Hi arty. Here's some more base fomulas that can shed more light on the inner workings of the event.
1) Modelling the source of heat as a giant central glob. We derive the thermal loop circuitry to determine how the heat flows from the source to the steel within the concreteor cladding.
Ts = Tso - (Rc + Ra + Rr + Rc) P + Ta
Tso = source temperature (buttuming max. 533 degrees) Ts = steel temperature Ta = initial temperature of steel (buttume 25 degrees) Rc = thermal resistance of concrete Ra = thermal resistance of air Rr and Rc = radiative and convective thermal resistances. P = heat flow in watts-or power that is generated by the heat source. (buttume linear rate of burning of fuel frow start to collapse)
buttume Rr and Rc = 0 and thermal capacity to be zero (it can be factored later to suit our model).
We get Ts = Tso - (Rc + Ra) P + Ta
2) Note that in your calculation of max temperature, time domain was not included. Which means that we buttume that IF we continue to expend all the fuel at a certain rate, the structures' temperature continues to rise from their initial temperatures and will ONLY reach the max temperature after ALL the fuel is expended and not before. So buttuming linear heat transfers, the temperature of the steel structures should rise from 25 degrees at a constant rate to reach 533 degrees at the end. So in between, the transient energy equations will show that the steel would be less than 533 degrees before that.
3) Analysing any typical combustion scenario, we get three general energy equations to model the three stages of any fire.....namely the initial rise in temperature....the steady state condition... and the eventual dying out.
First stage:
Where Qt = Total transient energy Qloss = Total energy losses
Steady state: Qt - Qloss = 0
End stage:
Knowing the typical losses in any scenario, we can then estimate the instantaneous energy that have to be expended at any point in time in the event. Finer details can then be added later to tweak it slowly to become increasingly representative of the actual physical event.
Cheers.
