The present investigation was undertaken to apply theoretical methods to the ventilation of polluted air in a room where carbon dioxide was not homogeneously diffused. In the case of one-dimensional diffusion, C is the concentration of carbondioxide at time T (=nδT) and subscripts m, (m+1) and (m-1) denote space mδX, (m+1) δX and (m-1) δX, respectively, and superscript + denotes time (n+1) δT. In the case of two-dimensional diffusion, subscripts j, k ; j, k-1 ; j, k+1 ; j-1, k ; j+1, k ; denote spaces x=jh, y=kh ; x=jh, y=(k-1) h ; x=jh, y=(k+1) h ; x=(j-1) h, y=kh ; x=(j+1) k, y=kh, respectively. Assuming that the concentration of carbon dioxide depends on time and space, as described in the previous paper, the following equation can be obtained : ∂C/∂T=D (∂2C/∂X2) where X is a distance from the source of evolution of carbon dioxide and D is a constant (not equal to 0). Three well-known finite-difference approximations to the above equation are forward-difference, backward-difference, and central-difference equations. According to Schmidt's, Dussinberre's, and Crank-Nicolson's methods, following equations can be obtained : Forward-difference equations C+m=(Cm+1+Cm-1)/2 C+m=(Cm+1+Cm+Cm-1)/3 C+m=Cm+1-Cm+Cm-1 Backward-difference equations C+m=(C+m+1+C+m-1+2Cm)/4 C+m=(C+m+1+C+m-1+3Cm)/5 C+m=(C+m+1+C+m-1+Cm)/3 Central-difference equations C+m=(C+m+1+C+m-1+Cm+1+Cm-1+2Cm)/6 C+m=(C+m+1+C+m-1+Cm+1+Cm-1+4Cm)/8 C+m=(C+m+1+C+m-1+Cm+1+Cm-1)/4 In the case of two-dimensional diffusion : Forward-difference equations C+j, k=(Cj-1, k+Cj+1, k+Cj, k-1+Cj, k+1)/4 C+j, k=(Cj-1, k+Cj+1, k+Cj, k-1+Cj, k+1+2Cj, k)/6 C+j, k=(Cj-1, k+Cj+1, k+Cj, k-1+Cj, k+1-2Cj, k)/2 Backward-difference equations C+j, k=(C+j-1, k+C+j+1, k+C+j, k-1+C+j, k+1+4Cj, k)/8 C+j, k=(C+j-1, k+C+j+1, k+C+j, k-1+C+j, k+1+6Cj, k)/10 C+j, k=(C+j-1, k+C+j+1, k+C+j, k-1+C+j, k+1+2Cj, k)/6 Central-difference equations C+j, k=Cj, k/3+(C+j-1, k+C+j+1, k+C+j, k-1+C+j, k+1+Cj-1, k+Cj+1, k+Cj, k-1+Cj, k+1)/12 C+j, k=Cj, k/2+(C+j-1, k+C+j+1, k+C+j, k-1+C+j, k+1+Cj-1, k+Cj+1, k+Cj, k-1+Cj, k+1)/16 C+j, k=(C+j-1, k+C+j+1, k+C+j, k-1+C+j, k+1+Cj-1, k+Cj+1, k+Cj, k-1+Cj, k+1)/8 It was found that above equations were available for the theoretical study of ventilation of polluted air diffused heterogeneously in a room.
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