# Heat exchangers and energy balances

#### saratavares

I have to do a project using Aspen and need to do some math before hand. Can you please help me? Here's the problem:

A heat exchanger with 10 m2 of heat transfer area is provided to supply 58 kW to a water stream available at 15 ° C and 1 bar. The available hot fluid is freon-12 at 32 ° C and 7 bar.

Determine the amount of water that can be heated and the freon flow required for the purpose.

Thank you so much!

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#### Chestermiller

Mentor
Is the freon-12 a saturated liquid under these conditions? If so, are you going to assume that all the freon evaporates to form a saturated vapor at 7 bars?

More importantly, is this a homework problem?

#### saratavares

Is the freon-12 a saturated liquid under these conditions? If so, are you going to assume that all the freon evaporates to form a saturated vapor at 7 bars?

More importantly, is this a homework problem?
Hello. Yes it's a saturated liquid under these conditions, and yes I think it will all evaporate. It's not a homework problem, it's a project I have to do for University at the end of the semester. I have few time to do it and I have searched all over the internet and I can't solve it so I would appreciate it if you could help me. At least with some tips. Thank you.

#### Chestermiller

Mentor
Hello. Yes it's a saturated liquid under these conditions, and yes I think it will all evaporate. It's not a homework problem, it's a project I have to do for University at the end of the semester. I have few time to do it and I have searched all over the internet and I can't solve it so I would appreciate it if you could help me. At least with some tips. Thank you.
You need to specify either the outlet temperature of the water or its mass flow rate.

As far as the F12 is concerned, the open system (control volume) version of the first law of thermodynamics applied to the F12 side of the heat exchanger gives us:
$$0=\dot{Q}+\dot{m}(h_{in}-h_{out})$$where $\dot{Q}$ is the rate of heat addition to the F12 (-58 kW), $h_{in}$ is the specific enthalpy of the F12 entering the heat exchanger, $h_{out}$ is the specific enthalpy of the F12 exiting the heat exchanger, and $\dot{m}$ is the mass flow rate of the F12. What do you get for the specific enthalpy change of the F12 in passing through the heat exchanger? What do you get for the mass flow rate?

#### saratavares

You need to specify either the outlet temperature of the water or its mass flow rate.

As far as the F12 is concerned, the open system (control volume) version of the first law of thermodynamics applied to the F12 side of the heat exchanger gives us:
$$0=\dot{Q}+\dot{m}(h_{in}-h_{out})$$where $\dot{Q}$ is the rate of heat addition to the F12 (-58 kW), $h_{in}$ is the specific enthalpy of the F12 entering the heat exchanger, $h_{out}$ is the specific enthalpy of the F12 exiting the heat exchanger, and $\dot{m}$ is the mass flow rate of the F12. What do you get for the specific enthalpy change of the F12 in passing through the heat exchanger? What do you get for the mass flow rate?
How do I calculate $h_{in}$ and $h_{out}$? I know that h=u+PV but I don't know the specific internal energy (u) or the volume.

#### Chestermiller

Mentor
How do I calculate $h_{in}$ and $h_{out}$? I know that h=u+PV but I don't know the specific internal energy (u) or the volume.
I hope you didn't think you were going to be able to solve this without any physical property data on F12. Get yourself a set of thermodynamic tables for F12, either from a textbook or on the internet.

#### saratavares

So I found this table. 7 bar equals 700 kPa, so this is the part of the table that would matter for that pressure. Would I have to replace the H in the equation you showed me to calculate the mass flow rate?

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#### Chestermiller

Mentor
So I found this table. 7 bar equals 700 kPa, so this is the part of the table that would matter for that pressure. Would I have to replace the H in the equation you showed me to calculate the mass flow rate?
Sure. But before addressing that, please answer this question: Is the F12 under these conditions (a) a saturated vapor or (b) a superheated vapor?

#### saratavares

Sure. But before addressing that, please answer this question: Is the F12 under these conditions (a) a saturated vapor or (b) a superheated vapor?
I think its a superheated vapor.

#### Chestermiller

Mentor
I think its a superheated vapor.
Correct. So what are you taking as the exit state of the F12 from the exchanger.

There is definitely information missing from this problem. Are you sure you have provided the complete problem statement?

#### saratavares

Yes I'm sure so. Although I have to do it using a program called Aspen, don't know if you are familiar with it, and maybe with the tips you gave me and using the program it can help finding the miss information.

#### Chestermiller

Mentor
Yes I'm sure so. Although I have to do it using a program called Aspen, don't know if you are familiar with it, and maybe with the tips you gave me and using the program it can help finding the miss information.
Aspen can't help you with that unless there is additional information available involving conditions at the juncture with other equipment in the process. Where did the value you cited for the heat load come from? Certainly, if you are using Aspen, you must know the process flow rate.

#### saratavares

Aspen can't help you with that unless there is additional information available involving conditions at the juncture with other equipment in the process. Where did the value you cited for the heat load come from? Certainly, if you are using Aspen, you must know the process flow rate.
It was from the problem, I didnt calculate it.

#### Chestermiller

Mentor
It was from the problem, I didnt calculate it.
What is the exact word-for-word statement of the problem?

#### saratavares

What is the exact word-for-word statement of the problem?
It's exactly what my first post on this thread says. Do you think that knowing the initial temperature and pressure of the water and that it was transfered 58w to it in a 10m2 area will give us the final temperature and pressure of water? It also asks to:
b) Characterize the flows that leave the permuted
c)Graph the freon-12 output temperature variation with the heat transfer area
d)show the models for the prediction of thermodynamic properties

#### Chestermiller

Mentor
It's exactly what my first post on this thread says. Do you think that knowing the initial temperature and pressure of the water and that it was transfered 58w to it in a 10m2 area will give us the final temperature and pressure of water? It also asks to:
b) Characterize the flows that leave the permuted
c)Graph the freon-12 output temperature variation with the heat transfer area
d)show the models for the prediction of thermodynamic properties
There is still a lot of information desperately missing. Any information of the design details of the heat exchanger like number of tubes, diameter, metal, etc? I feel like you are holding back vital information. By this point in your training, you should know what info is necessary to design/analyze a heat exchanger.

#### saratavares

There is still a lot of information desperately missing. Any information of the design details of the heat exchanger like number of tubes, diameter, metal, etc? I feel like you are holding back vital information. By this point in your training, you should know what info is necessary to design/analyze a heat exchanger.
No I don't have any of that information. What I've said until now it's all the information they gave me.

#### saratavares

There is still a lot of information desperately missing. Any information of the design details of the heat exchanger like number of tubes, diameter, metal, etc? I feel like you are holding back vital information. By this point in your training, you should know what info is necessary to design/analyze a heat exchanger.
Do you think any of these formulas would help?

#### Chestermiller

Mentor
Do you think any of these formulas would help?
Well, you have closure on the F12 side of the exchanger if you assume that it leaves the exchanger as a saturated liquid at 7 bars. That gives you the exit temperature and the exit specific enthalpy. But, on the water side, you need to know the exit temperature of the mass flow rate to provide closure.

#### Tom.G

Definitely not my field, but it seems there is enough data for a solution; especially if it is looked at as a condenser for the F12.

Could this be an 'Ideal Situation' question by the OP. Since the F12 inlet and outlet pressure & temperature are known and the total energy transfer is given. They are asking for the F12 flow rate constrained by the coolant (water) temperture and pressure (15C to 100C, 1bar).

Cheers,
Tom

#### Chestermiller

Mentor
Definitely not my field, but it seems there is enough data for a solution; especially if it is looked at as a condenser for the F12.

Could this be an 'Ideal Situation' question by the OP. Since the F12 inlet and outlet pressure & temperature are known and the total energy transfer is given. They are asking for the F12 flow rate constrained by the coolant (water) temperture and pressure (15C to 100C, 1bar).

Cheers,
Tom
The outlet temperature and pressure (and mass fraction liquid) of the F12 are not specified in the problem statement. To get closure, at least on the F12, one would have to assume (without justification) that the outlet condition is a saturated liquid (or some other mass fraction liquid) at 7 bars (and about 26 C). Then, the mass flow rate of the F12 could be calculated.

There is no information on either the outlet temperature of the water or its mass flow rate. Certainly, the outlet temperature cannot be 100 C or the 2nd law of thermodynamics would be violated. The outlet temperature of the water cannot be higher than the inlet temperature of the F12.

"Heat exchangers and energy balances"

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