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16.4
Solid Phase Phenomena
This section contains examples that test the one-dimensional heat conduction solver in FDS, along with
those that include pyrolysis.
16.4.1
Simple Heat Conduction Through a Solid Slab (heat_conduction)
Analytical solutions of transient, one-dimensional heat conduction through a slab can be found in Refs. [33]
and [34]. Four cases are examined here. In each, a slab of thickness L = 0.1 m is exposed on one face to
an air temperature of Tg = 120 ◦ C. The other face is insulated (adiabatic). The convective heat transfer from
the gas to the slab is q̇00c = h (Tg − Ts ), where h is constant, and Ts is the slab face temperature. No thermal
radiation is included.
Case
k
(W/m/K)
0.1
0.1
1.0
10.0
A
B
C
D
ρ
(kg/m3 )
100
100
1000
10000
c
(kJ/kg/K)
1
1
1
1
140
140
heat_conduction_a
heat_conduction_b
120
120
100
100
Temperature ( C)
Temperature ( C)
Bi
hL/k
100
10
1
0.1
h
(W/m2 /K)
100
10
10
10
80
60
40
80
60
40
20
20
0
0
0
500
1000
1500
0
2000
2000
4000
Time (s)
8000 10000 12000 14000
Time (s)
70
140
heat_conduction_d
heat_conduction_c
120
60
100
Temperature ( C)
Temperature ( C)
6000
80
60
40
50
40
30
20
20
10
0
0
10000
20000
30000
40000
50000
0
10000
20000
30000
Time (s)
Time (s)
144
40000
50000