# Heat Exchanger

## Homework Statement

Hi,
I need someone to help me with this question. I tried to find the answer for two weeks I could not finde it. Anyone with the required experience can help!! I will be so grateful.

Question:

A shell-and-tube heat exchanger is to act as a condenser: saturated ethyl alcohol (ethanol) vapour at pressure of 1 atm is to be condensed on the shell side and cooling water will be used in the tubes. U-tubes will be used (giving two passes on the tube-side). They will be steel, with a total length (end-to-end of a U-tube) of 6m, 15 mm inside diameter and 17.5 mm outside diameter. Thermal conductivity of steel can be taken as 50 W/m/K.

It is required to condense a maximum vapour flow of 5000 kg/h with no sub-cooling of the condensate. Cooling water is available with a maximum summer temperature of 25°C and with the temperature-rise (DT) limited to 30°C. A search of the literature shows that a heat transfer coefficient of around 5000 W/m2/K can be expected on the shell side for condensing ethanol. Fouling factors on the inner and outer tube surfaces may be assumed to be 0.0001 m2×K/W and 0.0002 m2×K/W respectively.

Determine the number of tubes required, the overall heat transfer coefficient and the effectiveness of the heat exchanger.

Fluid properties may be evaluated at mean fluid temperature. Other assumptions made must be fully justified.

## Homework Equations

They are in my attempted solution

## The Attempt at a Solution

My answer is attached as an image[/B]

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It would help if you added units to your calculations. If you think you can condense more than 1 kg/s of ethanol with 0.01 kg/s of water it must ring all alarm bells...

It would help if you added units to your calculations. If you think you can condense more than 1 kg/s of ethanol with 0.01 kg/s of water it must ring all alarm bells...
Yes I know but I have not coz I think my answer is wrong :(. If you have any idea only on how can i get the number of tubs I will be able to solve the rest!!

Chestermiller
Mentor
Your heat capacity for water is 1000 x too high. It should be 4.2. Also, I looked up the heat of vaporization of ethanol at its atmospheric boiling point of 78.4 C, and it is 841 kJ/kg.

Your heat capacity for water is 1000 x too high. It should be 4.2. Also, I looked up the heat of vaporization of ethanol at its atmospheric boiling point of 78.4 C, and it is 841 kJ/kg.
I but Cp.w = 4.3 in my answer. So now can I assume that the in temperature of the ethanol as 78.4?
I do not really know I am doing wrong and what I am doing right.

Chestermiller
Mentor
$$\dot{Q}=(1.389)(841)=1168\ kJ/sec$$
$$\dot{w}=\frac{1168}{(4.184)(30)}=9.31\ kg/sec$$

The atmospheric boiling point of ethanol is 78.4 C. Didn't you look that up? How can you get the log-mean temperature difference without knowing the ethanol temperature?

$$\dot{Q}=(1.389)(841)=1168\ kJ/sec$$
$$\dot{w}=\frac{1168}{(4.184)(30)}=9.31\ kg/sec$$

The atmospheric boiling point of ethanol is 78.4 C. Didn't you look that up? How can you get the log-mean temperature difference without knowing the ethanol temperature?
$$\dot{Q}=(1.389)(841)=1168\ kJ/sec$$
$$\dot{w}=\frac{1168}{(4.184)(30)}=9.31\ kg/sec$$

The atmospheric boiling point of ethanol is 78.4 C. Didn't you look that up? How can you get the log-mean temperature difference without knowing the ethanol temperature? Can You see this is the number of tubes correct?

And about the log-mean temperature difference, I thought I will not use it coz I do not have exit temperature of the ethanol and I can not put any temperature from my head!!

Chestermiller
Mentor
View attachment 108650
Can You see this is the number of tubes correct?
No. If you didn't take into account the ethanol temperature, you could not have gotten the number of tubes correct. And you didn't even calculate the required heat transfer area.
And about the log-mean temperature difference, I thought I will not use it coz I do not have exit temperature of the ethanol and I can not put any temperature from my head!!
If the ethanol enters the shell as a saturated vapor at 1 atm., what is its temperature? If it exits the shell as a saturated liquid at the same pressure, how much has its temperature changed? So what is its exit temperature? What is the temperature difference between the water and the ethanol at the water inlet to the heat exchanger? What is the temperature difference between the water and the ethanol at the water exit from the heat exchanger?

No. If you didn't take into account the ethanol temperature, you could not have gotten the number of tubes correct. And you didn't even calculate the required heat transfer area.

If the ethanol enters the shell as a saturated vapor at 1 atm., what is its temperature? If it exits the shell as a saturated liquid at the same pressure, how much has its temperature changed? So what is its exit temperature? What is the temperature difference between the water and the ethanol at the water inlet to the heat exchanger? What is the temperature difference between the water and the ethanol at the water exit from the heat exchanger?
I am really grateful for the help you gave me I will try to solve it again and I will send you my work tomorrow to check if they are right. Can You please tell me which equation to use to get the required heat transfer area , the number of tubes and what is the name of the table to get the final temperature of the ethanol. So I can follow what you give me. Thanks a lot.

Chestermiller
Mentor
The final temperature of the ethanol is the same as the inlet temperature, 78.4 C. Its temperature doesn't change when it condenses at constant pressure.

Getting the number of tubes is going to be a trial-and-error procedure. You are going to have to guess a number of tubes, and then calculate the heat transfer for any one of the tubes, given the flow rate, heat load, and temperature differences. Start out by assuming, say, 10 tubes. Calculate the Reynolds number for each tube. Calculate the internal Nussult number for each tube. Get the internal heat transfer coefficient. Get the overall heat transfer coefficient. Etc.