Rushing past ... .
A bottom survival limit is set by the thermal capacity of the material and melting is determined by the phase change energy. Most people don't need to know the latter for steel :-). BUT cooling, thermal insulation, what's beyond the section in question may all add to survivability by taking heat away. As lightning delivers the energy effectively instantaneously as far as thermal issues are concerned, I'd expect lightning to need fewer C (Coulombs) to melt a bar than you'd need over a a longer period. Thermally its Watts per volume that matter.
Iron / Steel:
Latent heat 420 J/kg/k
LH of fusion: 96-140, 272 kJ/kg different sources
Melt 2100-2800 F-> Say 1400C
Ambient to melting temperature ~= 1400 x 420 = ~~ 600 kJ/kg
Melt - Say 300 kJ/kg to get it nicely splattered.
Heat + melt = 600 + 300 = Say 1000 kJ
30,000 A will dissipate I^R.t J
Use 20,000 A for 1 mS
E = I^2.R.t
R = E/t/I^2 = 1000 kJ /.001 / 30,000^2 =~~ E3 x E3 / E9 ~= 0.001 Ohms.
Higher than I would have expected.
To not melt from sheer heat absorption alone a 1 kG sli=iug of steel has to have a face to face R of
R <~~~= 1 milli Ohm
SG of steel is ~~~= 8
Resistivity of steel ~~~= 1 to 2 x 10^07 Ohm.meter.
1kg = 1/8 SG x 1/1000 tonne = 1/8000 m^3 = 0.000125 m^3
Using square wire because it's late :-)
t = thickness of slice in m
R= t/A Rho = t^2/V.Rho
so t = sqrt(R . V . E^7)
t = sqrt(0.001 x 0.000125 x E^7)
= sqrt(1.25) =~ 1.1m
Which has to be wrong as it makes cross section (1/8000)/1.1 m^2
or about 11 mm square iron bar to resist 30,000 A for 1 mS.
Hard to believe.
However - the same energy to achieve full melting of the same kg of steel would equally well be delivered by 3000 A in 100 mS.
Or 300A in 10 s IF no heat energy was lost.
So if the answer is correct (unlikely) you may just about not melt a 11mm square steel bar in open air at 300A.
Note that whereas for water the energy for vaporisation is > energy for heating from ambient. because steel has such a long way to go from ambient, the heating energy is about 2 x actual melting energy (if I read the tables right).
Anyone is welcome to revisit both the assumptions, constants, theory and figurings above.
The odds of there not being an error are close to zero.
I'm off to sleep - dentist's appointment for sore tooth 6.5E0 hours from now.
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