Heat transfer between warm air and cold water

[wbogen]

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.

 

[MintJulep]

I'd use a psychrometric chart or program.

 

[DRWeig]

This sounds too much like a school homework problem...

If so, this is a reminder that student postings are not allowed.

Good on ya,

Goober Dave

 

[wbogen]

Nope, not homework.
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.

 

[dvd]

Seems pretty unrealistic to assume constant properties like wall and air temperatures. So science fiction is appropriate.

 

[wbogen]

A large spinning space city, a cylinder 2000 meters in radius, 5000 meters long, with sunlight directed to the floor of the interior constantly, but the ends of the cylinder facing not the Sun but black space (3 degrees K).

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.

 

[dvd]

Never really thought about "natural convection inside of a spinning cylinder in a low gravity zone." Obviously the spinning cylinder is in a solar system if it is receiving enough sunlight to provide warming, so it has balanced forces from gravitational attraction to the sun and centrifugal force from an orbit. Natural convection is based upon buoyancy of the moist air relative to ambient air. The air in the cylinder "sticks" to the spinning cylinder and forms a boundary layer. I would be curious about the balance of forces required to allow buoyancy-driven flows. Seems to me the place to start is with a force balance. I wouldn't mind getting paid to think about this for a while. Got any money?

Sounds like you've got yer work cut out for ya.

 

[wbogen]

Thanks but I've done the calcs already on the distribution of air pressure and forces inside the cylinder, etc. What I'm trying to do now is balance the heat flow into and out of the city/cylinder. I would prefer to use simple conduction through the metallic endcaps and then radiation to 3K space, rather than complex, high-maintenance HVAC equipment, I just need to figure out if I can get 250W/m2 through that endcap with 3K vacuum on the outside and 72F air on the inside.

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.

 

[MintJulep]

Uhmmm.

Natural convection doesn't work in zero gravity. It's driven by difference in weight.

 

[wbogen]

"A large _spinning_ space city". Turns once every 90 seconds, producing 1 gee of acceleration on the inside floor of the cylinder and zero gee at the axis. Google 'O'Neill Colonies'. Mine is a simpler design than those.

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.

 

[btrueblood]

Why do only the endcaps "see" 3K deep space? Calculate the view factor for all the other surfaces, they'll see the sun over an approx. 0.5 degree arc (I'm assuming you want an Earth-simulated environment), but see deep space for the rest of their view.

 

[wbogen]

The plane that the city/cylinder rotates in is the same as its orbital plane so the ends face darkness constantly and the sides of the cylinder (underside of the 'floor') receive sunlight, some used as power by PV panels, about 1/4th of it conveyed inside to illuminate the interior. So the sides are not available to use as radiators.

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.

 

[ivymike]

offhand, if you wanted to find the lower limit of heat transfer from the air to the wall (to make sure you have at least enough) I think that the "completely dry" scenario would be the pessimistic case, due to LHOV of the water increasing the heat transfer rate as water condenses on the wall.

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.

 

[btrueblood]

"the ends face darkness constantly and the sides of the cylinder (underside of the 'floor') receive sunlight"

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.

 

[btrueblood]

PS - the "guys" on this forum include more than few quite intelligent members of the opposite sex.

 

[MintJulep]

The is no gravity in the axial direction therefore there will be no convective flow in the axial direction.

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.

 

[wbogen]

ivymike, I'd be happy to get the 'dry' solution but I'm not sure how to find that in a textbook, especially since some weird version of variable gravity convection will be necessary to bring more warm air against the cold wall. At the endcaps, a little distance from the axis, the 'gravity' should be strong enough to let the cooler, denser air drop toward the floor, dropping the pressure enough near the axis that fresh warm air will move toward the endcap. Though the center of each endcap may be permanently shrouded in fog and ice.

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.

 

[LostHippie]

if you are generating roughly 1g at the inner surface of the cylinder, and assuming similarly sized plant and building structures, then the friction layer will extend theoretically beyond the axis (about 1500m for earth) so this verifies that the air is spinning about the axis at roughly the same rate as the cylinder itself in steady state...this would mean that you are going to have a pressure profile set up in this system...and thus you will have an adiabatic cooling effect as the air rises (roughly 10 degrees C per 1000m elevation change non-condensing, and 5 degrees C per 1000m elevation change condensing). seems like there would be a pressure drop at the endcaps that would drive axial air flow...but again this heat transfer would be dependent on the velocity of the incoming air, the absolute humidity of the incoming air the mean temperature of the incoming air at a distance (which would be lower near the axis than it would be near the inner surface), the thickness of the condensate film layer, etc. The condensate layer normally thickens on a vertical plate as you move further down due to accumulating condensate, but with a cylindrical wall the total area this is spread over will combat against that and add further complexity to the system. The condensate later also affects total heat transfer, so this could quickly turn into a ridiculously complex problem...

I know I didn't answer your question, but I though I would let you know how complicated this can get...

 

[Xera]

Where is the air coming from in the first place? Bottles?

 

[wbogen]

To LostHippie (man, I should have thought of a cool handle): Yes, assuming 14.7 psi at the floor, I get 13.1 psi at the axis or a drop of 1.6 psi. So I get an adiabatic cooling effect of 32 degrees C non-condensing. So if the RH at the floor (or 'ground') is more than 32%, and some of that air rises to the axis, we'll get rain?

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.