Variation in tube wall temperature as steam condenses to form liquid

[sanka]

I'm having a bit of difficulty conceptually understanding a problem. Hoping someone here can clear it up for me.
In a simple circular condenser tube (which is cooled by water or air) what happens the tube wall temperature as the steam inside is condensed? Intuitively I would have thought that as the steam is condensed inside the tube to form liquid condensate, the tube wall temperature would decrease along the length of the tube (from inlet to outlet) as the condensate film becomes thicker as more steam is condensed. Does that make sense? Or is the wall temperature governed by the cooling medium on the tube exterior and thus, remains constant along the length of the tube as dictated by the cooling medium - implying that it is independent of the condensate film thickness?

I know that the condensate film acts as a barrier to heat transfer and thus, is a thermal resistance but I am just trying to understand what happens to the wall temperature as a result of this. I suppose that the steam temperature remains relatively constant along the tube length (isothermal heat transfer for condensation) For the thermal resistance to increase along the length (due to the film), a temperature difference must be present and this must increase along the length. For the temperature difference (ΔT=Tsteam-Twall) to increase, the wall temperature must then decrease (as the steam temp remains constant).

Maybe I've answered my own question! But I would be interested to hear any other ideas on the matter.

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[Chestermiller]

The tube wall temperature is governed by both the cooling medium outside the tube and the condensing vapor inside the tube. There is resistance to heat transfer on both sides of the wall. Inside the tube, where the vapor is condensing, the temperature at the interface between the condensate and the vapor is determined by the pressure, as a result of vapor//liquid equilibrium. (assuming the pressure is constant in the condenser). The temperature at the wall is lower than this, and heat is conducted through the condensate. As the condensate layer gets thicker, the rate of heat transfer (and condensation) decreases. Outside the tube wall, you have convective heat transfer occurring, determined by the outside heat transfer coefficient. The wall temperature is higher than the bulk water or gas temperature, and heat is conducted through the thermal boundary layer from the wall to the bulk. The rate of heat conducted through the outside boundary layer must match the rate of heat conducted through the inside condensate layer at each location.

Chet

 

[gmax137]

...what happens the tube wall temperature as the steam inside is condensed? ...

Not that it really changes anything in the question or the replies, but in the condensers I'm familiar with (large steam power plants) the cooling water runs inside the tubes and the condensing steam is on the outside. One effect of this is that the condensed liquid can drip off the tubes; I think the condensate layer thickness is therefore pretty much constant throughout the unit.

 

[sanka]

the temperature at the interface between the condensate and the vapor is determined by the pressure, as a result of vapor//liquid equilibrium. (assuming the pressure is constant in the condenser). The temperature at the wall is lower than this, and heat is conducted through the condensate. As the condensate layer gets thicker, the rate of heat transfer (and condensation) decreases

Thanks a lot for your response Chet, I appreciate it.
For the most part I understand everything you said. However, one thing is still bothering me and I have highlighted it in the quotation above. You say the temperature at the wall is lower than the temperature at the interface, which of course must be the case for condensation to occur. I know that a temperature difference must be present at each point (locally) along the tube length or else no heat would flow. The issue I am having difficulty with is what exactly happens this temperature difference along the length of the tube? Specifically, as the condensate film grows in thickness (as more steam condenses, more liquid mass is added) along the tube length, does the resistance provided by the thickening film, lead to a reduction in the wall temperature? At least I would have thought that to be the case...

 

[Chestermiller]

Thanks a lot for your response Chet, I appreciate it.
For the most part I understand everything you said. However, one thing is still bothering me and I have highlighted it in the quotation above. You say the temperature at the wall is lower than the temperature at the interface, which of course must be the case for condensation to occur. I know that a temperature difference must be present at each point (locally) along the tube length or else no heat would flow. The issue I am having difficulty with is what exactly happens this temperature difference along the length of the tube? Specifically, as the condensate film grows in thickness (as more steam condenses, more liquid mass is added) along the tube length, does the resistance provided by the thickening film, lead to a reduction in the wall temperature? At least I would have thought that to be the case...

Well, as I suggested earlier, it also depends on what is happening on the other side of the wall. Both heat transfer resistances (inside and outside) need to be considered. If the fluid flow rate outside the tube is very high, its temperature won't change much. If this were the case, the temperature difference across the condensate film divided by the temperature difference between the wall and the bulk flowing coolant would be equal to the heat transfer coefficient on the coolant side divided by the heat transfer coefficient on the condensate side (effectively equal to the thermal conductivity of the condensate liquid divided by the condensate film thickness).

Chet