Theoretical analysis of misalignment effects on radiative heat flux in cone calorimeter experiments

The cone calorimeter is a standard apparatus used to evaluate how materials respond to heat and fire under controlled conditions. Accurate characterization of the radiative heat flux is critical, as it directly influences ignition behavior, burning rates, and flammability metrics. This study extends a previous view factor model by incorporating the effect of sample inclination on the radiative heat flux distribution. A mathematical formulation (MF) of the view factor between the cone heater and inclined samples is developed using contour integrals derived from Stokes’ theorem. To verify its accuracy, detailed Monte Carlo (MC) ray-tracing simulations are performed, directly modeling the cone heater’s helical coil geometry. The MF and MC predictions are in close agreement under baseline alignment, with a mean relative difference of 0.49% and 95% of spatial heat flux values within ± 5 % . Similar agreement is observed across a range of tested inclinations, demonstrating that the MF accurately captures the radiative heat flux distribution. Given its substantially lower computational cost compared to the MC approach, the MF offers an efficient and reliable tool for modeling heat flux in cone calorimeter experiments. Additionally, a normalized coefficient of variation ( C v ∗ ) is introduced to quantify spatial non-uniformity, showing that inclination generally increases flux variability. These results highlight the importance of accounting for sample inclination when interpreting cone calorimeter data and establish the MF as a practical method for efficient, accurate radiative heat flux prediction. • Mathematical formulation predicts cone calorimeter misalignment effects. • Monte Carlo shows close agreement with view factor formulation. • Inclination increases spatial non-uniformity of radiative heat flux. • Mathematical formulation offers a low-cost substitute for Monte Carlo.