:Part 3 : Theoretical Analysis of the Effective Heat Conductivity of Fiber Assembly
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概要
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A coefficient of effective diffusion is required to analyze the washing process of fiber assembly e.g., yarn, fabric, etc. The coefficient of effective diffusion has been estimated by analyzing theoretically the heat transmission under steady state within fiber assembly, and its effective heat conductivity was calculated.<BR>The effective heat conductivity of fiber assembly, λ<SUB>e</SUB> (cal/cm·°C·s) is calculated by the following equation, when fibers are arranged at right angles :<BR> λe/λw=1/b(∞Σk-0) (-1) <SUP>k</SUP> (b<SUP>n</SUP>-βb<SUP>-n</SUP>) A<SUP>n</SUP><BR>And when fibers are arranged in equilaterally triangle shape, the above or following equation can be used : <BR>λe/λw=1/b(∞Σk-0)2A<SUB>n</SUB> ((√a<SUP>2</SUP>+b<SUP>2</SUP>/2) <SUP>n</SUP>-β (√a<SUP>2</SUP>+b<SUP>2</SUP>/2) <SUP>-n</SUP>) sin nψ<BR>where, <BR> n=2k+1<BR>β=the parameter derived from the heat conductivities of fiber and medium<BR> λ<SUB>w</SUB>=the heat conductivity of the medium (cal/cm·°C·s) <BR>a, b, ψ=the parameters depending on the arrangement of fibers in the fiber assembly<BR>An=the coefficients which satisfy the boundary conditions and can be obtained by applying the least squares method along the boundary lines<BR>The results calculated by these equations agreed well with experimental data and the results previously reported.
- 社団法人 日本繊維機械学会の論文