Heat Transfer Problem

[coachmark]

Hello- I am new to the forum. I am an ME who specializes in hydraulic/pneumatic circuit design and special applications. I have recently been tasked with a heat transfer problem that, after review of my college text (25 years old), indicates that i may have to re-learn Laplace Transforms. Before i go back to University after dinner tonite, i figured i would ask around and maybe someone could help. Here is the problem:

How many Watts/square inch are required to maintain a temperature of 122 degrees F on the inside wall of a stainless steel cylinder 16 inches in diameter(wall thickness = .0625")when there is an air flow of 5730 standard cubic feet per minute of 77 degree F air?

We are building a heated blanket that wraps around the cylinder to heat it up. There will be a 1" air gap between the inner (heated) side of the blanket and the outer surface of the cylinder.

In case anybody wants to know, this is for a dilution tunnel used in automotive emissions testing. The tunnel is 50 feet long. I appreciate any input and will make myself available for hydro/pneumatic questions which i am much better qualified to answer. Thank you very much.

 

[vpl]

1) Is the 77[°] air on the inside of the tunnel (i.e., next to the inside surface of your cylinder?)

2) Will the heated blanket remain on all the time or is this a transient problem?

3) Do you have a drawing of your setup that you can share?

4) There's a free heat transfer text that you can download:

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

http://www/ahtt.html

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[coachmark]

Yes, the 77 degree air is inside the tunnel. The air outside the tunnel is static. This is for a transient test. The engine duty cycle calls for a 108 second period where the diluted exhaust temperature will fall to 77 degrees. It is understood by the customer that the blanket heater will need to be turned on for some time period before the 108 second interval - it is expected that the 'pre-heat' time will be determined empirically.

Some of these tests run for hours and hours. I have checked around various dyno labs for similar situations, and many indicators point to a value of around 1 watt/sq. in. A 50 foot long heated blanket that wraps around an 18 inch diameter cylinder will require 35kW. Thats alot of power (and money).

I must verify this number. I appreciate the help.

Mark Zeleney

 

[corus]

The heat flow from the blanket to the cylinder will be by radiation. The heat transfer coefficient to the air inside should be fairly easy to determine say by reference to

http://www.cheresources.com/convection.shtml.

You'll also need to know the emissivity of the tube and blanket and then solve a non-linear equation involving the quartic term for radiation, as well as for a transient solution. You'd be better using a finite element package or solve it by finite differences in my opinion.

corus

 

[IRstuff]

Sounds pretty reasonable. Your air flow is running about 47 mph, so the convective HTC is pretty high.

At 25 W/m^2-K, you'd need 0.4 W/in^2 just for the air. You must also account for heat loss outward away from the heater blanket, as well as the air gap inefficiency, so 1 W/in^2 doesn't sound that far out of bed.

The power you calculated should be for the 16 in diam, so, more like 31 kW.

TTFN

FAQ731-376

 

[coachmark]

Thanks all for the help. I am continuing on the solution. More comments still welcome. I will share when we zero in on it.

Mark