Forced laminar flow

[peteswift]

We have a cylindrical shell that requires cooling by around 380 kW it is 380 mm outside dia with a .75 mm fluid film of gearbox oil. The pressure drop across it has to be minimal (i.e. preventing turbulent flow regime) with flow rate around 20 L/min. I have tried calculating it but is the Hydraulic radius method valid for very thin fluid films since two plates is not one of my standard cases in my books. It seems to that the standard method of improving cooling is by preventing a Thermal boundary layer developing. Any ideas.

Thanks for ANY help in advance.

 

[rjw57]

Some quick calcs tell me that for a 150 degC temp rise (20 - 170 degC) on SAE50 motor oil, you need about 90 L/min. Mdot = Q_remove / (Cp_oil * dT_oil). This obviously means that at 20 L/min, the dT is much higher and probably unacceptable (assuming you are using something like motor oil). Also, the hydraulic diameter of a long slot (I assume this is what you are looking for) is 1/2 the width of the passage (width very small relative to length) per Crane 410. Are the 380mm OD cylindrical shell and the casing that keeps the oil retained rotating relative to one another or are you just flowing oil between two stationary shells? This makes a difference to your heat transfer calcs. Also, if stationary, is the flow around the shell or down the longitudinal axis of the shell?

 

[rjw57]

Pete,
Correction to my last post. The hydraulic radius (not diameter) is 1/2 the passage width. This means the hydraulic diameter is 4x this value or 2x passage width. Sorry...

 

[peteswift]

Doh!!! just spotted a mistake the power should be 3.8 kW. This represents a worst case and will probably be around the 2.5 kW level.

The casing is stationary and the fluid flows through a gap and the fluid is Dextron 2 automatic gearbox oil. Ro = 787, k = 0.17 W/mk cant remember cp but can look it up tomorrow.

I tried using the wetted perimeter method, which at long narrow slots approximates to the gap size. In order to find a convection transfer coefficient. This seems to give some strange results but I have to check them.

I am trying to finalise the flow path should I have one pass front to back, go around the circumference, try and put features to minimise laminar flow. Since Mdot = Q_remove / (Cp_oil * dT_oil) assumes that the heat will end up in the oil.