7 replies to this topic

[ptcruiser]

Hi, I am looking for the basic approach/equation to use to calculate the time it will take a fluid in an insulated pipe to heat up 5 degrees C if the outside air temperature is known.

 

Consider the fluid in the pipe to be water, the environment surrounding the pipe is air. I know the k and h for the pipe, insulation, air, and water, as well as the diameters of the pipe and pipe with insulation.

 

The fluid is not moving in the pipe as well and the length of the pipe is known.

 

I know how to calculate the heat loss/gain but was unsure how to use that to calculate the time it would take the water to heat up in the pipe.

 

Could the lumped capacitance method work? If so, how do I include the insulation in my calculations? (pipe wall thickness is known)

 

Thanks!

Edited by ptrearchis, 16 September 2014 - 01:44 PM.

[PingPong]

What is the temperature of the fluid in the pipe?

 

What kind of fluid is in the pipe? What is its viscosity?

 

What is the ambient air temperature?

 

What is the insulation thickness?

[ptcruiser]

Hi,

Di pipe- 1.37"

Do pipe- 1.5"

Insulation thickness is 1.5"

Assume water in pipe at 20C and that air temperature is 30 C. Want to know how long would take for water in insulated pipe to heat up to 25 C

100 L of water is in the pipe so can estimate that to be 344 feet for the pipe length or 105.15 m

Edited by ptrearchis, 17 September 2014 - 08:44 AM.

[PingPong]

First calculate the U value (overall heat transfer coefficient; I guess that will be in the order of 1 W/m².K) and the outside area A of the insulation.

 

Then calculate how much heat is required to heat up the mass of water plus steel pipe plus insulation by 1 ^oC.

 

Then use Newton's Law of Cooling, which also applies to Heating, to calculate the time to heat from 20 to 25 ^oC against air of 30 ^oC.

Note however that if it is sunny, the solar radiation will speed up the heating (by increasing U).

[ptcruiser]

Hi, thanks! So are you saying calculate U and A to use in q = U* A * ΔT where ΔT=1 or a different equation involving mass or density to get q?

 

This pipe is indoors so I was going to ignore radiation.

 

Which equation for newton's law of cooling were you saying to use that includes a dT/dt?

[PingPong]

No no no.

 

Let's for the moment ignore the mass of the insulation as that is small compared to the water plus steel.

 

You already know the mass (kg) of water. Multiply that with the specific heat (J/kg.^oC) of water.

 

Calculate the mass (kg) of steel, and multiply that with the specific heat (J/kg.^oC) of the steel.

 

Add those two and you have the heat capacity per degree (J/^oC) of the system.

 

 

 

And let's for the moment forget Newton, but let's do it very simple:

 

The average ΔT between air and fluid is 7.5 ^oC. Use that together with U and A to calculate the average Q (in Watt = J/s)

 

To calculate the time t you should then ........ (well, you really should be able to guess that yourself).

[ptcruiser]

Thanks for your help! 

[ptcruiser]

I ended up calculating heat capacity per degree C as you mentioned and then calculated q/L using delta T divided by the some of the resistances from convection and conduction. I took the q/L and multiplied by length of pipe to get an average q for the delta T average value of 7.5 degrees C.

I then calculated time as delta T of 5 degrees C (25 minus 20) times the heat capacity over the average heat gain if this makes sense?

Thanks!