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148 2 Mass transfer e 1 Ga,e1-2 Ga,2-e1 Ga,1-2 Ga,2-3 Kitchen Ga,2-1 Ga,e2-2 3 Living room Hall 2 Fig. 2.11 Ground floor of example building Summing and reshuffling gives: Ga,2-e2 Ka;2-e1 ‡ Ka;2-e2 ‡ Ka;2-1 ‡ Ka;2-3 Pa;2 ‡ Ka;2-e1Pa;e1 ‡ Ka;2-e2Pa;e2 ‡ Ka;2-1Pa;2 ‡ Ka;2-3Pa;3 ˆ 0 or: Pa;2 X Ka;ij=e ‡ X Ka;ijPa;j ˆ X Ka;iePa;e which is an equation with three unknowns: air pressure in the living room (Pa2), air pressure in the kitchen (Pa1) and air pressure in the hall (Pa3). Besides the living room, kitchen and hall, the ground floor also includes a garage and a toilet, while the staircase forms a link with the first floor and its three bedrooms and one bathroom. For each, all flows entering and leaving have sum zero. The result is as many equations as the building has spaces. In matrix notation: Ka ‰ Š n;n Pa ‰ Š n ˆ Ka;ePa;e n (2.36) Solving that system of non-linear equations demands iteration. If the building is warmer or colder than outdoors, then all leaks must be located first. All spaces get a node at each leak height, after which thermal stack with outdoors against a reference height complements the pressure differences between the neighbouring nodes at another height. Among nodes above each other in the same space, very large air permeances are assumed. With the indoor temperatures in all spaces and the outdoor temperature known, stack changes into a known term in the balance equations. Otherwise, in the unheated spaces, the temperature will depend on the transmission losses, the heat gains and the temperature of the entering air. This requires consideration of conservation of energy. The correct temperatures then follow from assuming temperatures first, followed by alternately solving the


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