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Figure 1 The physical representation of our model is illustrated in Figure 1. The convection of air from air supply to the air return vent near the ceiling is represented by the PDE part. The diffusive term is intentionally omitted since it plays a relatively minor role in dispersing indoor pollutants as suggested in [10]. Another design consideration involved is the modeling of the COz concentration near the ceiling since this is where we see most effect from human-generated CO. One explanation is that the warm breath from a human occupant acts as a “bubble” of gas that rises to the ceiling, since it is more buoyant than the ambient, cooler air. Thus, the air coming from lower in the room is modeled as a source term on the PDE across its entire path. The fact that this bubble of air does not immediately rise to the ceiling but only gradually (as observed in the response of the CO, concentration in the room due to changes of the human’s COz2 input shown in Figures 5 and 8, during the occupant experiments) is captured by the ODE part of the model, which behaves as a filter between the unknown CO, emission rate of humans and the CO. concentration in the room. Figure 1. The physical representation of the model. Fresh air with CO2 concentration U(t) enters the room from the supply vent, and exits the room after convection and mixing with human breath, V(t), which rises to the ceilings, and the measured COz2 concentration at the return vent is u(1, t).
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