The Effect of Wind on the Rate an Outside Spigot Freezes

[bob012345]

Suppose one forgot to protect outside water spigots against below freezing winter air. If there is a stiff wind, will, as I think, the spigot freeze sooner than if the air is calm at the same temperature?

Also, wouldn't the case of calm air actually be more complicated to model because the boundary layer of air is heating up and reducing the heat flow accordingly while the case of moving air keeps the boundary layer of air at the fixed temperature of the air?

 

[256bits]

The way I look at it is forced convection vs natural convection.
And you can look up the boundary layer conditions for both.

 

[anorlunda]

That's why your car radiator has a fan. Either the car is moving, or the fan runs. Both make the cooling more effective.

 

[bob012345]

That's why your car radiator has a fan. Either the car is moving, or the fan runs. Both make the cooling more effective.

Sure, but isn't there is a limit where the flow of air makes no difference beyond a certain speed when the boundary layer temperature is effectively the air temperature and the best one can have is Newton's Law of Cooling?

 

[erobz]

Sure, but isn't there is a limit where the flow of air makes no difference beyond a certain speed when the boundary layer temperature is effectively the air temperature and the best one can have is Newton's Law of Cooling?

The convection coefficient has dependencies on the flow velocity, and the geometry of what the flow is passing over. I believe the primary dimensionless parameter characterizing it is the Nusselt Number.

 

[bob012345]

The convection coefficient has dependencies on the flow velocity, and the geometry of what the flow is passing over. I believe the primary dimensionless parameter characterizing it is the Nusselt Number.

But isn't this heat flow by conduction?

 

[gmax137]

Sure, but isn't there is a limit where the flow of air makes no difference beyond a certain speed when the boundary layer temperature is effectively the air temperature and the best one can have is Newton's Law of Cooling?

Yes, at some point the heat transfer rate would be "conduction limited" by the resistance of the pipe wall. But for this case (small household plumbing pipe) I don't think you're likely to see that -- the convection resistances at the inner and outer surfaces of the pipe wall are going to be limiting.

 

[bob012345]

Yes, at some point the heat transfer rate would be "conduction limited" by the resistance of the pipe wall. But for this case (small household plumbing pipe) I don't think you're likely to see that -- the convection resistances at the inner and outer surfaces of the pipe wall are going to be limiting.

The water is assumed static in the pipe. Where is convection coming in?

 

[gmax137]

The water is assumed static in the pipe. Where is convection coming in?

Maybe there is some small natural convection? It would certainly be small as there is no real elevation difference to work with. I don't know, it's not a scenario I have ever analyzed.

Maybe @Chestermiller can help? Or our other resident engineers.

 

[erobz]

The water is assumed static in the pipe. Where is convection coming in?

All three modes of heat transfer are happening in your example, radiation likely is negligible.

The heat transfer problem is characterized by convection from the water to the pipe wall, conduction across the pipe wall, and convection to the environment.

This illustrates the problem through a plane wall, but the concept is the same for a cylindrical wall.

Surely we have to be in the neighborhood of what you are after?

Maybe you're asking if because the fluid is static (no bulk velocity) it's no longer convection. That I don't know.

There is a statement in the text book I pulled that from:

"Convection includes energy transfer by both bulk fluid motion (advection) and the random motion of fluid molecules (conduction or diffusion)."

 

[bob012345]

Of course the car radiator is a dynamic situation where hot fluid is pumped through it and ambient air flows past it. The spigot is turned off and the water is still but with some temperature gradient between inside the wall and the outside spigot exposed to the freezing air in the OP. Fortunately, my outside spigots are wrapped with insulation which traps some air and protects against exposure to wind. I also pile bags of leaves around them as an extra layer of protection. We recently had well below freezing temperatures with stiff 25 mph winds. Nice wind chill! Not as bad as that day in Chicago many years ago when the wind chill was -82 F on December 24th in 1983.

 

[Chestermiller]

The water pipe and water within it acts like a cooling fin, conducting heat from inside the warm house to the air outside. The more vigorous the wind, the more heat is removed by the wind and the colder spigot end of the pipe gets (assuming that the outside air temperature is lower than the temperature inside the house). If the outside air is very cold, the water in the spigot can freeze.

 

[hutchphd]

All three modes of heat transfer are happening in your example, radiation likely is negligible.

I am not convinced that this is true for air temperatures only marginally subfreezing. On a clear night radiative cooling (space is quite cold!!) certainly leads to increased frost damage to crops.
Pleas convince me radiative cooling it is negligible.

 

[gmax137]

View attachment 319571

My interest here is finding out something about the inside surface coefficient (h1 in the figure provided by @erobz ) -- in my work life we routinely solved these problems where the inside fluid was flowing, ie, forced convection (we used empirical correlations eg, Dittus-Boelter). In the OP problem, the inside fluid is static and eventually solid (freezing ice). I'm curious if there is a developed correlation applicable to that scenario.

The reason for my interest: in recent cold weather the condensate drain on my (newly installed) tankless water heater froze. This caused the condensate to backup and leak into my garage. After I got it thawed and flowing I added insulation to the outside end of the drain line:

EDIT: following @Chestermiller 's post, maybe analyzing this as a pipe is not the way to go; as he said it's more like a fin. A fin of composite materials, with the outside coefficient based in convection & radiation (thanks @hutchphd) heat transfer, and the inner guts of the fin based on conduction.

 

[Frabjous]

I am not convinced that this is true for air temperatures only marginally subfreezing. On a clear night radiative cooling (space is quite cold!!) certainly leads to increased frost damage to crops.
Pleas convince me radiative cooling it is negligible.

I believe that radiative cooling occurs at a rate of around 1 degree C/hr for sheet metal/windows. I would argue that for a faucet which has a less favorable surface area to volume the rate of temperature drop would be dramatically less.

 

[erobz]

I am not convinced that this is true for air temperatures only marginally subfreezing. On a clear night radiative cooling (space is quite cold!!) certainly leads to increased frost damage to crops.
Pleas convince me radiative cooling it is negligible.

Well, I did say "likely negligible". When its windy, there is usually a lot of cloud cover. ( for instance, in the blizzard that just went through it was hard to see 30 ft in front of you driving with headlights) In that case the faucet isn't radiating to deep space (like it is on a very clear night), its radiating to our lower atmosphere, which is significantly warmer than deep space, and only marginally colder than the faucet. In most earth-bound engineering applications, we usually consider radiation to the surrounding environment (not deep space) as our baseline thermal potential. But I agree, its strength will depend on the opacity of the atmosphere to IR in this instance.

 

[256bits]

I am not convinced that this is true for air temperatures only marginally subfreezing. On a clear night radiative cooling (space is quite cold!!) certainly leads to increased frost damage to crops.
Pleas convince me radiative cooling it is negligible.

On a calm clear night, or on a calm clear day, or even on a windy night or day, the grass blade is radiating to the upper atmosphere or space, a place much colder than the blade of grass.
On a windy day/night the radiative heat transfer would be similar, yet here the conductive heat transfer from the air to the blade is possible, limiting the temperature drop of the blade of grass to that similar to the bulk temperature of the air, overcoming the radiative heat transfer.
It does take all that much wind to disturb the ground layer of air.

 

[Nik_2213]

For 'historical reasons', our wall-mounted garden spigot is fed by a pipe which emerges from house, turns, meets a screw-down 'service' valve, runs along wall for a 'cubit' then rises a 'cubit'... (*)
All straight copper pipe with remarkably reluctant compression fittings...
When the old 'service' valve finally seized and its rusted wheel snapped off, I took the opportunity to replace it, up-grade up-bend to one with wind-out drain port, and spigot to modern model with integral non-return valve...
And, yes, replace their 'tired' insulation wrap, which I suspect has been harvested for nesting by garden birds...

IMHO, just insulating your condensate drain-pipe is not enough, you must shelter it, too...
Plus, given such wintry conditions, provide an alternate, in-garage path so that, in extremis, blocked drain will over-flow to a convenient catch-pot such as a translucent plastic 'jerrycan' depth-gauged with vivid food-dye and a DIY 'spar-buoy'...

*) 'cubit': A common, but variable 'WTF ??' length between 12 in and 50 cm...