Design Analysis of an Electric Induction Furnace for ... - AU Journal

AU J.T. 9(2): 83-88 (Oct. 2005)
Similarly,
Qsh = MC m
θ
sh
.................................12
where, C m = average heat capacity of molten
Aluminum, (= 992J/kg K);
θ sh = amount of superheat temperature,
taken as 40°C.
and,
Q
s
= K
sGs
.......................................13
where, K s = quantity of slag formed in (kg),
taken as 8% of furnace capacity;
G s = heat energy for slag = 18kJ/kg.
Total heat energy induced (Hammond,
1978), in charge due to eddy current is given
by:
3 2 2 4
π f H
mBmaxdm
Q
ec
=
.................. 14
8ρ
where, f = frequency of power supply,
50Hz;
B max = maximum flux density, H;
ρ = resistivity of charge metal, ( for
aluminum, ρ = 2.83 x 10 -8 Ωm).
Therefore,
8ρQec
Bmax
=
....................15
3 2 4
π f d
m
H
m
Also
Qth
Qec = ........................................ 16
t
where, t = time in seconds to attain
maximum flux.
The allowable current density in the
inductor is given by:
I
J = ............................................... 17
A t
(J ranges from 20 to 40A/mm 2 ).
where, I = current in inductor in amperes, A;
A t = cross sectional area of conducting
tube (mm 2 ), take external diameter of
inductor coil, d t2 = 8mm and internal
diameter of inductor coil, d t1 = 6mm.
The number of turns of the inductor can
be determined from:
μ NI
B
r
μ
max
= o
.....................................
L
where, N = number of turns of inductor coil;
I = current in coil in amperes, A;
18
L = H in = length of coil in metres, m;
μ o = permeability of free space = 4 π x
10 -7 Hm -1 ;
μ r = relative permeability of charge
material, (for non-magnetic material μ r = 1).
Therefore,
Bmax
L
N = ........................................... 19
I
μ o
The resistance of the copper coil inductor
at ambient temperature is given by:
ρ
cl
Rθ o
= .......................................... 20
A
t
where, ρ c = resistivity of copper
=1.72 x 10 -8 Ωm at 25°C;
l = total length of copper tube, m;
= πD in N
as:
Resistance at any temperature θ is given
R
θ
= R
1 + αθ ( θ − θ )]
θ
[
o
o o
.................. 21
where, αθ o = temperature coefficient of copper
at 25°C;
= 3.9 x 10 -3 K -1 .
Coil loss due to resistance is:
2
P c
= I ...........................................22
R θ
Heat loss through conduction (Shrets et
al. 1987), from furnace walls to copper coil:
πH
m
( θ
2
− θ )
QL
=
1 1 d
2 1 Din
1 d3
[ ln + ln + ln ]
2 λzi
Dc
λas
d
2
λcu
Din
....................................... 23
where, λ = thermal conductivity, with
subscripts for zircon, asbestos, and copper
respectively;
λ zi = 2.093w/m K; λ as = 0.117w/ m K;
and λ cu = 380w/m K;
d 2 = outer diameter of crucible = D c +
2B r , m;
d 3 = inductor diameter surrounding
crucible + 2 thickness of coil, m;
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