U-value of air? Why 25 W/m2K? 1

[asiga]

I've been told to assume that the U-value of air is 25 W/m2K. However, in other calculations I'm using the thermal diffusivity of the same volume of air (2.208*10-5 m2/s at 30ºC), and, since both values are related, I'd rather prefer to obtain the U-value from the thermal diffusivity, so that my calculations are coherent.

Given that the thermal diffusivity is alpha=lambda/(c*rho) , I can get the conductivity as lambda = alpha * rho * c = 2.208*10-5 m2/s * 1.1644 kg/m3 * 1005.7 J/kgK = 0.0258565 W/mK

And then, since U = lambda/thickness, I get U = 0.0258565 W/mK / 1m = 0.0258565 W/m2K

So, I'm getting "25" in the result, but divided 1/1000.

Going to the engineeringtoolbox website, it gives me 25.72 for conductivity of air at 30ºC

So, where's the catch?

Thanks a lot!!

 

[Latexman]

For conduction, U = k/[Δ]x

[α] = k/([ρ]C[sub]P[/sub])

I'm not seeing a relationship.

Good Luck,
Latexman

 

[asiga]

Why don't you see a relationship? U and k are related. And alpha and k are related. Therefore, alpha and U are related. That's what I was doing in my post.

 

[IRstuff]

Do the dimensional analysis. Your U value is in W/m^2-K, but your thermal conductivity is in W/m-K; that gives you a thickness of air for the U value

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[TiCl4]

Asiga,

Where did you get to assume 1 meter for the thickness? I don’t think you understand what thermal boundary layers are, based on your 1 meter assumption. U = k/Δx is the calculation for heat transfer through a solid layer with skin temperatures of each side of the layer known - i.e. conduction. Air transfers heat via convection, not conduction. For fluid heat transfer, the calculations get more complex and depend greatly on the conditions.

Generally, U = [1/ho + Δx/k + 1/hi]^(-1)*

*for heat transfer between two fluids that are separated by a solid layer (refractory, metal wall, etc). This equation is valid when the resistance to transfer through the solid wall is relatively small compared to the fluid resistance AND when the curvature of the wall is small (i.e. a large diameter tank that can be approximated as a "flat" surface). If the curvature is significant (i.e. pipes), then you have to factor in Do, Di, and Dlm (log mean diameter). This also neglects any fouling factors. For heating/cooling a solid isothermal block of something in air U = 1/h.

ho = individual heat transfer coefficient of the interior fluid
Δx = thickness of the solid wall
k = thermal conductivity of the solids wall
hi = individual heat transfer coefficient of the exterior fluid

For fluids, ho and hi are calculated from the Nusselt number. This equation varies based on application (forced vs natural convection, transfer geometry like vertical or horizontal plate, etc).

For natural convection of air on a vertical plate,

Nu = h*L/k = α * [Gr*Pr]^m, where

h = individual heat transfer coefficient of the specific fluid
L = characteristic length of the heat transfer area. For a large diameter vertical tank whereby you calculate Nu based on a vertical plate, L would be the height of the tank.
Gr = Grashof number
Pr = Prandtl number
α, m = constants based on the geometry chosen to analyze (i.e. vertical plate).

You can look up other correlations for Nusselt number for the geometry you are analyzing.

I believe the general recommendation of 25 W/m2K is the recommendation for heat transfer to surfaces because the thermal boundary layer for air is usually the governing resistance to heat transfer. People have run these calculations for a variety of reasons and found this to be a reasonable approximation.

 

[asiga]

Ok, ok, point taken about the thickness.

However, forget about the U-value for a moment, because there's another problem that seems to come first: the thermal conductivity of air seems to be anyway in the order of 25 W/mK instead of the 0.0258565 W/mK that I'm getting in my calculations above. Check here for example:

https://www.engineeringtoolbox.com/air-properties-viscosity-conductivity-heat-capacity-d_1509.html

Why this big difference with a 1/1000 ratio?

 

[MortenA]

Some process simulator may use this value as a default value for a 2 sided HX if you are interested in calculating both side but you dont want to size the HX - so you are just interested in the energy ballance. In order to do the calculation the software needs the U value - but instead of calculating it rigerously you use a default value.

 

[TiCl4]

Asiga,

The link you provided calculated 23 mW/mK at standard conditions. I think you missed the milliwatt part. That is close to your original calculation for conductivity.

 

[asiga]

That was it, thanks a lot. So, in conclusion, it seems it makes sense to have two different inputs: one, the thermal diffusivity for the fluid simulation, and two, the U-value for considering the air-to-surface transfer within the thermal boundary layer, and consider them as independent and unrelated.

 

[TiCl4]

Thermal diffusivity is related to U. The Nusselt equations factor in momentum and thermal diffusivity using the Prandtl number. So technically thermal diffusivity is one portion of the calculation of U, and not independent.

 

[asiga]

But you said "I believe the general recommendation of 25 W/m2K is the recommendation for heat transfer to surfaces because the thermal boundary layer for air is usually the governing resistance to heat transfer. People have run these calculations for a variety of reasons and found this to be a reasonable approximation."

From that sentence, I conclude that 25 W/m2K has an experimental basis (and yes, you are right that the purpose of this U-value is to transfer from air to surface, considering the top of the thermal boundary layer). So, if it's experimental, and it's used often, I shouldn't try to relate it to the diffusivity, should I?

 

[TiCl4]

I guess my point was that if you are going to use 25 W/m2K as an approximation, then you don’t need diffusivity or a calculation of U at all(since you are assuming a U value of 25.). If you need more rigorous analysis and will calculate U, then thermal diffusivity is part of that calculation and is found in the Prandtl number.

 

[IRstuff]

the 25 W/m^2-K is the high-end of what most authors consider to be natural convection. A more typical number might be more like 5 W/m^2-K

https://www.sfu.ca/~mbahrami/ENSC 388/Notes/Natural Convection.pdf

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[prex]

I usually take, for vertical walls, 10 W/m[sup]2[/sup]K for calm air and 20 W/m[sup]2[/sup]K for a fairly developed windy condition. Consider also that these figures include the effect of radiation (some 50% in the lower figure). So you can't state a single value for the exchange in ambient air, and an evaluation for a given situation won't give a very narrow figure, unless all the conditions (geometry, orientation, emissivity, wind, etc.etc.) are clearly stated

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[asiga]

Oh, what a big variation of values across authors...

@TiCl4: I need the thermal diffusivity too, because there's also a fluid simulation going on, with air-to-air transfer. My initial interest was to relate both values (air-to-air and air-to-surface), in order to avoid redundancy in the input parameters. However, from all the posts in the thread, it seems clear that the thermal diffusivity in air-to-air and the U-value in air-to-surface don't have a straightforward connection, so having both parameters as input can be legit and non-redundant.

Thanks a lot.