Cooling Air Fluids/Thermo Help

I am looking to cool my air supply before applying it to an application in a temperature chamber. The chamber will be at -40°F the air supply from outside the chamber will be ambient temperature. I want my supply air to be cooled to the -40°F before it enters my application. I was thinking simply routing the air through coiled copper would do the trick in the chamber but I was hoping to have some assurance via equations( length and size of tube needed to ensure all heat has been removed) I am thinking this should be simple but I keep finding stuff in books over complicating the process(I think)

Please Help.

You need to contact a specialist in air conditionning application

WAYYYY too much stuff that you havent tough about....

I dont get it how people thinks some things are simple.

An air conditioner has condenser and evaporator and much more going on to actually cool the air from hot to cold. I will already have the chamber cold. I just need to figure out the rate at which the air in a tube will cool based on length, area, flow rate, tube thermal coefficient etc....

-40°F --- There is environmental testing equipment available for rent and purchase that can accomplish this.

I don't know that it would be cost effective to design your own..

Ha I guess I wasn't clear on this I have the temp chamber its built and designed and goes to -40. I have something that requires actuation via compressed air inside the chamber. I want to monitor the holding ability for the air at the cold temp. My air source naturally is outside the chamber so I need to send air in but before it is use the air I want it dropped down to the temp of the chamber.

Ahhhh now I understand....

You assume natural convection outside a straight tube.

You need to have the dimensions of the tube, then your mass flow than will go in the tube.

Calculate forced flow inside and then natural convection on the outside. Add 15-20% lenght to be sure.

I'll work on that after 4pm...

I was thinking it would be along the line of Q=hA(Tw-Tt) but this wont help me figure out the tubing required though because I don't know Q ahead of time or do I?

A little more background into the situation the air will be filling a container that shouldn't leak air in the cold temp chamber. I intend to put a flow meter inline to measure if air is moving through the system, since once the proper pressure is achieved it should be static assuming the container isn't leaking. I just want to ensure that the air going into the container and anything that might pass through the flow meter is cooled to the temp chamber so it doesn't skew my pressure or give me "fake" flow readings( allowing more flow to build up pressure after the air cools)

I know the temp of the chamber or tube surface, and the temp of the air going in at 90PSI, the heat constant h for air is known. I am just not making the connection to figure out the surface area of tube to achieve the temp change.

I dont have time to work it but yes you know Q if you know your max mass flow.

You have Q max then you find the convection factors (inside and outside) and you'll find the length. It's been a long time since I've done this I would need to look at an example. Its a very classic exercise.

First you write the differential equation for heat transfer ( you follow a slug of air 1 unit long) and get
Rho *A*c *dT/dt=h*p*(T0-T)
for a unit length of pipe
rho = density of air
A cross sectional area of pipe (and slug of air 1 unit long)
h = overall heat transfer coefficient ( approximately equal to the inside coefficient since stagnant outside h0<<hi)
p= perimeter of pipe
The solution at any point along the pipe, x= t*v is:
Ta-T=(Ta-T0)*exp(-q*t)
q=hp/(rho*A*c)
Ta= warm air entering pipe
T= temperature along pipe at time t after entering pipe
T0= cold outside temperature
Now it is obvious you can't get to T0 in t< infinity, so you will have to decide a more reasonable value, say T2>-40

From the solution you will next get the transit time, t= tf
tf=1/q*Ln(Ta-T0)/(Ta-T2)

Ln natural log
And L= tf*v
L = length of pipe
v = velocity of fluid (from mass flow rate and assumed diameter)

Of course, you may have to iterate to get the hi coefficient which is dependent on the mass flow rate and the diameter of pipe.

So you start with an assumed diameter and the required mass flow rate to get v and h and a realistic final temperature, T2 to get tf

And finally use
L=tf*v
to get the length of pipe.

How can anybody read this???

Thank you for the information. Let me try to clarify and make sure I am following. Using your variables I know Ta, T0, P, h, q, and A. I use "tf=1/q*Ln(Ta-T0)/(Ta-T2)" to find out the time it takes to exchange the heat.

Next I use "L= tf*v" to solve for the length. Since this should be built up pressure in the line not moving much do I solve for v using my pressure = 1/2*rho*v^2?? Also where does the cross section come into play. Thank you for bearing with me.

Well, I looked over your comments and now understand that you want a ready source of air at pressure and -40 deg in a container. I solved the usual problem of continuous flow which is not your case.

Before tackling this problem, you must state the accuracy needed of the p and T needed, and the demand rate , i.e. the maximum delivery of this air to the experiment so that you can properly design the container and the tube delivery system.

This is not a simple problem as you suggested, unless you have plenty of time between experiments.