feel like a total idiot - temp rise in heated pipe

[rhirsch]

I've searched for this throughout the forums. Its seems so simple, but I am simply not getting it:

I have a pipe with gas flowing in it. I know the input temp and output temp I want. I know how much power I am going to put to the heater I know the diameter. I know the flow rate. I think I know everything to be able to discern the required length of the tube to achieve the desired output temp. But I am not seeing how to do it.

Here is the data:
Tin=5 deg C
Tout (desired) = 120 deg C
Mass flow rate, mdot= 3.6 kg/day
Heat input, qconv = 300W
Inner Tube diameter Di= .5 in
Outder Tube diameter Do = .5125 in (sorry about units switch)
h = 25 W/Km2

The problem I am having is that I think I can do the problem if I know the heat flux, but this flux is dependent on the length of the tube (because the surface area increases with length).

so I know
qconv=qdot*Vtube and
qdot=mdot * Cp *(To-Ti)

assuming its insulated and all the heat goes from the heater, through the pipe and into the gas. Then:

qconv=mdot * Cp * (To-Ti) * A * L

and then

L = qconv/(mdot * Cp * (To-Ti) * A)

but this means that the length gets longer if I increase the power for the same temp differential. This makes no sense, and why don't I need the convection coefficient?

I haven't done this stuff in years (decades) and I am obviously doing something wrong. This should be simple....


argh

 

[MintJulep]

assuming its insulated and all the heat goes from the heater, through the pipe and into the gas. Then:

Then the length doesn't matter does it?

 

[rhirsch]

yeah see, that is the problem, clearly that never happens, so where do I go from there?

the thing in insulated, but of course heat leaves, but I dont really have a good way to measure how much. Even if I did, it would just tell me that 5W is leaving through the insulation and 295 must be going into the gas stream and I would be back to where I started again.

There is something fundamental I am missing.

 

[rhirsch]

Actually, now that I htink about it.... even if all the heat goes into the pipe, why doesnt it matter what the length is?

it takes power to raise a temperature of a substance and time to raise it based on its heat capacity.

So if the differential volume of gas isnt in the pipe long enough to raise the temp up to what I want, then I wont ge tthe proper output temp. So, at least in my head, the longth should matter.

Said a different way, if the only way for heat to leave the system is through the gas, then I expect that the heater block (or tube wall) will rise to some temperature while the gas heats until some sort of steady state is reached. And that steady state gas temp is based on the length of the tube if I want a certain To.

Am I wacky here?

 

[IRstuff]

Depends on the verisimilitude desired from the answer. If the degree of accuracy is +/-50%, then sure. However, if you need that more tightly controlled, then you'll need to measure the temperature of the gas. If you do that, then the problem is nearly length independent, assuming you have sufficient length and mixing to achieve the desired result at all.

TTFN

FAQ731-376

 

[rhirsch]

"assuming you have sufficient length"

this is what I am trying to determine. For the details I posted above, if the answer is 5cm then yeah +/-90% is just fine. But if the 'sufficient length' is 200 cm, then my accuracy must be better.

Let me ask a different way:

Is 90cm sufficient? is 30cm sufficient? How do I know?

 

[Unotec]

If you have a flow, and know the gas characteristics, you can calculate how much residence time inside the exchanger you require

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

 

[rhirsch]

"If you have a flow, and know the gas characteristics, you can calculate how much residence time inside the exchanger you require"

I totally agree. I am asking how.

 

[IRstuff]

I was referring to your desired control over the TEMPERATURE.

TTFN

FAQ731-376

 

[rhirsch]

ah.. sorry irstuff.

No I will be controlling the temp to within +/- 3 degrees so around 2%

 

[Unotec]

q is heat flux in watts, watts are J/s or m^2.kg/s^-3


<<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]

how are you going to control the temp, and where is the sensor?
Laminar/turbulent?
volumetric flow?
gas specific heat?

you should do a dimension check on your first equation:

mdot*spec_ht*delta_T = Pin to the first order. If you ignore mixing and convection, then, you can apply Pin instantaneously, and achieve the desired temperature in zero length; obviously impractical and physically impossible.

TTFN

FAQ731-376

 

[jasno999]

I might be missing somehting but I would find the heat transfer thruogh the pipe. YOu need the metal conductivity and thinckness, and the insulation conductivity and thickness alogn with the pipe length (You can assume a length to start).

Then you can figure the amount of heat transfer you have per that given length of pipe. That is the only heat you are goign to lose so you can figure out the temperature at the exit per a length.

 

[MintJulep]

The heat can only go two places. Into the gas, or out through the insulation.

The magnitude of heat transfer in each direction is a function of delta-T between the pipe temperature (for now, let's assume it is constant through its thickness) and the gas and ambient air.

You have correctly calculated the heat needed to cause the desired temperature rise in your original post.

What you are missing is the temperature of the pipe. To achieve that heat transfer a shorter pipe needs a higher temperature, a longer pipe a lower temperature (assuming the flow parameters are the same).

You don't need the coefficient of convection because by definition all it is is the magic factor to numerically equate qdot with mdot*delta-T. And it's not a constant down the length of the pipe.

So, any length will do. You really only need to worry about it if you are interested in limiting the pipe surface temperature, or keeping the useful heat:lost heat ratio to some limit.

 

[prex]

Your equations are confusing me.
The power input you need is Q(W)=W(kg/sec)xC(J/kg°C)x (T[sub]out[/sub]-T[sub]in[/sub])(°C) and I suppose this gives your 300 W.
Now you must input this heat through tube wall; the equation is, in a first approximation: Q(W)=h(W/m[sup]2[/sup]°C)x[&pi;]xD[sub]i[/sub](m)xL(m)x (T[sub]w[/sub]-(T[sub]out[/sub]+T[sub]in[/sub])/2)(°C)
So you need to define the wall temperature to determine the length: see MintJulep's post for a discussion.

prex

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[rhirsch]

OK here we go:

unotec

q is heat flux in watts

heat is a quantity of energy in joules
heat rate,q, is a quantity of power in watts
heat flux,q", is a quantity of power through a surface W/m2
volumetric power generation or flux, qdot is a measure of power generated over an entire volume.

ok. This is all straight out of the textbook as are the equations I started with. I am having trouble applying the equations.

IR stuff
how are you going to control the temp, and where is the sensor?
Laminar/turbulent?
volumetric flow?
gas specific heat?

sensor and control temp are irrelevant. This analysis is all open loop. power into the gas, will heat the gas to a certain temp depending on residence time in the heated tube.

Lets just do turbulent, I believe the equations I started with assume that condition.

Its a compressible gas, but the pressures are low. Lets just do the analysis as if it were a liquid.

the gas is H2, the specific heat capacity of H2 is 14.31 kJ/KgK. the value should be irrelevant. I'm nlooking for the equations to use.

jasno999
I might be missing somehting but I would find the heat transfer thruogh the pipe

I dont think I do need to know that, and if I did I would need to know more quantities than you listed. I would need to know the outside temp of the pipe for example. There are three important quantities required to do this. I need to know the heat loss through the insulation, the temp of th outside of the pipe and of course the heat lost through the insulation. Perhaps we are getting closer.

MintJulep and prex
The heat can only go two places. Into the gas, or out through the insulation.
I think you hit the nail on the head. I have not been paying attention to both. So let me repose the question this way.

an insulated aluminum block of dims LxWxD, is generating a heat rate of P watts.
The block has T cm of insulation all around it which has a conductivity of K W/mK.
There is a pipe of diameter D going through it with gas, with heat capacity Cp, flowing in it at mdot kg/s.
The ambient air temp is Ta,
the outlet temp of the gas is To,
and the inlet temp is Ti.

How long should the pipe be within the block for the desired To?

I will try to answer this again on my own. But help would be appreciated.

 

[MintJulep]

How long should the pipe be within the block for the desired To?

That is the wrong question to ask.

ANY length can be made to work, the shorter the pipe the hotter it needs to be.

The solution is iterative. You can either pick any arbitrary length and calculate the pipe temperature, or pick any arbitrary pipe temperature and calculate the length.

Keep going until you find a solution that satisfies whatever constraints you might have on length, temperature, or any parameters that are a function of them.

You can't solve for both length and temperature simultaniously (I think).

 

[rhirsch]

I sort of agree, except as I mentioned I have a fixed power input and fixed insulation thickness.

The way I am attacking this right now, is to set up a lumped model. Looks like this:


<-q1 q2->
Tinf-/\/\/\/\-Tins-\/\/\/\-Ta-\/\/\/\/\-Tpipe-\/\/\/\/\-Tgas
1/h1A1 R1 | R2 1/h2A2
|
q=300W

Setting up this equation

I get q=q1+q2

q1= (Ta-Tinf)/(1/h1A1+R1)
q2= (Ta-Tgas)/(1/h2A2+R2)


I'm losing myself again (i've always hated heat transfer).

You can either pick any arbitrary length and calculate the pipe temperature,...

OK lets start here, how do I do this? then it seems that if I finda Tpipe. I should be able to go back above and plug in for Tpipe and redo those equiations. Does this seem right? The end result will either be a new power input or a required minimum insulation. Do I have this more right now?

 

[rhirsch]

more htoughts:

So, I can find the heat going into the fluid by this formula:


q=mdot*Cp*(Tout-Tin)

then to find the pipe temp
q=hA(tpipe-Tgas) where tgas is the mean temp of the gas

Sound right?

This will let me choose a length that I like and find the pipe temp and the power input.

Please tell me I have this part right....

 

[MintJulep]

Close. q2 = 300W.