9 Numerical Simulation on the Slab Heat Transfer Behavior …
105
where x, y and z directions are considered as slab length, height and width directions
respectively, such as those shown in Fig. 9.2, T c is the temperature, ρ is the density,
t is time, c is the specific heat, and λ c is the conductivity.
9.3.2 Initial Conditions
For the characteristic of the object, only one parameter, i. e. temperature of the
slab, need to be set up as initial condition. So, the slab is assumed to be at uniform
temperature of 300 K, when charged to the reheating furnace.
9.3.3 Boundary Conditions
Oxide Scale. There are six faces, i. e., upper surface, lower surface, right surface,
front surface, bake surface and symmetry face, for the studied geometry as those
shown in Fig. 9.2. Apart from the symmetry face, all the surfaces are exposed to
hot combustion gases environment during reheating process. The combustion gases
consist of some oxidizing gases, such as H 2 O, CO 2 , and O 2 . Under high temperature
conditions, metal easily reacts with the combustion gases. As a result, an oxide
layer, which consists of FeO, Fe 3 O 4 and Fe 2 O 3 from inside to outside, forms on
these surfaces of the slab. But, the percentage thicknesses of the three oxide layers
are not the same. And researcher [12] has suggested that FeO, which forms next
to the metal, comprise about 95% of production. The second is Fe 3 O 4 , which is
the intermediate phase, about 4%. The least is Fe 2 O 3 , which is the outermost layer
of the scale, only about 1%, when the temperatures are higher than approximately
873 K. Therefore, in this work, it is assumed that the scale layer consists of only one
component, FeO, like any other literature [13, 14]. The thermal properties of FeO are
listed in Table 9.1. Meanwhile, in this case, the thickness of scale can be represented
as Eq. (9.2) [12]:
δ
2
= δ
2
0 + k 0 te
−Q/RT
.
(9.2)
where δ is the scale thickness, δ 0 is initial scale thickness at time t = 0, t is the
oxidation time, k 0 is a constant of 6.1, Q is the activation energy of iron oxidation of
169,452 J/mol, R is the gas constant, and T is absolute temperature.
Although, the oxidation reaction is exothermal reaction, the rate of heat release
is almost negligible. So, in this work, the effect of the heat of oxidation reaction on
temperature field within the slab is neglected [13, 14].
As mentioned previously, the oxide scale has poor thermal conductivity, large
specific heat and less surface emission rate compared to that of slab, so the existence
of the oxide layer on the slab surface can affect the heat transfer behavior. A thermal
105
where x, y and z directions are considered as slab length, height and width directions
respectively, such as those shown in Fig. 9.2, T c is the temperature, ρ is the density,
t is time, c is the specific heat, and λ c is the conductivity.
9.3.2 Initial Conditions
For the characteristic of the object, only one parameter, i. e. temperature of the
slab, need to be set up as initial condition. So, the slab is assumed to be at uniform
temperature of 300 K, when charged to the reheating furnace.
9.3.3 Boundary Conditions
Oxide Scale. There are six faces, i. e., upper surface, lower surface, right surface,
front surface, bake surface and symmetry face, for the studied geometry as those
shown in Fig. 9.2. Apart from the symmetry face, all the surfaces are exposed to
hot combustion gases environment during reheating process. The combustion gases
consist of some oxidizing gases, such as H 2 O, CO 2 , and O 2 . Under high temperature
conditions, metal easily reacts with the combustion gases. As a result, an oxide
layer, which consists of FeO, Fe 3 O 4 and Fe 2 O 3 from inside to outside, forms on
these surfaces of the slab. But, the percentage thicknesses of the three oxide layers
are not the same. And researcher [12] has suggested that FeO, which forms next
to the metal, comprise about 95% of production. The second is Fe 3 O 4 , which is
the intermediate phase, about 4%. The least is Fe 2 O 3 , which is the outermost layer
of the scale, only about 1%, when the temperatures are higher than approximately
873 K. Therefore, in this work, it is assumed that the scale layer consists of only one
component, FeO, like any other literature [13, 14]. The thermal properties of FeO are
listed in Table 9.1. Meanwhile, in this case, the thickness of scale can be represented
as Eq. (9.2) [12]:
δ
2
= δ
2
0 + k 0 te
−Q/RT
.
(9.2)
where δ is the scale thickness, δ 0 is initial scale thickness at time t = 0, t is the
oxidation time, k 0 is a constant of 6.1, Q is the activation energy of iron oxidation of
169,452 J/mol, R is the gas constant, and T is absolute temperature.
Although, the oxidation reaction is exothermal reaction, the rate of heat release
is almost negligible. So, in this work, the effect of the heat of oxidation reaction on
temperature field within the slab is neglected [13, 14].
As mentioned previously, the oxide scale has poor thermal conductivity, large
specific heat and less surface emission rate compared to that of slab, so the existence
of the oxide layer on the slab surface can affect the heat transfer behavior. A thermal