Hi Joe
I believe the magnitude of the difference depends on the weather location, that is to say you may find different results depending on the outside environment temperatures and solar irradiation. Besides to the outside environment condition, the difference depends on thermal mass of the building. For heavy weight construction building the difference between steady state and dynamic analysis is higher compared to that of light weight. For zero thermal mass building, all input being the same E+â??s conduction model is expected to produce similar result as U.A.DT, simple because, the dynamic conduction model can be reduced to steady state form. This can be shown mathematically.
So, if you would like to see this for yourself, change all construction/materials objects in E+ IDF to resistive type, turn off all solar and internal radiant gains to zero, and eliminate the long-wave radiant exchange with the sky by setting the outside layer of the external surfaces absorptance to near zero value, then I expect you to get similar results.
Now, let us see how the building thermal mass affects the difference that you saw.
In the steady state approach the heat gains are the same as the load, but in dynamic analysis, the heat gains do not necessarily become load immediately because the radiant component of the heat gains are first absorbed by the construction (Walls, floor, roof, and internal mass), and then are released as load (e.g., cooling) at slow rate than the heat gain rate. Thus, the radiant heat gains at current time become load at a later time (mostly within 1-3 hours later for light weight and 5-7 hours for heavy weight). The fraction of the heat gain (radiant) that becomes load at a later time is temporally stored as internal energy of the construction reflected as temperature increase of the construction. This temperature increase depends on the thermal mass. This stored energy at later time may change direction of the heat flow (toward inside of the room or toward outside) because of the change of the outside condition (1-15 hours later after first absorbed). Therefore, radiant component of the heat gains is partly delayed and part of this delayed heat may not become load due to change in the stored energy heat flow direction, which depends how long it was delayed and the change in the outside boundary condition. Therefore, the dynamic analysis (e.g. E+) properly accounts for the part of the radiant heat gains delayed and distribution in time, and part of the radiant heat gains the would never become load at all when the thermal mass and the outside environment favors part of it to flow back out. For these reasons, in general, the difference between the dynamic and steady state analysis results increases for heavy weight construction building and large daily outdoor air dry bulb temperature range. This is true for any building energy or load analysis programs that have dynamic analysis capability (e.g. E+, ESP-r, DOE2.1 ... etc). Also it is worth mentioning that you may see difference between E+ and DOE2.1 results because of differences in their heat balance model assumptions.
Back to you statement, it may not be quite correct to say E+ under predicts. On the other hand one may prefer to present it as the steady state analysis over predicts. The under prediction and over prediction statements depends your reference for your comparison. I think in general the difference may reduce in cooling dominated climate such as Miami.
Hope this helps,
Bereket Nigusse
Florida Solar Energy Center --- On Sat, 10/27/12, Joe <joebater@xxxxxxxxx> wrote:
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