Coil efficiency

[mfqd]

Hi,

I have a heat storage tank with 1 coil inside it, used to heat the water in it.
I have made my calculations, but stil i would like to ear other opinions.
How can i determine de coil efficiency?

Thanks

 

[willard3]

BTU in/BTU out = thermal efficiency

 

[mfqd]

Hi,

I know that, but how can i determine the BTU in anda out, if each of the temperatures are variable: from 20º to 80 º. They are permenantly changing.

thanks

 

[pastyl]

If you mean heating coil with a fluid flowing in it then you have that
m*Cp*DT=U*A*(MTD)
where:
m= mass of fluid flows in the coil (kg/s)
Cp=const.pres.thermal capacity of fluid (J/kgK)
DT=difference of fluid in and outlet temperatures Tin-Tout (K)
A=(2?D)L , A=external area of coil,D=diameter and L=lenght of coil.
U=overall thermal coefficient= 1/ ((1/hi)+(x/k)+(1/ho))
where
hi=fluid heat transfer conv. coeFficient (inside coil) (W/m2K)
ho=water heat transfer conv. coeeficient (W/m2K) (appr.500)
x=coil thickness (m)
k=coil metal cond. coff.(W/mK) (appr.20-40)
You can find hi at any heat transfer book following the equation
Nu=(hi*D/k)=0.023*Re^0.8*Pr^(1/3)
(k=thermal conductivity here)
Final
MTD= (Tin-Tout)/ ln((Tin-Twater)/(Tout-Twater))
But if you mean electrical coil then you have
M Cp DT/Dt=Qe
where
M=water tank mass
Cp=4.189 (Kj/kgK)
Qe=electrical coil capacity (kW)
DT=rising of temperature (K) within a time (Dt) sec

 

[mfqd]

Hi Pastyl,

Thank you for the reply.
I understood perfectly, because i have used those equations, but with each one of the equations, you can calculate 2 different values.
How do you obtain the efficiency?

Thanks!

 

[pastyl]

The two cases i.e. heating the tank with electrical coil and heating the tank with a flow stream, flowing inside a process coil, are governed by different physical lows and these has the result of different governing equations.
Now as far the efficiency and for the first case, if I understood well the term, you can say that:
efficiency=Tin-Tout/Tin-Twater
Thus the efficiency becomes high as the temperature of the water comes close to the stream leaving temperature.
Now for the second case you can say that efficiency is the left hand side of the governing equation I wrote before divided by electric power i.e sgrt(3)*V*I*cosf
Regards

 

[mfqd]

Great!

that was simple and logical!
In fact i have seen that, i remember now. But i'm too lasy

Thank you ver much for the help! I've appretiated!

Best Regards

 

[mfqd]

Dear Pastyl,

I have thoughted that i have solved this case but not...
I've taked a look to my previous replies and i noticed that my actual doubt was already exposed previously.

I have a transient model. I have a coil with a water stream, and a tank with water almost standstill. the water temperature in the tank increases with time, so de heat transfer rate also changes.
There is anothe problem. with stratification, the temperatures at the top and bottom of the tank are different. So, because of all of this how can i estimate the coil efficiency?

I've taked a look in Holman, but i didn't find something like this. The effectiveness analisys is only for 2 fluid strams (heat exchangers).

Thanks once more for the attention!

 

[prex]

What do you mean by efficiency?
Assuming what you need is calculating the water temperature rise as a function of time, I would go as follows:
-discard the stratification problem, it is a second order phenomenon and it is very difficult to account for it without any data coming from tests. If you are not studying something for research, you shouldn't worry too much about it. Also the temperature difference as an average will not be affected very much.
-so now we have a single (initially known) temperature for water, a known coolant flow rate and inlet temperature
-from the equations by pastyl above you can calculate the only remaining unknown, the coolant outlet temperature
-note that the MTD expression by pastyl may be simplified to (T_in+T_out)/2-T_water
-note also that for these relationships for MTD to work correctly, the coolant flow rate must be sufficiently high so that T_out is still well above T_water
-this gives you the rate of heat input to the water, and from this you can calculate the temperature increase of water after a chosen time interval
-with the new water temperature you recalculate everything as above for a new time step and so on till (asymptotically) the water temperature equals the coolant inlet temperature

prex

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[mfqd]

OK.

I understood. To obtais efficiency, i will make some iterations, with some time step intervals. for each timestep i will make all the calculations you said, and with them perform the efficiency calculations.

I think i will manage this way, with goo results. If not, i will post some more questions

THANKS PREX!!!!!!!

 

[pastyl]

Dear mfqd

Note also that you can calculate water temperature rise by writing down the heat balance in a control volume around the tank where you have

MCpDT/dt=m*Cp*DT

were left hand side is the properties of the water in the tank and right hand side of the stream (and ignoring tank heat losses)

The temperature decrease of stream can be calculated as above noted by prex and the equations I wrote before. Time intervals can be taken acc. the accuracy you want.

Finally you do not need to worry about the different temperature levels in the tank, because the model I propose is simplified and it can accepts uniform temperature of water in the tank

Best Regards

 

[willard3]

MFQD:

Efficiency:
the ratio of the useful energy delivered by a system to the energy supplied to it, ie, btu in / btu out

I don't really think you mean efficiency but am having a hard time understanding what you do mean.

 

[Latexman]

mfqd,

The solution of the differential equations for your case are documented in Kern's "Process Heat Transfer" and in Perry's Chemical Engineers' Handbook under "Batch Operations" inone of the sections on heat transfer. Unfortunately, your tank is not well mixed and it will deviate from the classical assumptions of these solutions, but that's life!

Good luck,
Latexman

 

[mfqd]

Dear Willard3,

As you mentioned in a previous reply, "BTU in/BTU out = thermal efficiency ". So, why do you say now that you don't understand?

thanks

 

[quark]

There is nothing like coil efficiency. When you do heat balance of the fluid passing through the coil and that in the tank, you should always get equal values unless there is heat loss.

You should check for effectiveness of coil if you want to transfer heat at a certain rate to the contents inside the tank.

 

[mfqd]

Ok. I understood. Maybe i want to refer to "effectiveness".
I'm Portuguese, and the translation of both words: efficiency and effectiveness is the same, as long as their meaning. So i fall in mistake easely.

Quark, please clear me this: when we check for effectiveness of the coil, we check if the coil's properties like: area, thermal conductivity, etc., are capable to transfer the amount of heat thar we want with a specific rate. Correct?

Thanks!!!

 

[quark]

Yes, that is correct. Technically all heat exchangers are 100% efficient but differ in the rate of heat transfer. Holman, as you referred in your other thread, is one of the best books (another one is by Incropera and Dewitt) that can make things clear.