Ventilation of Polluted Air in Rooms. VII. : Studies on Theoretical Equations for Ventilation of Polluted Air diffused heterogeneously in Room. (6)

Abstract

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/〓X2) 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.