Constant external temperature heat transfer

[Sprode]

Hello everyone.

My first time posting here so I apologize if I break any etiquette.

I used to be quite good at heat transfer but it has been 4 years since I took the course, and I am really starting to confuse myself.

Here is the problem. I have attached a sheet to help visually, but basically:

I have a copper tube taking room temperature air and feeding into an oven. The oven will be held at a constant temperature. I want it to be as close to 850C as possible, but I also need the air exiting the pipe to be as close to 850C as possible. This is because I am wanting the air out of the tube and the "valve" in the middle to be as close to 850 as possible. I am specifying a diameter of 1 inch (ID) for the tubing, and I can control the flow rate.

As I understand the problem, it should be quite easy. Knowing the flow rate, I need to find a length of tubing that would allow enough time in the tube for the air to heat up. It took me a while to realize I could not assume constant tube temperature, only constant external fluid temperature, and have not been able to make any real progress since then.

 

[IRstuff]

How is the air circulated within the oven itself?

TTFN

FAQ731-376

 

[Sprode]

The oven is not circulated. Electric heating coils are built into the insulated walls. There is no fan moving the air around on the inside or anything like that.

 

[IRstuff]

Then why run it through this "oven?" Wouldn't it be faster and more economical to simply wrap the piping with heater tape?

TTFN

FAQ731-376

 

[Sprode]

This is actually a test on a wastegate valve that has to be done at temperature. The idea is that the air as it flows to the wastegate and the wastegate itself should be at a similar, common exhaust temperature to simulate time operating conditions.

 

[Sprode]

I was hoping someone could jump in with a quick heat transfer equation/method that could relate all of these variables in an easy closed form solution. Is this somehow more complicated in a way I am missing?

 

[KiwiMace]

I'm with IRstuff on this one.

Then insulate your valve. Run the air heater for a while and bring the valve up to operating temp within the insulation. A lot easier than trying to build an air to air heat exchanger.

 

[IRstuff]

There is no closed form solution, there are only approximations, particularly at this temperature, which involves both convective and radiative transfer.

You can start with the basics:

(1.2 kg/m^3)*(1080 J/kg*K)*(850ºC-25ºC) = 505 W/cfm

You can download a free textbook:

http://web.mit.edu/lienhard/

http://www/ahtt.html

There is a section on heat exchangers.

TTFN

FAQ731-376

 

[Sprode]

I finally found a proper example and I was able to solve this using a couple lines of equations.

I used Ra and Pr (and various other lookups) to solve for Nu. That gave me my h value.

From there the only unknown was emissivity, which i simply set for its worst case scenario.

I need almost precisely 3.25 meters of tubing at my specified flow rate and diameter. I did not use the above calculation, although I suppose if I were to fix the length and vary the flowrate that would have been used again.

Thanks for the help,
-John