Heat flow: u-factor question

  1. How do you determine the u-factor of a window assembly? I understand that the u-factor is reciprocal of the sum of resistance (U=1/Σr) for wall assembles, but I’m unable to find any relevant arithmetic for windows. I understand that heat flow rates vary between the center of glass and frame, and that u-value of windows is representative of a whole system, but is there not an arithmetic means to determine the u-value at the center of the window? For example, let’s say I have a ¼” double pane glass with a ½” of argon gas between them (1” total thickness). What is the u-value of the glass at the center? Do I use U=1/Σr? Is that correct?
  2. jcsd
  3. A wall comprises several elements "in series" (eg the heat flows through plaster, then brick, then insulation etc). That's why you can add the thermal resistance.

    In the case of a window it's more complicated. The glass part is similar (eg You have glass, argon, glass "in series") however there is another path in "parallel" through the frame. See equivalent electrical diagram attached. To find the overall thermal resistance you would apply the same rules that you would for calculating the equivalent resistance of an electrical circuit (http://en.wikipedia.org/wiki/Series_and_parallel_circuits).

    However there is an additional complication. The values you have for the thermal resistance are probably quoted "per square meter". So you have to take into account that the frame and glass have different areas.

    If you have already calculated the thermal resistance of the glass part "per square meter" then one way is you use an "area weighted average" to arrive at the thermal resistance "per square meter" for the combination.

    In more complicated cases you have to calculate the actual resistance of each part by multiplying by the actual area of that part, then doing the series/parallel calculations and then finally dividing the end result by the total area to get back to an overall thermal resistance "per square meter". Just bear in mind that the end result is only valid if the ratio of frame to glass stays roughly the same. Clearly if you had a very small window that was all frame and no glass you couldn't use the same figure "per square meter" for the thermal resistance to calculate the heat loss.

    Attached Files:

  4. So just to answer this bit...

    In short Yes...

    Google can find the thermal resistance of each material but it's specified "per meter thickness" so...

    Work out the actual thermal resistance of each part by multiplying the thermal resistance of the material by it's thickness in meters.

    Add them together eg..

    Rtotal = Rglass + Rargon + Rglass

    This gives you the thermal resistance for the 1" thickness.

    Take the reciprocal to give the U Value.

    Experts will complain it's more complicated because I have ignored surface effects. Coatings are very important these days to the performance of glass sealed units.
    Last edited: Dec 6, 2013
  5. This helps tremendously. I take it that the objective to thermally broken frames is to reduce the heat flow and improve the overall thermal performance. Let me attempt to apply this information and I may have more questions pertaining to this thread.
  6. Yes.

    It's particularly important for metal framed windows. Without a thermal break you can also get condensation on the metal frame inside.
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