Shaft Heating due to Bearing Lube Oil Flow

[sry110]

I am having a major brain-fart and would appreciate any help. I am looking at an application where I have a 140 lb. carbon steel shaft sitting in a journal bearing that has 1.5 GPM continuous flow of ISO VG32 oil supplied at 131 deg.F. The ambient temperature is -58 deg.F. I want to get the shaft temperature up to 32 deg.F. What I am trying to figure out is whether the given oil flow will maintain the desired shaft temperature.

So to simplify things, I'm looking at it like this:
I have a 140 lb. block of carbon steel (Cp = 0.12 Btu/lb-degF)
I have a continuous flow of 131 deg.F ISO VG32 oil (Cp = 0.45 Btu/lb-degF) flowing onto the block
The ambient air temperature is -58 deg.F
The desired temperature of the block is 32 deg.F
What oil flow (at the given conditions) is required to achieve this?

I started by trying to calculate the heat transfer rate from the oil:
Q = mass flow rate x Spec.Heat x deltaT
= (1.5 gal/min x 7.328 lb/gal) x (0.45 Btu/lb-degF) x (32 -(-58) deg.F)
= 445 Btu/min

So now I have heat transfer rate of the heating medium (flowing oil) based on maintaining the steel at 32 degF, but how do I know if the flow rate is sufficient?

 

[berkshire]

do you know the length and surface area of your shaft, and can you calculate the heat rejection rate of your shaft to the ambient air?
B.E.

You are judged not by what you know, but by what you can do.

 

[desertfox]

Hi sry110

Well I did a calculation to see how much heat was required to raise the shaft to the required temperature and I calculated about 6732Btu, so at your present flow rate it would take about 15 minutes to get to the right temperature assuming all the heat gets into the shaft without loss.
What I don't know of course is how much heat actually gets to the shaft and how much heat is lost to atmosphere and other surroundings.
Can you do some practical measurement testing?

 

[MintJulep]

I started by trying to calculate the heat transfer rate from the oil:
Q = mass flow rate x Spec.Heat x deltaT
= (1.5 gal/min x 7.328 lb/gal) x (0.45 Btu/lb-degF) x (32 -(-58) deg.F)
= 445 Btu/min

Oil comes in at 131F and leaves at an unknown temperature. So this is incorrect.

Start, as Berkshire suggested, by calculating the heat rejection of a 32F shaft into a -58F space. Radiation will not be negligible.

Oil exit temperature will NOT be the same as the shaft temperature.

Heat transfer from oil to shaft will be roughly proportional to the average oil temperature and a convective heat transfer coefficient for the oil-shaft interface.

Heat transfer out of the oil will be proportional to change in temperature of the oil.

It might be safe to neglect heat transfer from oil to bearing housing - or it might not.

That's two equations and two unknowns, so solve.

But by "gut", no way.