Calculating Max humidity for a house
I want to write some code to control my whole house humidifier. I want my code to calculate the percentile relative humidity above which dew will form on my windows.
I have sensors for air temperature and humidity inside and out, and pressure, which better be the same because I don't live in an airplane.
I'm trying to brush up on my math so I can understand the clausius-clapeyron equation. I think I understand that there's a basic algebra cheater formula but that it doesn't work outside of common humidity ranges and I want my code to be solid.
I also suspect I might need to add a temperature sensor to the internal surface of the windows. But I'm hoping that there might also be a formula to calculate with that temperature will be given the indoor and outdoor and the r value of the window.
I'm hoping they can look something like this below. Disclaimer: I do not expect in any way these examples below work
InnerSurfaceTemp=TempIn-((TempIn-TempOut)/RVal) MoldRH=Rh where dewpoint=indoor temp MaxRh= MoldRH-2. ( For a safety threshold)
What formula can I use to determine the inner surface temp of a window?
And what formula can I use to determine the maximum indoor RH to prevent condensation on that window surface?
I think this is a physics problem but please forgive me if I am barking up the wrong tree.
1 answer
Practically (or engineeringly) speaking you'd need the surface temperature sensors; or experimentally determined fudge-factor values. Experimentally you might determine which window is most prone to form dew first and measure that one, though this may, depending on ventilation, vary significantly when cooking or showering are happening due to local variations in internal humidity from those activities; or merely having people in a particular space for a while, (such as sleeping in a bedroom, or socializing in living room) since people breathing affects the local humidity. More ventilation will tend to reduce those local effects by mixing the air, or directly removing the very moist air in the case of kitchen and bath vent fans.
Thing being that your internal temperature sensor is measuring where it is, and the temperature profile near a window with colder air outside it is not simple to model, since the colder surface of the window sets up convection currents as it cools the inside air next to it, which sinks and is replaced by warmer air from above, that is cooled, and sinks... and the temperature of the air in the room is almost never uniform anyway, since the walls and windows are removing heat while the heating system is adding heat. The thermostat setting controls the temperature where the thermostat is, and everywhere else varies - how much depending on details of the construction, insulation, air sealing, heating system design, etc.
The R-value tells you the heat input required to maintain a temperature differential across a window (or wall, ceiling, floor, door, etc.) It does not in any direct way tell you how the effect on the temperature of the surfaces of those items, though they are certainly affected by the flow of heat - so the inside surfaces will be cooler and the outside surfaces will be warmer than the simplified assumption that inside temperature == temperature of the inside surface and outside temperature == temperature of the outside surface. Windows being comparatively poorly insulated they have a lot of heat flow and those assumptions are thus thrown off by a greater extent than they are for a better-insulated section of wall.
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