Things were slow at work today and I decided to take my old brain out for a test drive. The question is, Is there a difference between a Copper Heat Exchanger and a Stainless Steel Heat Exchanger. (Disclaimer: It has been decades since I took a Thermodynamics Class and if I remember I got a “C”
This is purely a mathematical exercise, reality WILL be different.
Wrong Answer.
Thermal conductivity (K, W/(m C) (Watts / meter thickness / delta degree C)
k(cu) = 400 W/mC
k(ss) = 16 W/mC
therefore a Cu HE is 25 times better than SS.
WRONG
this ignores the inefficient of moving heat out of the hot side water and into the cold side water of the HE.
Short Answer.
This information is taken from Engineering Tool Box on the web at
http://www.engineeringtoolbox.com/overall-heat-transfer-coefficients-d_284.html
Overall Heat Transfer Coefficients for some common Fluids and Heat Exchanger Surfaces
For practically still fluids - average values for the overall heat transmission coefficient through different combinations of fluids on both sides of the wall and type of wall - can be found in the table below:
Fluid Transmission Surface Fluid Overall Heat Transmission Coefficient
(Btu/ft2 hr F) (W/m2 K)
Water Mild Steel Water 60 – 70 340 - 400
Water Copper Water 60 – 80 340 - 455
Stainless Steel is not quite as good as Mild Steel but you can see there is not a lot of difference due to the Transmission Surface. Therefore the Total efficiency of the HE should not be significantly affected by the difference between Cu and SS.
Further down I estimate a 13% increase in cooling time for the SS Chiller versus the Cu Chiller.
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The much Longer Answer.
Facts and assumptions
Tube in a Tube Counterflow Heat Exchanger
Cooling Water (Volume as required)
Entry Temp = 60 F = 15.6 C Exit Temp = 150 F = 65.6 C (adjust cooling flow as required)
Wort to be chilled (Volume = 5.5 gallons, 20.8 liters, 20,820 ml)
Entry Temp = 212 F = 100 C Exit Temp = 70 F = 21 C
Energy to remove from the wort
1 calorie = 1gm of water 1 degree C. (we will use calories not Calories [kcal] )
dT = 65.6C – 15.6C = 50C
Mass = 20820 gm
E = 50 * 20820 = 1,041,100 calories
The Heat Exchanger is a tube in a tube counterflow
assume 12 ft long 1/2 diameter inner tube with a 0.035” wall thickness (0.000889 m)
The media is water and the Exchanger wall is either copper or stainless steel
Heat transfer has units of Power per transfer Surface Area per delta Degree
Such as Watts / (m^2 x deg C) or (W/m2C)
The heat exchanger consists of Cooling Water | Exchanger Wall | Hot Wort.
The overall Heat Transfer Coefficient is an inverse sum of the Heat Transfer of each part, similar to summing resistances in series.
1 / UA = [ 1 / h1A1 ] + [ tw / kw A ] + [ 1 / h2A2 ]
Coolant Wall Wort
A = exchanger surface area, assume 12 ft of 1/2" tube.
= 12ft x 12in/ft x .50 x pi = 226 in2 = 0.146 m2
k = thermal conductivity k(ss) = 16 W/mC k(cu) = 400 W/mC
h = convective heat transfer for each fluid (W / m2 C)
h(w) = 500 W/m2C to 10,000 W/m2C
500 would be static no flow no stir.
10,000 would be best case turbulent flow.
[We will run the final case with 5,000 W/m2C as a real world case]
We are concern with the effect of SS versus Cu so we will use the most efficient water transfer to see the greatest effect of the two exchanger materials.
Since the surface area is the same for each part of the equation the area is removed.
1/U (cu) = [ 1 / 10,000 ] + [ 0.000889 / 400 ] + [ 1 / 10,000 ]
= [ 1 / 10,000 ] + [ 1 / 449,900 ] + [ 1 / 10,000 ]
U(cu) = 4945 W/m2C
with 0.146 m2 surface the power exchange is 722 W / C
1/U (ss) = = [ 1 / 10,000 ] + [ 0.000889 / 16 ] + [ 1 / 10,000 ]
= [ 1 / 10,000 ] + [ 1 / 18,000 ] + [ 1 / 10,000 ]
U(ss) = 3913 W/m2C
with 0.146 m2 surface the power exchange is 571 W / C
With the Entry / Exit temperatures assumed above the average
dT = [ (100 - 60) + (21 – 15.6) ] /2 = 22 C
Heat Transfer (cu) = 722 W/C x 22C = 15,884 W = 3797 calorie / second
Heat Transfer (ss) = 571 W/C x 22C = 12,562 W = 3000 calorie / second
Previously we calculated the total energy to be removed from the boiling
Total Calories to exchange = 1,041,100 calories
Therefore
With Copper HE Time to chill = 1041100 cal / 3797 cal/s = 274 sec (4.57 min)
With Stainless HE Time to chill = 1041100 cal / 3000 cal/s = 347 sec (5.78 min)
Therefore SS is 26% longer than Cu.
As the efficiency of the water to water heat transfer becomes less efficient the effect of SS versus Cu becomes less significant, the time to chill will increase but the difference between SS and Cu will decrease.
Sensitivity Study
Use a Water Heat Transfer Coefficient of 5000 W/m2C
With Copper HE Time to chill = 1041100 cal / 1909 cal/s = 545 sec (9.1 min)
With Stainless HE Time to chill =1041100 cal / 1686 cal/s = 617 sec (10.3 min)
SS is 13% longer than Cu this is should be closest to the real world answer.
I am not an expert ! I assume there are some errors in my calculations.
Please be gentle with the replies...
I don't own one of these yet, but I will. When I do I will try to run some test to see now close I got with the model calculations.
David