How to determine temperature rise in an outdoor, recirculation loop?

[ftaok]

Hi,

I'm looking for some references to help me solve a problem that I have. We have an outdoor solvent tank which we intend to add a new pump loop to a building. The length of pipe will be 3000 ft to the building, and 3000 feet back to the tank. Hydraulically, we need to run 3" stainless steel pipe to the building and return the solvent in a 2" line.

The flow rate will depend on the users in the new building. At the highest demand, the flow from the pump will be 62 GPM and an assumed temperature of 75F. There will be a heat exchanger in the building to take the acetone and cool it down to whatever it needs to be so that the flow back to the acetone tank will be at 75F when it gets back. The flow of solvent back in this case will be about 7 GPM. This scenario will last for about an hour.

Most of the times, the flow rate will be 35 GPM to and from the building.

I'm looking to estimate the amount of heat input the pipe will see from convection and solar loading.

I've used the 3E Plus program, but the results seemed a little high; in the range of 50 BTU/hr/ft. And that doesn't seem to take solar radiation into account.

Here are the details.

Initial Temperature - 75F
Flow in 3" pipe - 62 GPM and 35 GPM
Flow in 2" pipe - 7 GPM and 35 GPM
Ambient Temperature - 100F

We're using bare stainless steel. I found some information for the effusivity of SS to be 0.3

I also found a solar heat rating of 350 BTU/hr/ft^2 for my area (Virginia, USA). The pipe will run in a pipe rack, so I guess it would be partially shaded.

Any help would be appreciated. Thanks

Frank

 

[IRstuff]

sounds plausible

14W/m^2-K*(3*inch*pi)(100°F-75°F) = 48.4 BTU/hr/ft

You have options; insulating the pipe would reduce both the convective and solar load.

TTFN

FAQ731-376

 

[ione]

I’m with IRstuff on this one: the response you’ve got from 3E Plus program is on the right order of magnitude.
Forced convection, assuming a wind speed of 1.6 m/s), together with the other inputs of your scenario, leads to a heat transfer coefficient of 14 W/(m^2 K).
I got only a slightly different value, that is 56.5 Btu/(h ft) instead of 48.4 Btu/(h ft), because I have assumed 3.5 inch as external diameter.

 

[ftaok]

Thanks for the reply regarding the 3E Plus program. I think I'll use the numbers generated by 3E and include that heat duty to the solar load.

I've found some data for emissivity of SS pipe, along with the solar load of 350 BTU/hr.ft^2.

When I use the 350 number, I get a much higher duty than when I use the Stefan-Boltzmann calc (q=e*sigma*(Thot^4-Tcold^4)*Area. The difference is 10x.

Not sure which one is legit.

Frank

 

[IRstuff]

You are mixing thngs. You have 3 heat loads:
> Ambient air --> that's the stuff coming from your software
> Ambient radiation --> that's the net radiation input
> Solar load --> that's 350 BTU/hr-sqft

Your only heat losses are what's transferred to the fluid, and the difference term in the Stefan-Boltzman equation.

TTFN

FAQ731-376

 

[ftaok]

IRStuff,

I think I have it straight now. I have a heat load from convection, a heat load from ambient radiation and a heat load from solar radiation.

The convection load I got from 3E Plus.

The ambient radiation load I got from the Stefan-Boltzmann equation.

It's the solar load that I'm having trouble with. I haven't been able to find a formula to go from the solar load to a heat duty. Doing some dimensional analysis, can I multiple the solar load (BTU/hr-sqft) by 50% of the surface area of the pipe (sqft) and wind up with a heat duty (BTU/hr).

Does emissivity come into play here? I'm guessing that the more reflective the pipe is, the lower the heat duty from solar radiation.

I just can't find any equations.

 

[IRstuff]

Technically, it's absorptivity that's involved. While we often laze out and use the same value, the sun's spectral content is centered around 550 nm, while a typical object, like your pipe, will have peak spectral emission more around 10 um. There's a general lack of detailed spectral characterization across that entire range for most materials of interest.

The basic solution comes through solving the simultaneous equation that roughly looks like:

P_sun+P(T)_conv+P(Tamb)_rad = P(T)_fluid+P(T)_rad

You might have to break that into two different equations if the pipe outer surface temperature differs from the pipe inner temperature. The fluid heat transfer is also more complicated than what I show, since it's a spatially distributed heat transfer, but then again, so is the other stuff, albeit not as significantly so.

TTFN

FAQ731-376

 

[zekeman]

The solar component is an important input here with 350BTU/hr-ft^2 the incident solar rqdiation at noon.

You need to make 2 guesstimates

1) if you are looking for worst case, I would use a high value of absorbtivity, say about0.3 to 0.4 top account for a dull or grimy surface of the SS.

2) since it is somewhat shaded I would use a factor of at most 0.4 to account for shadowing

So the net solar transfer would contain these 2 factors times the outside area of the pipe.

Since this is roughly 1/2 the total load you may have to get empirical data on your own or search the internet to get values based on surface conditions if you need more accuracy.

Absorbtivity is a very sensitive function of surface conditions, being very low for SS highly polished to fairly high for grimy surfaces.