Calculate thermal time constant and heat losses in a pipe

[nowis]

Hi all,

I'm trying to calculate the heat losses as well as the thermal time constant of a system with a forced water flow inside a horizontal plastic pipe. This is in order to determine what temperature and flow i should input to have a certain desired water temperature downstream of the pipe. I tried to solve the problem taking into account the forced convection inside the pipe, the natural convection outside the pipe, the conduction through the pipe wall and the axial conduction. The flow is laminar all along the pipe. I cannot solve this problem as I have to many unknowns (temperature inside and outside the pipe, upstream and downstream) due to the nonlinear external natural convection (it is not a constant wall nor a constant heat flux condition).
Is there a simple way to determine the temperature downstream of the pipe? Likewise, is there a way to quickly determine if the thermal time constant is mainly due to the axial conduction orto the convection?

Thank you for your help!

 

[IRstuff]

Have you looked at

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

Is this for school?

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[nowis]

Thanks for your reply IRstuff,

No it's not for school, it's for an interface i'm working on. I wish to simulate the system behavior but to do so i would need a better knowledge of the right equations.

I used the nusselt number, which basically is the biot number for a surface and a fluid flow. I found out that the heat transfer is mainly due to convective tranfer. The problem is the conduction used in this constant is the conduction between the water and the wall, not the axial conduction in the fluid.

Or at least that how I understand it!

 

[IRstuff]

The Biot number tells you whether you need to discretize your problem.

"I found out that the heat transfer is mainly due to convective tranfer."

May yes, may no. If your fluid is hot, then radiative cooling might be the dominant factor.

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[nowis]

Thanks IRstuff.

I think I didn't explain the problem well though, too much information is missing. What I am trying to do is to control the temperature of the water downstream of a long plastic pipe. I can control the input temperature by mixing cold (15°C) and hot (55°C) water in a mixing ball valve. My goal is to achieve quick temperature change rates downstream (at least 5°C/sec). I built a first prototype where I measure the water temperature just after the mixing valve's output and the temperature downstream. I noticed a big latency of 7 seconds before the change in temperature measured next to the valve occurs downstream.
The pipe is 2 m long and i have a flow of 3 GPM (12 l/min). I would like to understand weather this time latency is due to convective heating (so i need a better isolation for the pipe) or axial conduction (thus i need to increase the flow). I don't think i will have any radiative cooling with the temperatures i'm working on. So, basically I need to do a dynamic analysis of the system.

Sorry for the approximative English, i hope this description was understandable!

 

[IRstuff]

What is the ID?
Is your length of 2m correct?
How much air flow is there around the pipe?


There would be a 1.5 s transport lag for a 2-m long, 1/2" diameter pipe at 3gpm.

I don't see that it's either radiative nor convective, based on your temperature values. Convective is only about 44W, worst case radiative is 18W.

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize