Skin temperature and wall temperature in heat exchangers

[Markus1]

Hello, I want to calculate the maximum skin temperature of a fluid in the cold side channel of a heat exchanger with counter flow design. The maximum temperature will be achieved at the cold side outlet, where the hot side fluid enters the heat exchanger. Is the maximum skin temperature of the cold side fluid the same as the wall temperature (of the heat transfer area) on the cold side outlet? The wall temperature can be calculated with the heat transfer coefficient of the cold side fluid and the overall heat transfer coefficient and the maximum temperatures on the hot and cold side. Does this apply for the skin temperature of the fluid as well or will this temperature be much smaller? According to VDI Wärmeatlas the total heat load will be considered, but I think this can only give an average wall temperature and not the maximum temperature. A lot of questions and a little bit of confusion. Please help.
Best regards
Markus

 

[davefitz]

The skin temperature will be equal to the cold side fluid plus the "film drop" temperature difference , which equals the value of DT,film = (q/A) *(1/h + Rc)
where h= convective heat transfer coef at cold side outlet and Rc= fouling coefficient on cold side outlet.

The above only gives you the apparent average cold side outlet skin temperature, but there may be local variations due to variations in fouling coverage and fluid flow stratifications.

 

[Markus1]

Dear Dave,

thank you for your reply. If I want to see the maximum cold side outlet skin temperature, I suggest this will be during the start up conditions, when the fouling is the smallest.
Another thing is the term Q/A: Total heat load divided by total surface. Does this term apply, if only the critical outlet area is considered or is this term only suitable for the average skin temperature along the total heat exchanger surface? The calculation of the heat exchanger wall temperature gives much higher temperatures than the formula you stated, which means that skin temperature and wall temperature are different.
I used the graphical approach from VDI Wärmeatlas (Cb1, Picture 3), which leads to formula without fouling for the wall temperature:
(tw2-t2)/(1/alfa2)=(t1-t2)/(1/OHTC)
tw2: wall temperature cold side
t2: temperature cold side (here outlet)
alfa2: convective heat transfer cold side
t1: hot side temperature (inlet)
OHTC: overall heat transfer coefficient.

Why does this formula give higher wall temperatures?

Best regards, Markus

 

[davefitz]

The quantity (t1-t2)/(1/OHTC) is equivalent to the local value of (q/a), since (1/OHTC) = {1/hi+1/ho+Ri+Ro}= R

tw2-t2 is the "film drop", or the temperature difference between the cold outlet gas and the surface temperature. But the equation you presented does not include the fouling on the outlet surface. It should read:
(tw2-t2)/ {1/alfa2 + R2) = (t1-t2)/(1/OHTC)

I have assumed all surfaces are flat plates r very thin cylinders.

 

[Markus1]

Correct, by using local heat duty for small surface elements (here at the cold side outlet area) both formulas give the same value. Thank you.
For maximum skin temperature calculation I have assumed fouling to be zero. If fouling is considered on the cold side, the wall temperature tw2 is the skin temperature between the heat exchange surface and the fouling layer. If the Cold side fouling is not included in the formula the skin temperature seems to be the temperature between fouling layer and cold side fluid.

 

[Markus1]

Is it correct, that the formula for skin temperature gives the temperature between fouling layer and heat exchanger wall, if the fouling factor (cold side) is considered? But if fouling factor is not considered in the formula the calculated temperature will be the surface temperature of the cold side fluid? This temperature will be smaller than the temperature between fouling layer and heat exchanger wall. Is there some error in this theory?