Calculate the number of plates required for a heat exchanger

In summary, the cooling water inlet temperature is 4 degrees C and outlet temperature is 80 degrees C. The density and specific heat of water are 1000 kgm-3 and 4.2kJkg-1K-1, respectively. The density and specific heat of wort are 1060 kgm-3 and 4.0Kjkg-1K-1, respectively. The overall heat transfer coefficient is 3000Wm-2k-1 and the area of each plate is 0.75m2. The heat lost by the hot wort is equal to the heat gained by the cold water, and the flow rate ratio is 1.04:1. To calculate the
  • #1
sci0x
83
5
Homework Statement
Calc wort flow rate ratio and no. Of plates required to cool 360 hl hr-1 wort, in counter current flow from 98 degrees C to 15 degrees C using plate heat exchanger
Relevant Equations
Q=UAdT
Cooling water inlet temp is 4 degrees C
Cooling water outlet temp is 80 degrees C
Density of water is 1000 kgm-3
Specific heat water is 4.2kJkg-1K-1
Density wort is 1060 kgm-3
Specific heat wort is 4.0Kjkg-1K-1
Overall heat transfer coeff is 3000Wm-2k-1
Area of each plate is 0.75m2

For water: wort flow rate ratio I've said
Heat lost by hot wort = heat gained by cold
Mh x Cph x (Tih-Toh) = Mc x Cpc x (Toc-Tic)
(360)(4000)(98-15) = Mc(4200)(80-4)
Mc = 374.436
374.436:360
1.04:1

This is expected answer.

Im having trouble calculating no. Of plates req which should be 111
I should use log mean temp differemce in heat transfer rate eq

So q=UA(LMTD)
Overall heat trans co is in K so change C to K
LMTD is 83-75/ln(83/76) is 79.44 degrees C or 352.99 Kelvin
Q=3000(A)(352.99)

Q is also Mh x Cph x (Tih-Toh) = (360)(4000)(98C-15C) or 360(4000)(356.15K)
512856000=3000A352.99
A = 484.29
Each plate is 0.75m2 x 484.29 = 363.21 plates
Can someone show me how to get 111 here.
Q from past exam paper
 
Physics news on Phys.org
  • #2
sci0x said:
Relevant Equations:: Q=UAdT
Overall heat trans co is in K so change C to K
what about changing a temperature difference from ##\Delta ^\circ C## to ##\Delta K## ?

sci0x said:
LMTD is 83-75/ln(83/76)
You forgot the brackets
and the numbers are weird -- look up what LMTD means
 
  • #3
The heat load is ##Q=(36)(1060)(4.0)(98-15)=12700000\ kJ/hr=3519\ kj/s=3519000\ W##

The two end temperature differences are 18 C and 11 C. What is the LMTD based on these?
 
  • #4
Hi Chester, i messed up there:
dt1 is 98-80 = 18
dt2 is 15-4 is 11

LMTD is 18-11/ln(18/11) is 14.21

The heat load is 3519000W

3519000 = (3000)(A)(14.21)
A= 82.54m2

82.54/0.75 = 110 plates

Just wondering in your calculation Q=(36)(1060)(4.0)(98-15)
What units are the 36 in, to convert from 360hl hr-1
 
  • #5
sci0x said:
Hi Chester, i messed up there:
dt1 is 98-80 = 18
dt2 is 15-4 is 11

LMTD is 18-11/ln(18/11) is 14.21

The heat load is 3519000W

3519000 = (3000)(A)(14.21)
A= 82.54m2

82.54/0.75 = 110 plates

Just wondering in your calculation Q=(36)(1060)(4.0)(98-15)
What units are the 36 in, to convert from 360hl hr-1

How many hl are there in a m^3?
 
  • #6
Okay m3
1hl = 0.1m3
360hl = 36m3

Cheers
 

1. How do you calculate the number of plates required for a heat exchanger?

The number of plates required for a heat exchanger can be calculated by using the heat transfer coefficient, flow rate, and heat transfer area. The formula for this calculation is: Number of Plates = (Heat Transfer Area x Heat Transfer Coefficient) / Flow Rate.

2. What is the heat transfer coefficient and how is it used in the calculation?

The heat transfer coefficient is a measure of how easily heat is transferred between two fluids in a heat exchanger. It is used in the calculation by multiplying it with the heat transfer area and dividing by the flow rate to determine the number of plates needed for efficient heat transfer.

3. How is the flow rate determined for the calculation?

The flow rate is determined by the desired amount of fluid that needs to be heated or cooled in the heat exchanger. It can be measured using a flow meter or calculated based on the fluid's properties and the desired temperature change.

4. Are there any other factors that should be considered when calculating the number of plates for a heat exchanger?

Yes, other factors such as the type of fluid being used, the desired temperature change, and the design of the heat exchanger should also be taken into account when calculating the number of plates. These factors can affect the heat transfer coefficient and ultimately impact the number of plates required for efficient heat transfer.

5. Can the number of plates be adjusted after the initial calculation?

Yes, the number of plates can be adjusted based on the performance of the heat exchanger. If the desired heat transfer is not achieved, the number of plates can be increased or decreased accordingly to improve efficiency.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
3
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
6
Views
2K
  • Mechanical Engineering
Replies
4
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
7
Views
3K
  • Mechanical Engineering
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
961
  • Engineering and Comp Sci Homework Help
Replies
12
Views
3K
  • Materials and Chemical Engineering
Replies
10
Views
2K
  • Engineering and Comp Sci Homework Help
2
Replies
44
Views
6K
Back
Top