Unexpected LSF partition wall conductive R-value variation for different surface thermal resistances (or film coefficients)

[Paulo Santos]

Hello.

 

I am modelling lightweight steel framed (LSF) partition walls (THERM models available here: https://www.dropbox.com/s/gmaviienxzhp4rg/THERM_models.zip?dl=0 ) and simulated several surface thermal resistances (Rs), i.e, the reciprocal of the film coefficient (h).

The inner surface thermal resistance (Rsi) was fixed to 0.13 (hi=7.69) for a 20ºC indoor environment temperature, while the external surface thermal resistance (Rse) was changed from 0.00 up to 0.20 (with intermediate values: 0.04; 0.08; 0.13; 0.16), for a constant “exterior” (or unconditioned interior) environment temperature of 10ºC.

 

Very surprisingly, I found that the conductive (surface-to-surface) thermal resistance (R-value) changed significantly from 1.52 m².K/W up to 1.65 (+8%), as illustrated in the following chart:

 

The question is:

Does anyone have an explanation for this unexpected significant conductive R-value variation for the same wall by changing only the external surface thermal resistance (Rse)??

 

Thanks in advance.

BR, Paulo

[Paulo Santos]

I am using THERM version 7.6.1.0

Thanks. BR,

Paulo

[roro sell]

hi Paulo ,

i am trying to understand .

could you please tell in detail how you calculated what you call the surface-to-surface

conductive resistance ?

i assune by surface-to-surface you mean inner surface of the wall to outer surface of the wall .

regards

[Paulo Santos]

Hello.

Regarding your question:

"i assume by surface-to-surface you mean inner surface of the wall to outer surface of the wall."

Yes, you are right.

The conductive thermal resistance was computed as detailed next:

1. Making use of the THERM model computations I know the overall thermal resistance (Roverall) of the wall.

2. The inner (Rsi) and outer (Rse) surface thermal resistances are known and were imposed in the THERM model as boundary conditions (film coefficients).

3. The conductive thermal resistance (Rcond) was computed by the formula:

    Rcond = Roverall - Rse - Rsi   

Please let me know if you undersand this brief explanation or if you need more details.

Thanks. BR

[roro sell]

ok .

in short, my thinking at the moment is this :

if you expected a constant Rcond instead of a variable one when changing Rse, that expectation is an illegitimate extrapolation to 2D of a 1D heat transfer situation fact.

in a true 1D heat transfer situation your wall (having constant tenps on its inner and outer surfaces) is made of one homogeneous layer or more homogeneous layers ; and in any layer, the temperature is constant in the plane of the layer/wall and varies linearly in the direction normal to the wall (in other words, the isothermal surfaces are planes parallel to the wall surfaces) .

so the first derivative of temperature along the mentioned direction is constant. and the ratio of the heat flow along that direction  per unit of heat transfer surface area (called heat flux by some) and the said first derivative of the temp is a constant value in any homogeneous layer of the wall ; and that ratio is by definition, the thernal conductivity of the material that layer is made from .

now looking at things "from the other end", that means a layer of a certain constant thermal conductivity will always have a linear temperature distribution along its normal, such that the heat flux divided by the temperature derivative in the direction of normal is always the same value (the value of the thermal conductivity of that layer) , no matter the values of the temps on the inner and outer surfaces of the wall .

the thermal resistance of such a conductive layer is its thickness divided by its thermal conductivity . so, having a constant Rcond for such a layer when varying both or just one of the temps on the inner and outer wall surfaces comes from a constant conductivity within that homogenepus layer .

but in general. things described above do not apply to a wall that is NOT made of parallel homogeneous layers. you compute a fictitious Rcond, as if your wall would consist of parallel homogeneous layers but you use data from a true 2D heat transfer situation . and you wonder why the"law" valid in a true 1D situation (that Rcond is constant ; which comes from the constancy of the conductivity within the homogeneous layers) is not valid now.

i may be wrong and i do not have the necessary time to make the same simulation in another software, but i doubt the issue here is a computation problem in THERM .

regards

[Paulo Santos]

Dear Roro,

thanks for your wise explanations.

 

I also simulated in ANSYS using a 3D model and the conductive R-value also changed with different surface thermal resistances.

 

Making use of the THERM results i also computed the internal surface thermal resistance (Rsi) and compared with the input Rsi values:

 

Similar graph for external surface thermal resistance (Rse) :

Similar for Rsi + Rse:

 

As you can see, the computed surface thermal resistance is (in general) lower than the input values.

Shouldn't these values be the same or very similar??

 

If you need to characterize the studied LSF wall, what conductive R-value would you choose ??

 

THANKS in advance.

BR

[yalin uluaydin]

Hi Paulo,

Looked at your models and the only thing you are changing is the exterior surface heat transfer coefficient. Personally i think the explanation is pretty simple. As you know the reciprocal of the heat transfer coefficient is also same as the R value. So all you are doing is increasing the R-value of the wall when you change the coefficient. I'm not sure why you are surprised by this.

Yalin

[Paulo Santos]

Hello Yalin.

Thanks for your reply.

You need to distinguish between the overall R-value (Roverall) and the conductive surface-to-surface R-value (Rcond).

You are thinking about Roverall and I am concerned about Rcond.

Thanks. BR

Paulo

[roro sell]

hi Paulo,

it is still not clear to me how you calculated your so-called computed surface resistance. what you call your input surface resistance is the 1/h value , where h is what you provide in THERM ?

i think you should expect different values for the surface resistance in THERM (where it is not a calculated result but an input value) and the surface resistance calculated in ANSYS (where i guess it is a calculated result) .

why ? because the mathematical models for heat transfer by convection and heat transfer by radiation in the two softwares are respectively  DIFFERENT .

regarding your question

If you need to characterize the studied LSF wall, what conductive R-value would you choose ??

i once again state that according to my understanding, a fixed/unique value of Rcond has a meaning in the 1D heat transfer case only (that is when your wall is made of parallel homogeneous layers).

when you do not have such a wall (and your example is not such a wall), Rcond calculated by you with the recipe Rcond = Roverall-Rse-Rsi will not be a unique value. it will change when the temps of the inner and outer surfaces of the wall will change (you can achieve this in THERM for instance, by changing the input h value ) .

in the case of your wall, talking about a fixed/unique Rcond value for your wall is meaningless .

if what you are asking is:

what surface resistance values should i consider, those in THERM or those provided by ANSYS ?

then i think the choice has not much to do with a "scientifically" correct value if you usually work with THERM (which is standard practice in some places dealing with architecture or construction industry problems), then i do not see a reason to not use the THERM results (which once again, are based on a heat transfer by convection and radiation model that is likely simpler than the ones in ANSYS) . 

regards

[Paulo Santos]

Dear roro,

thanks for your reply.

 

Regarding your queries:

1. I am not comparing THERM and ANSYS surface thermal resistances. All values presented here were obtained or computed by THERM software.

 

2. “what you call your input surface resistance is the 1/h value , where h is what you provide in THERM ?”

Yes, You are right.

 

3. “it is still not clear to me how you calculated your so-called computed surface resistance.”

Sorry for the misunderstanding, but I will try to better clarify this point.

The computed surface resistances were calculated making use of the input environment temperatures (Ti=20ºC and Te=10ºC in these partition wall simulations), the average computed surface temperatures (Tsi and Tse)  and the computed heat flux (q in W/m2) across the wall. The formula was Rs = (T – Ts) / q

 

Thanks. BR,

Paulo

[roro sell]

ah, 

so that is what you mean by computed surface resistance..

well,

then i think you could ask Robin Mitchell your question about the difference between the surface reisitance you input as 1/h and the one computed by you ..

i am just throwing in a passing thought (which i have not considered carefully), re a possible source for the discrepancy noticed by you . .

if you write your last formula, so that it gives q not Rs, and consider it locally (that is for a very small petch of your wall border, one given by the calculation mesh), then you need to spatially average it for the whole wall border in order to get the spatially averaged q (this average value of q is the one you are referring to in your last post formula) .

so the formula i am talking about is ,

< q > = < (T-Ts) / Rs > 

where by a quantity X  between the signs < and  > , namely ,< X >  ,  i denoted its spatial average .

once again, this time, q and Ts and Rs have the meaning of local values, not spatial averages (over the whole wall border, either the inner one or the outer) .

you then spatially average both members of the equality . but please notice that the right member average IS NOT in general (T- < Ts > ) /< Rs > 

regards

[yalin uluaydin]

Hi Paulo,

I looked at the therm files and the u-value and R-values you list don't seem to match the curves. Taking the reciprocal of the u-value getting different values. The R-value is increasing while the U-value is decreasing with each step which is correct in the results. Maybe there's an error in the post processing outside of THERM?

On Friday, July 3, 2020 at 6:29:46 AM UTC-4, Paulo Santos wrote:

[Paulo Santos]

Hello Yalin.

Thanks for your reply.

You need to distinguish between the overall R-value (Roverall) and the conductive surface-to-surface R-value (Rcond).

You are thinking about Roverall and I am concerned about and ploted Rcond.

[roro sell]

hi Paulo,

i took a look at Appendix C of THERM 2.0 manual (available here

https://windows.lbl.gov/sites/all/files/Downloads/therm2.pdf ) and from the few explanations given there. it now seems to me the new question you raised (about the discrepancy between input surface resistance values and "computed" surface resistance values) is valid.

the fourth mentioned BC (on page 192 of the above mentioned pdf document) is the one we were talking about . it is called there convection/linearized radiation boundary condition .

if i understand well,  that relationship is considered in THERM computations to hold locally (that is for every patch determined by the calculation mesh on the inner surface of the wall or the outer surface of the wall) .

if that is the case,

then (according to my notations in my previous post), the spatial average of the right member of the equation i wrote in that post is indeed T - <Ts> / <Rs> .

because <Rs> is equal to Rs ; Rs being the (local) surface resistance value that is constant for every point on the wall surface (either the inner one or the outer) .

which is what you considered when making your graphs .

regards

[D. Charlie Curcija/LBNL]

I agree with this analysis. Varying surface film coefficient in 2D model changes the heat flow distribution across the model and will affect overall R-value (or L/keff). I did analysis on a homogeneous rectangle (1D) model with varying film coefficients and the R-value/keff remained constant, confirming that the model is correct.  

[Paulo Santos]

Dear Charlie,

thanks for your reply.

 

Yes, I agree with you and also performed a similar 1D analysis (assuming homogeneous wall layers), where the results are illustrated in this graph:

 

and found an almost constant conductive (or surface-to-surface) R-value if computed with the theoretical INPUTTED surface thermal resistances (Rcond1 in the plot).

 

However, if you calculate the conductive thermal resistance making use of the COMPUTED heat flux (q) and COMPUTED surface temps (Tsi and Tse):

          Rcond2 = (Tsi - Tse) / q

the obtained values are not so similar (red line in the graphic).

I believe that this small millesimal differences could be related with rounding errors, for which I have no worries.

 

 

However, I am concerned about the MAJOR differences found in a 2D LSF partition wall models for similar calculations, but this time to obtain the computed SURFACE thermal resistances, as shown in a previous post:

As you can see here, the theoretical INPUT inner surface thermal resistance is constant (Rsi = 0.13). However, the COMPUTED Rsi significantly increase with the increase of the external surface resistance (Rse), changing from 0.116 up to 0.138.

Shouldn’t the COMPUTED Rsi values (in red) be equal (or very similar) to the INPUTTED inner surface thermal resistance (Rsi in black) ??

 

Just in case you missed a previous post to Roro Sell, the COMPUTED surface resistances were calculated making use of the input environment temperatures (Ti=20ºC and Te=10ºC in these partition wall simulations), the average computed surface temperatures (Tsi and Tse) and the computed heat flux (q in W/m2) across the wall. The formula was:

        Rs = (T – Ts) / q

 

Thanks. BR,

Paulo

[yalin uluaydin]

Hi Paulo,

When there are materials in the wall with large differences in conductivity the parallel path or series type resistance calculations become less accurate or would say less applicable. Background for what you have found is provided in the Handbook of Fundamentals Modified Zone Method for resistance calculations of metal studs walls (HOF 2017 Ch.27). The heat flow through the assembly is dependent on the resistance of the materials outboard of the metal (sheathing plus film coefficient). The affected zone width varies (wider or narrower) with the thickness and resistance of the outer layers.

So in principle this is basically the case attributed to 2D lateral flow.

Width of the zone = L + zf * SIGMA(di)

L=width of metal flange

di=thickness of materials outside of flange

zf=zone factor per below

[Paulo Santos]

Dear Yalin,

thanks for your reply.

 

Yes, I agree with you regarding the big conductivity heterogeneity relevance in the thermal resistance calculations for these type of LSF walls.

I also know very well the figure you shared:

which was obtained from this journal paper:

https://www.mdpi.com/1996-1073/13/4/840

 

However, when you define as input boundary conditions some SURFACE thermal resistances (internal: Rsi and external: Rse) equal to a specified values and after the computations you obtained different output values, to me it is strange and hard to understand!!

See for instance this example, for an input Rsi = 0.13:

where the output computed Rsi differences ranges from -11% (for Rse = 0.0) up to +6.4% (for Rse = 0.20)!!

 

Do you have a reasonable explanation for this discrepancies??

 

Thanks in advance.

BR, Paulo

[yalin uluaydin]

Paulo,

I don’t think I would be able to share online the tables in the ASHRAE handbook but it is the same.

The point is changing the surface resistance on the outside is the same as changing the resistance or thickness of the sheathing. So in simplified terms you can add the surface resistance to the sheathing.

In the modified zone it is assumed the film coefficient is constant. However if you change that then is sort of the same thing as changing the sheating resistance. Maybe you can find more explanation in the following. I take it you may already know the MZM. A good amount of research by Kosny & Christian at ORNL so might be a good place to look.

http://www.steelframing.org/PDF/energy/thermal_design_guide_2015_edition.pdf

Kosny, J. Christian,J.E. " Reducing the Uncertainties Associated with Using the ASHRAE Zone Method for R-value Calculations of Metal Frame Walls.” ASHRAE Transactions v.101, Pt 2, 1995.

Christian, J.E., and Kosny, J., "Toward a National Opaque Wall Rating Label" Proceedings Thermal Performance of the Exterior Envelopes VI , ASHRAE ISBN 1-883413-29-X, December 1995.

Yalin