BR 187

This page demonstrates practical examples of thermal radiation calculations using BR 187 equations.

Complete Thermal Radiation Assessment

This example demonstrates a complete thermal radiation analysis workflow using BR 187 equations. We’ll calculate the thermal radiation received from a radiating surface (such as a fire through a window opening).

import ofire

# Step 1: Calculate source radiation intensity from the radiating surface
sigma = 5.67e-11  # Stefan-Boltzmann constant (kW/m²K⁴)
emissivity = 0.9  # Surface emissivity
temperature = 1273  # Surface temperature (K) - approximately 1000°C

I_s = ofire.br_187.appendix_a.equation_a1.radiation_intensity(
    sigma, emissivity, temperature
)
print(f"Source intensity: {I_s:.0f} kW/m²")

# Step 2: Calculate dimensionless parameters for the radiating surface
width = 4.0     # Radiating surface width (m) - e.g., window width
height = 2.5    # Radiating surface height (m) - e.g., window height
distance = 12.0 # Distance from radiating surface to receiver (m)

X = ofire.br_187.appendix_a.equation_a3.x(width, distance)
Y = ofire.br_187.appendix_a.equation_a3.y(height, distance)

print(f"Dimensionless width parameter (X): {X:.3f}")
print(f"Dimensionless height parameter (Y): {Y:.3f}")

# Step 3: Calculate view factor for parallel, centre-aligned surfaces
phi = ofire.br_187.appendix_a.equation_a3.phi(X, Y, additive=True)
print(f"View factor: {phi:.4f}")

# Step 4: Calculate received radiation intensity at the target
I_R = ofire.br_187.appendix_a.equation_a2.radiation_intensity_at_receiver(
    phi, I_s
)
print(f"Received intensity: {I_R:.1f} kW/m²")

This workflow calculates the thermal radiation from a radiating surface (like flames visible through a window) to a target receiver surface on an adjacent building, which is essential for external fire spread assessment.

Multi-Configuration Analysis

Find received radiation at different distances:

import ofire

# Source parameters
I_s = 120.0  # Source intensity (kW/m²)
width = 4.0  # Radiating surface width (m)
height = 2.5 # Radiating surface height (m)

# Test different distances
distances = [8.0, 12.0, 16.0, 20.0]  # Various separation distances (m)

print("Distance (m) | View Factor | Received Intensity (kW/m²)")
print("-" * 55)

for distance in distances:
    # Calculate parameters for centre-aligned configuration
    X = ofire.br_187.appendix_a.equation_a3.x(width, distance)
    Y = ofire.br_187.appendix_a.equation_a3.y(height, distance)
    phi = ofire.br_187.appendix_a.equation_a3.phi(X, Y, additive=True)

    I_R = ofire.br_187.appendix_a.equation_a2.radiation_intensity_at_receiver(
        phi, I_s
    )

    print(f"{distance:8.1f}     | {phi:10.4f}  | {I_R:18.1f}")

The results can be further analyzed by plotting the relationship between distance and received intensity using libraries like matplotlib or plotly for visualization.

Different Surface Configurations

Compare different view factor equations for various geometric arrangements:

import ofire

# Common parameters
width = 3.0     # Radiating surface width (m)
height = 2.0    # Radiating surface height (m)
distance = 10.0 # Distance to receiver (m)
I_s = 100.0     # Source intensity (kW/m²)

print("Configuration Analysis")
print("=" * 50)

# Configuration 1: Centre-aligned parallel surfaces (Equation A3)
X_a3 = ofire.br_187.appendix_a.equation_a3.x(width, distance)
Y_a3 = ofire.br_187.appendix_a.equation_a3.y(height, distance)
phi_a3 = ofire.br_187.appendix_a.equation_a3.phi(X_a3, Y_a3, additive=True)
I_R_a3 = ofire.br_187.appendix_a.equation_a2.radiation_intensity_at_receiver(phi_a3, I_s)

print(f"A3 - Centre-aligned parallel: {I_R_a3:.1f} kW/m²")

# Configuration 2: Corner-aligned parallel surfaces (Equation A4)
X_a4 = ofire.br_187.appendix_a.equation_a4.x(width, distance)
Y_a4 = ofire.br_187.appendix_a.equation_a4.y(height, distance)
phi_a4 = ofire.br_187.appendix_a.equation_a4.phi(X_a4, Y_a4, additive=True)
I_R_a4 = ofire.br_187.appendix_a.equation_a2.radiation_intensity_at_receiver(phi_a4, I_s)

print(f"A4 - Corner-aligned parallel: {I_R_a4:.1f} kW/m²")

# Configuration 3: Corner-aligned perpendicular surfaces (Equation A5)
X_a5 = ofire.br_187.appendix_a.equation_a5.x(width, distance)
Y_a5 = ofire.br_187.appendix_a.equation_a5.y(height, distance)
phi_a5 = ofire.br_187.appendix_a.equation_a5.phi(X_a5, Y_a5, additive=True)
I_R_a5 = ofire.br_187.appendix_a.equation_a2.radiation_intensity_at_receiver(phi_a5, I_s)

print(f"A5 - Corner-aligned perpendicular: {I_R_a5:.1f} kW/m²")