Pipe Heat Equation - Internal Convection 1

[compost]

I am doing a test to find the heat generated from a heap of compost.Is there an equation which gives me the rate of heat transfer. I am using a pipe buried in the compost heap. The inlet and outlet temp. of water is know and so is the mass flow rate. The specifications of pipe ie diameter and length are also known. The compost temperature is also known.

Is there any equation which gives me the rate at which the water gains heat. I have used 2 equations (one is mass * specific heat * temp. rise and the other one using Nusselt number and hence finding h for water and pipe and then calculating rate of heat transfer) but the results that I get in both cases is very different.Infact the answer that I get in the second case is 10times the first case.



Can anyone help.

 

[HamishMcTavish]

i'm not entirely sure what you're trying to do but have a look at this to see if it answers your question

http://rms1.agsearch.agropedia.affrc.go.jp/contents/JASI/pdf/society/42-0889.pdf

Cheers, HM

No more things should be presumed to exist than are absolutely necessary - William of Occam

 

[MintJulep]

Your experiment would seem to measure the heat transfer from a compost heap to a pipe with water flowing through it.

That is quite a different thing than measuring the heat generated in the heap.

 

[HamishMcTavish]

Also see the appendix A in the following

http://www.rmcgreenteam.ca/Composting Project Status Report (Feb 06).pdf

No more things should be presumed to exist than are absolutely necessary - William of Occam

 

[Dave41A]

If you know the mass flow rate and inlet and outlet temperatures of the water, then you have the heat transfer rate to the water from the compost.

If you are trying to do a Nusselt number analysis, presumably you are assuming some heat flux through the walls of the pipe or an inner pipe wall temperature, and working forward from there. The key here is that you have to make assumptions to begin the calculations. Further, any such analysis is overly simplistic since the total heat transfer coefficient from the compost to the water depands upon the condcution through the pipe as well as the contact resistance from compost to pipe, and the rate of heat transfer within the compost. There is probably no way to compute all this.

In short, your idea of using inlet and outlet temperature and mass flow rate is the right way to go.

Good luck.

 

[compost]

Hey Dave thanks for the reply...

during composting the temp of the compost heap crosses 70 degrees and remains like that for about 2-3 weeks. and it is this heat that we plan to trap..

the problem we are facing is when we dig to bury the pipe...the compost loses the heat to the surroundings...and we get compost at aroung 45 to 50 degrees during the test...

if we go ahead with the test at these compost temperatures, measure the heat flow and then assuming the same heat flow rate and compost at 70 degrees how correct would be my theoretical prediction for the temp of water at the pipe outlet...

 

[IRstuff]

Sounds to me like both of your calculations overestimate the amount of heat transferred. The heat rise needs to be multiplied by the heat transfer coefficient, as a minimum. You appear to assume 100% heat transfer, which is never the case.

TTFN

FAQ731-376

 

[IRstuff]

That should have been "temperature rise" and not "heat rise"

TTFN

FAQ731-376

 

[Dave41A]

compost:

I'll repeat what I think you're saying to make sure I have it clear in my head.

Presumably you are measuring the temperature of the undisturbed compost at 70 degrees using some sort of probe thermometer. All measurements are to some degree "instrusive" but the heat transfer up and out the thermometer probe is probably negligible.

However, before the test, you stir up the compost as you prepare to bury the pipe and its temperature drops due to exposure to the air. On top of this, during the test, it sounds like there is water flowing in this buried pipe. This will remove heat, lowering the temperature of the compost further.

I understand your question about the accuracy of the heat transfer rate...the short answer is that for a heat exchanger, Q=U*A*DeltaT. While area (A) would be the same in both the 45 degree and 70 degree tests, U does exhibit some temperature dependence, but I doubt it will change by much. So, yes, you could use the overall heat transfer coefficient's value at 45 degrees as an approximation to its value at 70. I am just not sure you'll ever really see 70 in actual practice since the heat transfer rate within the compost is probably pretty low and any compost temperature you build up will be decreased when you turn on the water pump.

As one way to proceed, you could bury the pipe (with water in it) and wait a few days for the compost heap to recover to 70 degrees (or build the copmpost heap on top of the pipe in the first place). Then turn on the pump and the compost temperature will definitely drop, especially if your probe is in the close vicinity of the pipe, which is acting as a heat sink.

Hope that helps,

Dave

 

[IRstuff]

That's an interesting sidebar. If you actually did manage to suck out all the heat, wouldn't the composting process significantly slow down, which will decrease the amount of heat production?

TTFN

FAQ731-376

 

[Dave41A]

IRStuff:

I dabbled in this a little once before, and like all biological processes, if the internal temperature gets too hot, the bacteria will actually start to die from over-heating, too cold, and they lose efficiency, so there's a happy medium.

I'm a little confused by your statement on 12 Dec: i.e. "the [temperature] rise needs to be multiplied by the heat transfer coefficient, as a minimum," which follows the assertion that both methods that he proposes "overestimate the amount of heat transferred."

If compost is measuring inlet and outlet water temps and knows the mass flow rate, shouldn't this be enough to measure the total amount of heat transferred to the water (i.e. mass * specific heat * temp. rise as proposed in the original post)? I don't see how the heat transfer coefficient factors in.

Dave

 

[Unotec]

You can calculate the transfer coeficient from here, though
But I think this is not what the PM is after

<<A good friend will bail you out of jail, but a true friend
will be sitting beside you saying ” Damn that was fun!” - Unknown>>

 

[IRstuff]

The OP stated a couple of approaches. The first appears to be simply the mass transport multiplied by the temperature difference, which ignores the actual thermal conductivity of everything between the compost and the water.

The second approach appears to be calculating the heat transfer within the pipe, again, ignoring everything outside.

Since the compost is mostly organic, with relatively low thermal conductivity, either of the two stated approaches would result in an overestimate of the available heat transferred.

But, again, if the objective is to make something that is efficient at removing heat, then the bugs are no longer going to be warm and cozy. If not, then one might wonder whether the investment is worth the return.

In both cases, the OP would need to include the thermal conduction path from the compost itself to the water, which includes the organic material, some air, and the pipe wall.

TTFN

FAQ731-376

 

[Dave41A]

IRStuff:

I'm still confused. Yes, there will be the thermal resistance within the compost, from the compost to the pipe, within the pipe, and from the pipe to the water, but since the original post asks "Is there any equation which gives me the rate at which the water gains heat?", then it seems to me that mass flow rate times the temperature rise (of the water) is all that is required.

In short, if the water gains X kJ/sec at steady state, then the compost is giving up X kJ/sec to the water. The thermal resistance is relevant only if one wants to actually compute the temperature profile between the compost and the water (which isn't necessary because the temperature of the compost can be measured directly).

Hope that helps,
Dave

 

[sailoday28]

compost (Mechanical) 10 Dec 08 10:16
I am doing a test to find the heat generated from a heap of compost.Is there an equation which gives me the rate of heat transfer.

Maybe this is too theoretical or impractical. Can you take a then metal hollow tube, coat with good insulation on inside and outside except for the ends? Insert a thermocouple at both ends.
Drill into compost to depth you are concerned about. Insert (or force) tube, vertically to that depth. Thermoucouples will thus give temp and a simple heat conduction calc will give heat flux at that depth and location. Repeat for other lcoations.

Regards

 

[IRstuff]

For a steady state solution, the thermal conductivity is only partially important, but for a dynamic condiction, which this is, since the water in the pipe is presumably flowing, the heat transfer is all about RATES, which requires knowledge of the thermal conductivity.

Remember that htc*area*deltaT results NOT in joules, but in watts, which is a heating rate. Yes, you can couch the problem solely in terms of deltaT's but the reason the deltaT would be different is because of the thermal conductivity.

Otherwise, why would someone go to the expense of making copper or aluminum heat sinks? Consider cooling your PC's processor; it's the compost pile, and the air is the water in the pipe. If you used a styrofoam heatsink, do you think that the processor would stay cool? The deltaT would be gigantic, but the heat flow would be nil.

TTFN

FAQ731-376

 

[sailoday28]

IRstuff (Aerospace)has a good point with the 'sidebar'. With my prior post, if practical, would give an idication of how the heat flux at a given location is varying with time.

 

[Dave41A]

The rate of heat transferred to the water is simply mass flow rate times the temperature change of the water times the specific heat of the water. Since mass flow rate of the water is indeed a rate, the resulting computation will be in kW (or BTU/sec):

(kg/sec)*(Temp change in K)*(kJ/kg-K) = kJ/sec = kW

Multiplying this result by the heat transfer coefficient (say, in W/m^2-K) will result in incorrect units and a wrong answer.

Compost: If you are trying to measure the RATE of heat tranferred from the compost to the water, mass flow rate * temperature rise * specific heat is all that you have to do (this would be the "rate at which the water gains heat" from the original post).

If you are trying to measure the RATE of heat "generated" by the compost, the compost (with pipe running through it)should be contained in a suitable well-insulated container so that (nearly) all heat generated within is transferred to the water. Then proceed as before to obtain a reasonable approximation.

If you are trying to measure the AMOUNT of heat generated by the compost (say, in kJ/kg), then the above computed rate needs to be integrated with respect to time (numerically) over the life cycle of the compost heap. This would be likely quite a challenge in practice and undoubtedly difficult to achieve with any precision.

 

[compost]

Indeed I am measuring the rate of heat transfer from the compost to the running water in the pipe. Although as we proceed with the experiment we would like to know the total heat generated by the compost in a given time.

For those who say that I will end up slowing the composting process. The optimum temp needed for the microbes in the composting process is in the range of 45 - 50 degrees. But we have compost crossing 70 degrees which again slows the process. So to cool the compost we need to blow air though it which is like 10 times the required air for composting.

So instead of blowing that much air and letting that heat escape why not trap it and reduce on the blown air...and with 70000 tonnes of compost a year at our plant the results might be quiet good.

 

[sailoday28]

Dave41A (Mechanical) and IRstuff (Aerospace
For actual heat transfer to the water, the change in inlet and outlet temp is necessary, but the change in internal energy of the control volume of water should also be taken into account. Calculation of internal energy of the water would require mass, specific heat and temperature variation as a function of distance along the pipe.
Calculation of heat transfered from the source would have to include change of internal enery of metal piping.

Have you any comments on my previous suggestion with the vertical tubes?

Regards