Ventilation of Polluted Air in Rooms. V. : Studies on Theoretical Equations for Ventilation of Polluted Air diffused Heterogeneously in Room (4)

Abstract

The present investigation was undertaken to apply theoretical methods to the ventilation of the polluted air in room where carbondioxide was not completely diffused. C_m+1, C_m, and C_m-1 are concentrations of carbondioxide at places (m+1) δX, mδX and (m-1) δX at time T (=nδT), respectively, C⁺_m is the concentration of cabondioxide at a place mδX at (n+1) δT, where superscript+denotes time (n+1) δT, subscripts m, (m+1) and (m-1) denote spaces mδX, (m+1) δX and (m-1) δX, respectively. Assuming that concentracion of carbondioxide depends on time and space, the following equation can be obtained, ∂C/∂T=D (∂²C/∂X²) where X is a distance from a source of the evolution of carbondioxide, and D is a constant (not equal to 0). Implicit difference analogue for the above equation can be obtained as follows, (∂²C/∂X²)_m=(C_m+1-2C_m+C_m-1)/(δX)² According to the Taylor's expansion theorem, the Schmidt's and Dusinberre's methods, following equations can be obtained, C⁺_m=(C_m+1+C_m-1)/2 C⁺_m=(C_m+1+C_m+C_m-1/3 respectively. In two dimensional diffusion, C_{j, k+1} and C_{j, k-1} are concentrations of carbondioxide at places x=jh, y=(k±1) h at time T (=nδT), and C_{j+1, k} and C_{j-1, k} are at places x=(j±1) h, y=kh, respectively, and C⁺_{j, k} is at a place x=jh, y=kh at time (n+1) δT. The following equation can be obtained as one dimensional diffusion, C⁺_{j, k}=(C_{j+1, k}+C_{j-1, k}+C_{j, k+1}+C_{j, k-1})/4 It was found experimentally that above equations were appropriate from the concentrations of carbondioxide in room.