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Python scripts for radiation calculations – Jabir Jamal
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Fire Engineering

Python scripts for radiation calculations

Thermal radiation is a distinct mechanism of heat transfer that allows spatially separated objects at different temperatures to transfer heat. 

Photo by Cullan Smith on Unsplash

Radiative Emissive Power

According to the Stefan-Boltzmann equation, the total energy emitted by a body is proportional to T⁴, where T is the temperature in Kelvin. The total emissive power is expressed as:

Where σ is the Stefan-Boltzmann constant (5.6704×10−8 W/m2·K4) and ε is a measure of the efficiency of the surface as a radiator, known as emissivity. 

Reference: Radiative emissive power E (An introduction to fire dynamics 3rd Edition, Equation 2.4):

Heat flux

The intensity of radiant energy falling on a surface remote from the emitter can be found by using the appropriate configuration factor or view factor F, which takes into account the geometrical relationship between the emitter and the receiver. 

Reference: Heat flux (An introduction to fire dynamics 3rd Edition, Equation 2.66):

Radiation Calculator 1

Radiation received at a parallel plane element dA1 from rectangular emitter A2. Normal to plane element dA1 passes through a corner of the rectangle emitter.

View Factor 1:

View factor is provided in Appendix A4 of the SFPE handbook for fire protection 5E:

The python script below can be used to calculate the heat flux received at the plane element parallel to the radiating panel:

Radiation Calculator 2

Radiation received at a plane element dA1 from rectangular emitter A2 located at 90°.

View Factor 2:

View factor is provided in Appendix A4 of the SFPE handbook for fire protection 5E:

The python script below can be used to calculate the heat flux received at the plane element located 90° to the radiating panel:

Radiation Calculator 3

Radiation calculator 3 is similar to Radiation calculator 1 except that there are four radiant panels parallel to the plane element dA1

View Factor 3:

Equation 1: View factor Fd1–2 (SFPE 5th Edition, Appendix A4):

Equation 2: Total configuration factor Fd1–2:

The python script below can be used to calculate the total heat flux received at the plane element parallel to the radiating panel:

GitHub

You can download the Jupyter notebooks used for this article from my repository here: https://github.com/jabirjamal/jabirjamal.com/tree/main/FE/FE_08 

Reference

  • Chapter 4 — Radiation Heat Transfer, SFPE Handbook of Fire Protection Engineering, 5E
  • An introduction to fire dynamics, 3E