5.5 Further Issues
381
Fig. 5.120 A simple packing of cubic particles
Fig. 5.121 A dense bed of poly-dispersed spheres
where ˆ
d p is the equivalent particle diameter. It indicates that F =
π
6
1
3 for black
surfaces at ϕ → 0.
Multiple-Sized Packing
For example, the conduction of a multiple-sized packed bed is shown in Fig. 5.121.
In general, the conductive flux for this case is
q c,i j =
T i − T j
R i j
= C i j
T i − T j
,
(5.257)
where R i j is the contact thermal resistance, and C i j is defined as
C i j =
1
R i j
,
P i − P j
≤
d i +d j
2
, i = j,
0, else
(5.258)
By Eq. (5.246), the conductive effective thermal conductivity is formulated as
381
Fig. 5.120 A simple packing of cubic particles
Fig. 5.121 A dense bed of poly-dispersed spheres
where ˆ
d p is the equivalent particle diameter. It indicates that F =
π
6
1
3 for black
surfaces at ϕ → 0.
Multiple-Sized Packing
For example, the conduction of a multiple-sized packed bed is shown in Fig. 5.121.
In general, the conductive flux for this case is
q c,i j =
T i − T j
R i j
= C i j
T i − T j
,
(5.257)
where R i j is the contact thermal resistance, and C i j is defined as
C i j =
1
R i j
,
P i − P j
≤
d i +d j
2
, i = j,
0, else
(5.258)
By Eq. (5.246), the conductive effective thermal conductivity is formulated as