How to calculate the heat that leaves the furnace through one opening? I recently read in the newspapers that one man died through the flame that left the iron furnace. I wasn't sure about this. Iron is melting at 1500 °C. The furnace they used is 8 cubic meters, he was standing one meter from the furnace. The opening is 1 squared meter. By the story, he was outdoors when malfunction door opened and made him burns from which he died. The temperature in our city that day was 35 °C. I wasn't sure about the story is this heat really enough to cause the burns that can kill you. I tried to calculate the heat that left with this formula (Q=m×c×ΔT) but I have no idea of the air heat after the accident, so I can't calculate ΔT.
I'm sure I'm missing something, could someone point me in the right direction?
 A: As mentioned, you can try Stefan's law. It says, that the radiation flux $j$ is $j=\sigma T^4$, where $\sigma$ is Stefan's constant $σ = 5,670 · 10e-8 J s^{-1} m^{-2} K^{-4}$.
In reality, furnice can be quite good chamber resonator, which radiates almost like black body (there is no reflection of any light within a resonator). So in that case only the cross-section of the doors is important, eg. we have T=1700K, S=1m$^2$. In that case we se, that radiation power is $P=S j=S \sigma T^4=473564 W \simeq 480 kW$, which is quite a lot. So in case of 1s long  exposure the furnice radiated  480 000 J of energy, which is equal to 0,13kWh. Now we have famous chicken-slapping problem (How many times do we have to slap a chicken, to be cooked), because we have to calculate how much meat we can coock with 0.13 kWh.
Let's assume 500W stove in that case we can cook for about 16 min. This is not sufficient to bake 80 kg of meat, but can produce quite crispy crust on a average steak, which can be fatal for the steak, eg. it can produce serious burns, especially if they are on head or other woulnerable bodyparts.
Bear in mind, that $j \propto 1/r^2$, so the distance betwen furnice and deceased is important. But as long as he was only couple of meters away, the order of magnitude is quite the same. He also wouldn't received all heat power, since he has limited cross-section, but in general, we are speaking about heat source, which can bake well done steak  in 1 s, which is quite dangerous. Combine that with hot potential hot gasses and here we are.
A: $Q=m×c×ΔT$ is not useful here.
What you can do is apply Stefan - Boltzmann (as an approximation), which tells us that:
$$P=A\varepsilon \sigma T^4$$
where:

*

*$P$ is the power emitted by the grey body radiator,

*$\varepsilon$ is the emissivity, which we can approximate as $1$,

*$\sigma$ equals $5.670373\times 10^{-8}\mathrm{Wm^{-2}K^{-4}}$,

*$A$ is the surface area of the radiator,

*$T$ is the temperature of the radiator.

This gives a number of $560\mathrm{kW}$ (kilowatt).
Note however that not all of this radiation reached the unfortunate victim, as it is emitted in all directions of a hemisphere. You can estimate the portion of this radiation that reaches the man from his frontal surface are and the surface area of that hemisphere.
A: I think there was a sudden burst of flame out of an opening in the furnace that impinged on his body, not from radiative heat transfer from the furnace.  This can happen very quickly allowing no time to move away.  This can occur due to a combination of extra oxygen combined with a localized higher fuel source, and/or sudden movement (collapse) of combustible fuel.
