Buried Air Duct Length Calculation
Buried Air Duct Length Calculation
(OP)
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
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





RE: Buried Air Duct Length Calculation
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RE: Buried Air Duct Length Calculation
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.
RE: Buried Air Duct Length Calculation
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See post: "Earth-air heat exchangers and solar chimneys for HVAC"
thread403-204634: Earth-air heat exchangers and solar chimneys for HVAC
http://www
There are lots of papers on this. Try an an Internet search for "earth air heat exchanger design"
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tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com
RE: Buried Air Duct Length Calculation
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
RE: Buried Air Duct Length Calculation
- MechEng2005
RE: Buried Air Duct Length Calculation
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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://w
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tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com
RE: Buried Air Duct Length Calculation
swguru
RE: Buried Air Duct Length Calculation
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
RE: Buried Air Duct Length Calculation
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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
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tsgrue: site engineering, stormwater
management, landscape design, ecosystem
rehabilitation, mathematical simulation
http://hhwq.blogspot.com
RE: Buried Air Duct Length Calculation
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.
RE: Buried Air Duct Length Calculation
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.