Role of Air Gap in Scrap Dissolution Process
- PDF / 742,473 Bytes
- 9 Pages / 593.972 x 792 pts Page_size
- 17 Downloads / 161 Views
e temperature of the air gap and parent scrap interface will always be greater than the initial temperature of the scrap (Ti). Therefore, Eq. [24] can be written as Tm
hl ha
ðT b T m Þ ha Dx k
þ1
>TP >Ti
½25
or Tm
hl ha
ðTb Tm Þ ha Dx k
þ1
>Ti
½26
Substituting the value of Dx in Eq. [26] and rearranging, ha Bia ¼ > hl Bil
1 1 ðhb 1Þ
Bil N1
½27
where the Biot numbers for air gap and liquid metal are defined as
TS Tp
hl ha
Tm
Tm
Air gap
kTm Dx
On solving Eqs. [21] and [23], the following relationship is obtained:
Let the first grid which is added due to solidification be of thickness Dx (Figure 5) where Dx is defined as Dx ¼
½22
where TP is the temperature at the interface of the air gap and the parent scrap. From Eq. [22], the interface temperature of the steel shell and air gap TS is estimated from TS ¼
III. SELECTION CRITERIA FOR DECIDING THE MINIMUM VALUE OF HEAT TRANSFER COEFFICIENT IN THE AIR GAP AND THE NUMBER OF GRIDS
½21
shell
Bia ¼
ha Lo hl Lo Tb Ti and Bil ¼ and hb ¼ k k Tm Ti
If ðN 1Þ Bil , then Eq. [27] can be rewritten as
Δx Fig. 5—The initial solidified shell ahead of the air gap.
ha Bia ¼ >ðhb 1Þ hl Bil
½28
METALLURGICAL AND MATERIALS TRANSACTIONS B
RESULTS AND DISCUSSION
The values of air gap heat transfer coefficient for different air gap thicknesses and outside surface temperatures of the parent scrap are shown in Figure 6. The air gap heat transfer coefficient lies between 1000 and 10,000 W/m2 K for an air gap thickness between 10 and 100 lm. The sensitivity of heat transfer coefficient to air gap thickness is found to be more when thickness decreases below 100 lm. The simulations are done for the conditions as well as physical properties of steel scrap as given in Table I. The Biot numbers (Bil) selected for simulations are 10, 25, 50, and 100. The ratios of air gap to liquid melt heat transfer coefficients are considered from 0.1 to 0.9. The location of boundary vs time (in dimensionless form) for different Biot numbers and ratios of heat
Boundary location
IV.
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
ha/hl = 0.10 ha/hl = 0.25 ha/hl = 0.50 ha/hl = 0.75 ha/hl = 0.90
0
0.5
1
1.5
Time
Fig. 7—Boundary location vs time for different ratios of air gap to liquid melt heat transfer coefficients (Biot no. = 10).
Boundary Location vs Time (with air gap) (Biot no = 25)
Boundary Location
Equation [28] gives the condition for the selection of a minimum number of grids as well as the condition for solidification to take place for the given superheat and ratios of air to liquid melt heat transfer coefficient.
Boundary Location vs Time (with air gap) (Biot no = 10)
1.4
ha/hl = 0.10
1.2
ha/hl = 0.25
1
ha/hl = 0.50 ha/hl = 0.75
0.8
ha/hl = 0.90
0.6 0.4 0.2 0
10000
Tp = 1535C Tp = 1200C Tp = 1000C Tp = 800C Tp = 500C Tp = 200C Tp = 100C
1000
0.1
0.2
0.3
0.4
0.5
0.6
Time
Fig. 8—Boundary location vs time for different ratios of air gap to liquid melt heat transfer coefficients (Biot no. = 25). Boundary Location vs Time (with air gap) (Biot no = 50) 1
Data Loading...
