Heat transfer between warm air and cold water
Heat transfer between warm air and cold water
(OP)
For your consideration:
A very large (100s of meters) vertical metal (stainless steel) wall maintained at, say, 35F.
Warm (72F) moist air flowing over the wall (natural convection, not forced).
Condensation flowing down the wall (at 35F?).
How to find the heat transfer rate between the warm air and the wet surface of the wall and the rate between the water layer and the wall?
Thanks for any help you can provide.
A very large (100s of meters) vertical metal (stainless steel) wall maintained at, say, 35F.
Warm (72F) moist air flowing over the wall (natural convection, not forced).
Condensation flowing down the wall (at 35F?).
How to find the heat transfer rate between the warm air and the wet surface of the wall and the rate between the water layer and the wall?
Thanks for any help you can provide.





RE: Heat transfer between warm air and cold water
RE: Heat transfer between warm air and cold water
If so, this is a reminder that student postings are not allowed.
Good on ya,
Goober Dave
RE: Heat transfer between warm air and cold water
Just playing with a design idea for a space settlement, to possibly use in a SF story, need to verify the heat balance will work. I'd rather not take excessive literary license with physical reality.
RE: Heat transfer between warm air and cold water
RE: Heat transfer between warm air and cold water
Assuming a steady-state, with the endcaps radiating as much heat out as the illuminated floor inside receives, why _wouldn't_ the endcap surfaces be at a constant temperature (perhaps varying with distance from the hub)? With constant illumination on the floor, why wouldn't the air hitting the cold endcaps be a constant temperature?
I'm trying to establish that a steady-state is possible, which is why I want to know if the metal endcap walls, with condensate running down them, can transfer the 250W/m2 needed.
RE: Heat transfer between warm air and cold water
Sounds like you've got yer work cut out for ya.
RE: Heat transfer between warm air and cold water
If a psychrometric chart is the way to go, a little advice on how to do so would be appreciated (I'm beyond rusty on its use). Thanks.
RE: Heat transfer between warm air and cold water
Natural convection doesn't work in zero gravity. It's driven by difference in weight.
RE: Heat transfer between warm air and cold water
So convection will vary with distance from the axis of the cylinder. All very fun to calculate.
But right now all I need to know is how to calculate the amount of heat that will pass through a cold, wet metal vertical surface from warm (72F), moist air hitting it. I'm trying to keep the request simple. Thanks.
RE: Heat transfer between warm air and cold water
RE: Heat transfer between warm air and cold water
Using the ends as radiators lets me set up a 'natural' circulation system: sunlight warms the land and ponds near the center of the cylinder, the warm moist air rises toward the axis, the cold endcaps dehumidify the air (condensate running back down to the streams and ponds) and dump the 6.3GW of heat the sunlight brings in.
I'm trying to do all this with minimal technology: no pumps, HVAC, etc.
But guys, can I please get an answer to my original question: how to calculate the heat flowing from warm, moist air into a cold, wet metal wall? We can discuss space city design in another forum somewhere. Thanks.
RE: Heat transfer between warm air and cold water
the completely dry case ought to be available in a textbook.
I wonder, however, if natural convection will be strong enough to dominate in this environment, or if conduction and radiation must also be considered.
RE: Heat transfer between warm air and cold water
Yes, I googled the term. Presumably you have the cylinder's axis of rotation aligned along the orbital velocity vector? I.e. one side of the cylinder is receiving light from the sun? What about the other side of the cylinder? And, my point is, even facing the sun, the sun only subtends an arc of 0.5 degrees, the other 179 degrees of arc is deep black space. Did you factor that into your calculations? "It can't be a radiator, it faces the sun" is a very terrestrial concept, and one of the mistakes made by people doing spacecraft thermal analysis for the first time.
Take shaped object and stick it in free space at 1 AU from the sun, assume a grey body - calculate the equilibrium temperature. For reasonable estimates of emissivity, you should get an equilibrium temp. very close to that of our home planet (amazing, ain't it?). At most, you might need to tweak emissitivty/absorptivity to get an equilibrium temp. very close to 70 F, but it won't be by very much.
But, I get the impression that the "water wall" is a plot device for your novel, i.e. you really want it to work this way. Fine. A typical heat transfer coefficient in normal, terrestrial free convection is around 5 Watts/m^2/degC. You should be able to calculate the heat flux from air to wall from that value, and you can arm-wave a few watts either way by saying that a certain amount of air current is generated by cold air sinking at the cold face and recirculating within the cylinder.
Let's say that you do this armwave, and get that 250 W/M^2 you wanted - how are you going to radiate that 35 deg heat to space?
My point would be that you shouldn't despair when you can't radiate 250 W/m^2 from a 35F panel surface. Real spacecraft are maintained quite comfortably at room temperature with very little active control. Simple passive measures (use of insulation, emissivity and absorptivity control of surfaces) quite easily keep things warm enough to (for example) keep hydrazine tanks from freezing. Biggest problem for comsats is keeping the lines from freezing during the eclipse periods, and the constraint is that line heaters draw from the battery, which is not getting charged by arrays when in Earth's shadow.
RE: Heat transfer between warm air and cold water
RE: Heat transfer between warm air and cold water
There may be some flow driven by a combination of convection and drag in the outer annulus. The drag will tend to drive a rotational pattern, and convection may cause some swirls within that.
But unless you do something to force airflow against the ends there will be very little flow there.
At any rate, whatever air does manage to reach the end will approach 100% RH at the surface temperature when condensation forms. If you know "bulk" temperature and RH you can get the change in enthalpy from the psychrometric chart per unit of airflow.
From there work backwards to figure out how much airflow you will need, then decide if that is reasonable.
RE: Heat transfer between warm air and cold water
btrueblood: No, the cylinder's axis of rotation is perpendicular to its orbital velocity vector. I did this so I wouldn't have to worry about trying to use precession to keep mirrors pointed at the Sun, as in Gerard O'Neill's Model 3 design. Trying to keep it simple. I'm still working on how to bring sunlight into the cylinder. I'm not trying to make it as Earthlike as O'Neill did, with the Sun 'moving' through the 'sky'.
I understand that a radiator can still work on a surface exposed to the Sun but I'm using the sides of the cylinder for energy input, not as radiators. Maybe I should have said at the start that I'm trying to see what kind of weather one can create in such a system. To me, that implies a heat engine, with heat entering at one point (more sunlight hitting inside the equator, of both the Earth and the city/cylinder) and heat exiting at the cooler poles (or endcaps) in order to set up some air circulation. One critique of O'Neill's designs was that they would feel more like a giant terrarium than a world.
I can believe that a grey body reaches a reasonable equilibrium temperature 1 AU from the Sun, but most satellites have unlit interiors and my design is more like a solar oven, with 100W/m2 hitting the 63 sq. kilometers of 'land' inside the cylinder. After all, we want sunlit parks and farmland. But that gives us 6.3 GW of heat to dump or, divided by the endcap area, 250W/m2.
If the endcap exteriors have an emissivity of 0.9 and are at a temperature of at least 17 degrees F, they should be able to radiate the 250W/m2. I'm planning on the endcaps being an array of heatpipes so the exterior temp should be close to the interior wall temp.
And, yes, I want the 'water-wall' to contribute to the weather and to the water cycle of the system.
PS - I have 5 sisters and we call each other 'you guys' all the time; maybe it's a Michigan thing.
RE: Heat transfer between warm air and cold water
I know I didn't answer your question, but I though I would let you know how complicated this can get...
RE: Heat transfer between warm air and cold water
RE: Heat transfer between warm air and cold water
Because of the zero gravity at the axis, the bulk of convection may happen at lower levels so maybe no rain until the air cools more near the endcaps.
To simplify the calculations maybe I should assume that most of the action happens 'far' from the axis, that we have 1/2 to 1 gee gravity available to move air and condensate around.
How does condensate affect heat transfer? Any rules of thumb?
To Xera: The oxygen, nitrogen, water, metals, some organic molecules and maybe rock and gravel would come from comets and asteroids. There's plenty available out there. For example, if we could somehow bring Hyperion (a small moon of Saturn) down to Earth and melt it, it could create a lake more than 200 feet deep over the entire United States.
RE: Heat transfer between warm air and cold water
You very well could get low level drizzle if you have a tropical environment around the inside surface...though more than likely you will get a cylinder of clouds around the axis...simply becuase the bergeron process (the main method of precip formation) relies on nucleation points as well as near-freezing temps...although you may get some drizzle from coalescence.
RE: Heat transfer between warm air and cold water
RE: Heat transfer between warm air and cold water
RE: Heat transfer between warm air and cold water
This might place an upper limit on the size one might make such a space city.
RE: Heat transfer between warm air and cold water
Ok, good.
"but I'm using the sides of the cylinder for energy input, not as radiators"
Argh. How are you going to PREVENT the surfaces from radiating? They will radiate, you can't change that. You can adjust the surface emissivity somewhat, but you can't make it zero. My point would be to "adjust" (in theory) the surface emissivity to get a thermal balance that just allows your endcaps to be whatever function you want them to be.
RE: Heat transfer between warm air and cold water
Actually, maybe I _would_ want to do that, if the weather effects from using the endcaps is too severe.