The present investigation was undertaken to apply theoretical methods to the ventilation of polluted air in room where carbondioxide was not homogeneously diffused. C is the concentration of carbondioxide at time nδT (=pδt), and subscripts m-1 (=q-2), m-1/2 (=q-1), m (=q), m+1/2 (=q+1), and m+1 (=q+2) denote spaces on one dimention in room (m-1) δX [=(q-2) δx], (m-1/2) δX [=(q-1) δx], mδX (=qδx), (m+1/2) δX [=(q+1) δx], and (m+1) δX [=(q+2) δx], respectively, and superscripts +, 1/2, -1/2, and - denote time (n+1) δT [=(p+2) δt], (n+1/2) δT [=(p+1)δt], (n-1/2) δT [=(p-1) δt], and (n-1) δT [=(p-2) δt], respectively, where δX/2=δx, δT/2=δt, Assuming that the concentration of carbondioxide depends on time and space as described in the previous paper, a following equation can be obtained : 〓C/〓T=D (〓
2C/〓X
2) where X is a distance from a source of evolution of carbondioxide, and D is a constant (not equal to 0). According to a implicit difference analogue for the above equation, Taylor's expansion theorem, Crank-Nicolson's method, Schmidt's method, Dusinberre's method and D δt/(δx)
2=1/2, following equations can be obtained : [numerical formula] [numerical formula] [numerical formula] [numerical formula] It was found that these methods were available for the theoretical study of natural ventilation of polluted air diffused heterogeneously in room.
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