the shape of the device. The set up looks something like this:

http://img12.imageshack.us/img12/6601/duct.jpg

The highlighted parts represent the solid cube and the "shroud."


My question is, given the variation in these geometries what would the characteristic dimension be for a case like this when calculating Re? Would it be the cube dimension, or the gap size between the cube and shroud? And what if the shroud is not some simple shape like that?

 

[boneh3ad]

It depends on what parameters you are varying and looking at. I would say basing it on the gap size would be more appropriate since that will have more to do with the heat transfer properties. When choosing a characteristic length, the key is just to try and determine what the most physically relevant geometry is for your given situation.