Searching for an equation - cfpm/heat exchange

[wilsonbb30]

Hi,
I am involved in a project that cools outside air to underground temperatures at 6' below ground in Florida soil. we are using thin wall PVC @ 4" diameter. i am looking for an equation that will tell me how long to make the pipe and what the ideal cfpm should be to achieve desired temperature for exiting air. this is my first time visiting a forum of any type and my experience in physics is limited. i have been educated in algebra, that should come in handy.

 

[russ_watters]

Unfortunately, heat transfer coefficients are generally found experimentally. The math required to calculate the fluid dynamics of convection is not only difficult, but pinning down the variables is near impossible.

Can you do some tests?

 

[Mech_Engineer]

It's possible to get at very least order of magnitude calculations (if not better, depending on knowing exact operating conditions) for heat transfer from a tube with fluid flowing through it. However, the equations are rigorous and have many pre-conditions and empirically calculated constants. A knowledge of heat transfer and fluid dynamics would be a must to really understand what's going on.

Modern heat-transfer textbooks will have these equations and their derivations in them, so that's an OK place to start. However, the equations' derivations will probably be based on Calculus and Differential Equations, so they will be quite difficult to follow for someone with an Algebra background.

 

[wilsonbb30]

Thank you russ for your reply. it appears i have stumbled on a complex topic. it seems pretty simple to me, the project I'm involved in, but the math behind it is boggling. i have found other test results online from a university that attempted the same project. they used 12" schedule 40 PVC, buried to a depth of 6' in Florida soil and measured to volume of air passing through at 1000 cfpm. it cooled the air stream from 90 degrees ambient outside temp to 82 degrees upon exiting the 100' underground pipe.

in my design of this project, i am using 4 underground pipes, all of which are 4" in diameter and I'm using thin wall PVC to maximize heat transfer and to provide 3X more surface area. In addition, I am running the pipe 300' instead of 100', and I am applying two 180 degree turns per pipe to allow the air inside to scramble a bit - evenly distributing the cooler air to achieve a more thorough consistency at exit point. I am also running the pipe at different depths to allow for gradual cooling to cut down on condensation. 4', 5' and 6' depths. i will be using an industrial exhaust fan to create positive pressure at the exit of the pipe. the cfpm flow of air through the piping should be around 5700 cfpm. i was hoping to be able to calculate the heat exchange that took place and run some numbers to see if my pipe length needs to be longer. it would look something like this: if the entry air temp is 90 degrees, and the pipe is 300' long and the air is moving at 5700 cfpm; what would the exit temp be? i could use the data from the university but i am not sure how to correct for the changes in the constants like pipe thickness and diameter. anyhow, there's my brainstorm for the week. thank you for your reply.

 

[Mech_Engineer]

I would say your first task will need to be calculating the Reynolds Number for the air flowing through the pipe. Where this number falls in the range from laminar to fully developed turbulent flow will deternime what calculations need to be used.

http://en.wikipedia.org/wiki/Reynolds_number

 

[RTW69]

Go to the "Build it Solar" website and go to the "Passive cooling: Earth Tubes" area. There are several articles posted that will be helpful. There has been quite a bit of research on this type of cooling but the heat transfer through soils is very complicated and there are economic trade offs between the length of the tube and fan energy.