Buried Air Duct Length Calculation 2

[swguru]

I have an application were I have a buried air duct that has an intake air temp of 40C and I need to determine the duct length to acheive an air exit temperature of 30C(geothermal application). Based on below, do the calculations look correct?

Paramaters:
Pipe inside dia (ID) = .055m
Buried depth (X) = .76m
Soil temp at depth (Ts) = 295K
K of Soil (Ks) = .5W/m-K
Air inlet temp (Tin) = 313K
Air outlet temp (To) = 303K
Soil surface & air temp (Ts / Ta) = 313K
K of air (Ka)= .027W/m-K
Prandtl No (Pr) = .7
Visc of air (v) = 192e7N-s/m^2
Mass flow rate (Vm) = .013kg/s

Heat flux on the duct calculated by;
q`=ho*dT where dT=Tave_duct-Ts
q'=137W/m^2

Duct length calculated from [ref Incroprera];
L=(Vm*Cp)/(pi*ID*q`)*(Tin-To)
L= 5.6m

Check:
To=Ta-(Ta-Tin)*exp(-(ht*A)/(Vm*Cp))
where; ht is total heat transfer coeff ht=1/(1/hx+1/ho)
hx is the convective heat transfer coeff hx = Nu*(ka/ID); calculated from Re=(4*Vm)/pi*ID*v and Nu=.023*Re^4/5*Pr^n, where n=.3 (soil cooler than air).
ho is the conductive heat trans coeff ho=Ks/X
For above I substituted Tave_duct for Tin. The resultant To is calculated to be 303.3K

 

[IRstuff]

Your convective heat transfer coefficient seems to high to me. The airspeed appears to be about 0.1 mph, so the convective coefficient should be more like 2 W/(m^2*K), but you have an H0 of 13 W/(m^2*K).

TTFN

FAQ731-376

 

[trashcanman]

I don't think it is quite that simple. It is similar to a problem I worked on (another previous thread) about water cooling time for a pipe line.

As the air moves, it cools. As the temperature drops, the heat transfer coefficient changes. I would solve it in step wise fashion.

1 Knowing the initial temperature, calculate the heat loss for a short distance, say 10cm.

2 Now, translate that heat loss to a temperature drop in the air. Now you know the temp. for the beginning of the next 10 cm.

3 Calculate the heat loss again.

4 Go to 2 (above).

5 Keep going till you reach the desired temperature. At that point, note the total length of duct. For more accuracy, the distance (dL) should be short, like 1cm. This takes longer computing time of course.

This can be easily programed in your computer. I did it for the water cooling in plain old GW BASIC.

 

[tsgrue]

.

See post: "Earth-air heat exchangers and solar chimneys for HVAC"
thread403-204634

http://www.eng-tips.com/viewthread.cfm?qid=204634&page=1

There are lots of papers on this. Try an an Internet search for "earth air heat exchanger design"

.



tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation

http://hhwq.blogspot.com

 

[vc66]

I agree with trashcanman... It seems stepwise calculation is the way to go.

IRStuff-- I believe the air speed is 10 mph, not .1 mph

mass flow = rho * A * V

V = mass flow / (rho * A)

V = .013 kg/s / ((Pi/4*(.055^2)m^2)* 1.2 kg/m^3) = 4.56 m/s = 10.2 mph

V

Mechanical Engineer
"When I am working on a problem, I do not think of beauty, but when I've finished, if the solution is not beautiful, I know it is wrong."

- R. Buckminster Fuller

 

[MechEng2005]

As Trashcanman stated, the heat transfer coefficient will change with the air temp. However, instead of (initially) doing a many-stepped calculation, you may be able to use a heat transfer coefficient evaluated at the average of inlet and outlet temperature. This will at least give you a rough idea. Then, you can decide if you need to do the steps.

- MechEng2005

 

[tsgrue]

.

You might also try out these software applications for analysis and design of earth-air heat exhangers for heating, cooling, and ventilization of buildings...

L-EWT

http://www.ag-solar.de/en/service/d_sim.asp

GAEA, KeepCool

http://nesa1.uni-siegen.de/softlab/gaea_e.htm

http://nesa1.uni-siegen.de

OIB

http://www.oib.or.at

WKM

http://www.igjzh.com/huber/wkm/wkmfr.htm

EnergyPlus

http://www.eere.energy.gov/buildings/energyplus/about.html

.



tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation

http://hhwq.blogspot.com

 

[swguru]

Gentlemen, Thanks very much for the feedback. Just getting back to the daily grind after the holiday season, so I be looking into this more over the next couple days. Happy New Year!

swguru

 

[swguru]

Trashcanman,

I calculated the heat loss for a short length. For my problem the result for the first 10cm is 1.1W, calculated from (2*pi*Ksoil*(Ts-Ta))/cosh^-1(X/r). To calc the temp drop of the air, do I need now recalculate the total heat transfer coeff (ht) and then calc To from To=((q'+ht)*Ts)/ht))? If not what equation would I use to translate that heat loss to a temperature drop in the air?

swguru

 

[tsgrue]

.

The literature is fairly well developed on this subject. Below is a list of papers with which to begin for background. Probably half of these can be downloaded directly from the W3 without charge. The others you should be able to obtain through your local public or college library...

Thermo-hydraulic design of earth-air heat exchangers, M De Paepe et al, Energy and Buildings, 2003

Analysis, design and testing of an earth contact cooling tube for fresh air conditioning, Joerg Henkel et al, Proceedings of Solar 2004

Subsoil Heat Exchangers for the Air Conditioning of Livestock Buildings, D Deglin1 et al, J Agric Engng Res, 1999

Parametric and experimental study on thermal performance of an earth–air heat exchanger, Ashish Shukla et al, Intl J Energy Res, 2006

A one-dimensional transient analytical model for earth-to-air heat exchangers, taking into account condensation phenomena and thermal perturbation from the upper free surface as well as around the buried pipes, M Cucumo et al, Intl J Heat and Mass Trnsfr

Annual thermal performance of greenhouse with an earth–air heat exchanger: An experimental validation, G Tiwari et al, Renewable Energy, 2006

Evaluation of earth-to-air heat exchangers with a standardised method to calculate energy efficiency, Jens Pfafferott, Energy and Buildings, 2003

Numerical simulation, technical and economic evaluation of air-to-earth heat exchanger coupled to a building, M Bojic et al, Energy, 1997

.


tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation

http://hhwq.blogspot.com

 

[magicme]

swguru

check your viscosity .... should it be 1.66E-5 ?

also, i think k = .02625 (assume 35C)

vc66 is right about the velocity, but i am calculating h = 23 inside the pipe (probably due to our different viscosities). if i use your h = 13, i get Texit = 30F as you do.

for a 10C temperature change, you can use air properties at the average in the duct (i wouldn't iterate for the first cut calculation, given that you are skipping the pipe wall conduction and contact resistance to the soil).

based on these numbers and the 5.6m length, i get Texit=25C , but my h looks a lot higher than yours, so that would explain my lower exit temperature.

this problem is well documented (as tsgrue saya) and if you are inside incroprera, all the equations are in there somewhere.

regards,

magicme





------------------------------------
there's no place like gnome.

 

[magicme]

swguru,
as usual, i have second thoughts on your question and my answer.

i assumed a constant pipe wall temperature at 22C, per your original data on soil temperature where the pipe is buried. my thinking is that (in a first-cut calculation) the air mass flow rate and net heat transfer (DT(air) = 10C) will not change the soil temperature, and the pipe wall is at soil temperature.

i think (?) that you calculated some kind of external effective convection coefficient (h = 13 ?) based on soil conditions, and that i misunderstood that to be your internal convection h..... i think?


regards,

magicme




------------------------------------
there's no place like gnome.