# How much radiant heat does molten steel give off?

I was watching sky captain and in one scene a dex fires a 1920s death ray at a steel plate and admires his handywork. It got me wondering just how close you could stand next to molten steel before the radiant heat burns you.

I’ve done a lot of work in steel mills. I’ve stood right next to slabs of steel that were just barely cool enough to keep their shape. It’s a wee bit warm. When you get close to the flowing molten steel it feels a lot like someone blasting you in the face with a hair dryer set on high (only without the windy part) but you can get pretty close to it without getting burned.

This isn’t a plant I’ve been to, but I have been to plants that look very similar to this. Note the bridge going across the molten steel. I’ve stood on a bridge like that (yes, it’s a bit warm up there).
http://www.nzsteel.co.nz/images/Standard/Hot-Mill_plant-hires.jpg

Again, not the same plant I’ve been to, but I’ve stood right next to slabs like this while troubleshooting a high precision laser device that measured the slab width for quality control purposes.

The quantity of molten steel matters a lot here. It’s just like standing next to an ice cube versus a glacier, or a bonfire versus a match.

Rob

I’m not sure what an upward limit there would be. Is vaporized steel still “molten”? I would guess that steel liquifies at some point, and vaporizes at some higher point. And maybe becomes plasma at some still higher point? And presumably, the higher the temperature the steel is, the more heat it also radiates.

It varies a bit from one alloy to another, but it looks like the melting point of steel is around 1500 C. That’s about a third the temperature of the Sun, and heat radiated is proportional to the fourth power of temperature, so a lump of molten steel at such a distance that it has an angular area 81 times that of the Sun would provide you about the same amount of heat. That’d mean a ball (or disk, face-on) of steel about 1.5 degrees in diameter would warm you up about as much as the Sun does on a clear day.

As you can see from Chronos’ answer, it depends on two things, the temperature to the fourth power and the angular area (a.k.a. solid angle) to the first power. If you were completely surrounded by molten steel, it doesn’t matter how far away it is, you’ll be cooked, just like you would if you were one foot away from a gigantic bonfire. Movies and video games get this wrong all the time, with people surrounded by flames or molten lava.

The only other factor that matters is the emmissivity, which depends somewhat on the material and the temperature, but for molten steel is probably not too far from 100%

1.5 degrees would only be 9 times the area. You’d need 4.5 degrees.

Thanks, I knew I was screwing up somewhere there.