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feel like a total idiot - temp rise in heated pipe

feel like a total idiot - temp rise in heated pipe

feel like a total idiot - temp rise in heated pipe

(OP)
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
 

RE: feel like a total idiot - temp rise in heated pipe

Quote:

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?

RE: feel like a total idiot - temp rise in heated pipe

(OP)
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.

RE: feel like a total idiot - temp rise in heated pipe

(OP)
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?
 

RE: feel like a total idiot - temp rise in heated pipe

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

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RE: feel like a total idiot - temp rise in heated pipe

(OP)
"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?

RE: feel like a total idiot - temp rise in heated pipe

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>>

RE: feel like a total idiot - temp rise in heated pipe

(OP)
"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.

RE: feel like a total idiot - temp rise in heated pipe

(OP)
ah.. sorry irstuff.

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

RE: feel like a total idiot - temp rise in heated pipe

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>>

RE: feel like a total idiot - temp rise in heated pipe

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

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RE: feel like a total idiot - temp rise in heated pipe

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.

RE: feel like a total idiot - temp rise in heated pipe

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.

RE: feel like a total idiot - temp rise in heated pipe

Your equations are confusing me.
The power input you need is Q(W)=W(kg/sec)xC(J/kg°C)x (Tout-Tin)(°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/m2°C)xπxDi(m)xL(m)x (Tw-(Tout+Tin)/2)(°C)
So you need to define the wall temperature to determine the length: see MintJulep's post for a discussion.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads

RE: feel like a total idiot - temp rise in heated pipe

(OP)
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.

RE: feel like a total idiot - temp rise in heated pipe

Quote:

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).

RE: feel like a total idiot - temp rise in heated pipe

(OP)
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?
 

RE: feel like a total idiot - temp rise in heated pipe

(OP)
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....

RE: feel like a total idiot - temp rise in heated pipe

Close.  q2 = 300W.

RE: feel like a total idiot - temp rise in heated pipe

If you are using electric heat you have direct control over power input and heat transfer coefficients are irrelevant.
The pipe has to be long enough to contain the heater, which can be designed to be less than an inch. The smaller you make the heater the more likely it is to burn-up if you lose gas flow.

Look at the design of Sylvania compressed air heaters.
http://www.sylvania.com/content/display.scfx?id=003684141

RE: feel like a total idiot - temp rise in heated pipe

(OP)
mintjulep

I dont get that. the only power input to the system is to the heater, this heat must be shared between the loss into the flowing gas stream and the loss through the insulation to the ambient air. So why would you assign the entire 300W to q2?

Compositepro
I have control over the power input but I am fixing it to 300W. The way the model works is that the entire aluminum block will be generating 300W because I will just presume that the  block spreads the heat evenly. At this point I dont care about the actual heater implementation. I just want to spend 300 watts heating a block and find out how long the tube in the block needs to be in order to get my gas temp up to 120C
 

RE: feel like a total idiot - temp rise in heated pipe

I think you are in the right track. Just remember that your focus is not how much heat you're generating but how much the gas it taking away.
You have to calculate the heat removal rate per unit of length. It's been a while since the books, but I think chapter 3 on the fundamentals of heat and mass transfer by Frank Incropera has the exact same scenario you. Basically you have a radial system with energy generation.
It is a simple process but with many equations.

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

RE: feel like a total idiot - temp rise in heated pipe

You have already determined that you need 300 W INTO THE GAS.

If you don't put 300 watts into the gas, you will NEVER get the temperature out you need.

So the heater needs to provide those 300 watts + whatever is lost through the outer insulation.

RE: feel like a total idiot - temp rise in heated pipe

(OP)
MintJulep,

Ah, OK it was just a misunderstanding. I have a 300W heater. I dont know how much will go into the gas (yet).

But yeah, for the purposes of this analysis I think either one is fine.

unotec,
I'll take a gander hopefully it is there.

thanks.

RE: feel like a total idiot - temp rise in heated pipe

(OP)
Still being dense and still not getting my answer:

Ok, I looked at incropera book again. I see the example you are talking about but it is not answering what I need. As per MintJulep, I know the amount of heat going into my gas stream. I need to know how long a tube needs to be to get my temp to rise by 115 degrees.

Ok, so lets choose a length 100 CM. and I have 300 watts. I'll even choose a diameter 1.25 cm.

so now I know my heat input per unitlength:

q'=300/(2*pi*r)

ok, so now how do I figure out the temp rise associated with this heat input?

i'm totally missing something I feel  like im right back where I started
and perhaps I am, just, in this case I have picked a length along with the power.

q"=Qconv/(Pi*D*L)=7600 W/m2

tout=Tin+q"*2*pi*r/(mdot*Cp)*L

whoops! and there goes the involvement of the L which means I am back to where I started.

This very frustrating. If 300 watts goes into my flowing gas stream, there must be a maximum temp that is gets to for a fixed length, flow, and Cp. Forget the implementation, I can keep increasing the heater power until 300W goes into the gas stream, but the freakin length must matter somehow!

This seems so damn basic and I simply can not find it in the book! So, who can show me how stupid I am and how easy this is. All the information should be here. I'll list it again:

Q watts goes into the flowing gas
the gas flows at mdot Kg/s
The temp going into the pipe is T1
The temp coming out of the pipe is T2
The heat capacity of the gas is Cp
The Inner Diameter of the pipe is Di
The outer Diameter of the pipe is Do
The length of the pipe is L
the convection coefficient is h

you get the gist.

Im just looking for the relationship to find T if I have everything else, or to find L if I have everything else. All of these terms must matter.

every time I do it, the damn length term keeps dropping out.
If I increase the flow rate, the output temperature must drop so the flow rate must matter.
based on a flow rate, there must be a minimum length for enough heat to get into the gas stream to raise the temp to T2.
I realize the pipe temp will change with these scenarios, so the pipe properties must matter.


-help....












 

RE: feel like a total idiot - temp rise in heated pipe

Please do read also the advice that is given. Go back and see what was said about wall temperature: this datum is lacking in your list, you need it to solve your problem.
And if you don't know it, make a guess, use the set temp for the thermostat in the heater or whatever.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads

RE: feel like a total idiot - temp rise in heated pipe

(OP)
I think if you go back to my 11:35 posat on oct 22, you'll see that I understand about the temperatures and picking htem. Which is fine. I was having trouble regardless of what they were, that is why I kept everything as variables.

Here is what I ended up doing (for those that may search for a similar thing).

I presumes that I could insulate the system well enough that most of the of the heat (an order of magnitude) went into the gas as opposed to leaving through the insulation.

Then I presumed a pipe size and that 300 watts went into the gas.

then I got a volumentric heat generation rate of a specific pipe size of A*L. qdot=Q/(A*L), where A is the crossectional area of the pipe. I presumes all the heat is flowing into the pipe and it is acting like a generator.

Then using hte heat generation rate, i found Tout based on various lengths of tubing. As the tubing gets longer, the tout rises as does the power. using:

Tout=(qdot*A*L+mdot*Cp*Tin)/(mdot*Cp)

Once I have Tout, then I know delta T and

q=qdot*A*L

noting that in each equation I am changing only L.

This gives me reasonable numbers and tell me that if I have a 30cm tube of 1/2" I will get the temperature I need with 120 watt of heat. I will use a 300 watt heater, and hope for the best.




 

RE: feel like a total idiot - temp rise in heated pipe

So your conclusion is that q=qdot*A*L=Q : in other words you confirm that what you assumed as an input is the result.
The point you miss is that the outlet temperature does not depend on length: if you need 120 W to heat up your fluid flow rate, this will be true for a heating length of 30 or 300 cm.
If your heater delivers 300 W and is 30 cm long, well that should be fine with your numbers. Go on with testing, you'll probably get a higher outlet temperature and regulating the heater you'll come to the result you need.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads

RE: feel like a total idiot - temp rise in heated pipe

(OP)


Prex,
Yeah, but the way that I set it up is that the longer the tube the more power goes into it. I just picked a length a found a qdot that I used for whatever length. so I'm not sure I missed the point, I just used a guess at a particular instance and extrapolated form there.

I know its not the most accurate way to do it. The correct answer requires h and a good understanding of how much heat leaves the system and how hot the pipe gets (never mind that its not really a pipe, but a block with holes in it).

Thats why I doubled it, and will let my controller do the work.
 

RE: feel like a total idiot - temp rise in heated pipe

You need to get your story straight.  Earlier, you claimed it was open loop, so there is no control, and now, there is.  Which is it?

And, you keep refering to "more power."  That's a math error.  Your input power is divided aross the length you design for.  There is never more power demand than what you put in.

TTFN

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