The heat conduction under steady state within a fiber assembly was theoretically analysed, and its effective heat conductivity λ
e; (cal/cm•°C•sec), was calculated as follows:
In case of the right angle arrangement, λ
e; /λ
w; =1/b∑<∞><k=0>(-1)
k(b
n-β
b-n)A
n; .
In case of the equilateral triangle arrangement, the above equation can be used, or λ
e; /λ
w; =1/b∑<∞><k=0>2A
n; {√<a
2+b
2>/2}
n-β(√<a
2+b
2>/2)
-n sinnφ where, n=2k+1 β=parmeter derived from the heat conductivities of fibers and medium λ
w; =heat conductivity of the medium (cal/cm•°C•sec) a, b, φ=parameters depending on the arrangement of fibers in the fiber assembly A
n; =coefficients which satisfy the boundary conditions and can be obtained by applying the least square method along the boundary lines
The results calculated by these equations agreed well with both experimental and reported data.[1, 2]
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