{'fraction_non_alphanumeric': 0.014666666666666666, 'fraction_numerical': 0.005333333333333333, 'mean_word_length': 5.791855203619909, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Mathematical framework for predicting the thermal behaviour of spectrally selective coatings within an industrial near-infrared furnace

Abstract A transient finite difference thermal model based on the heat equations is developed, valid for spectrally selective surface coatings on any substrate material within a near-infrared (NIR) furnace. Spectral radiative heat transfer equivalent to a blackbody provides the heat source. Both radiative and natural convective cooling are accounted for. A Monte Carlo ray tracing algorithm is formulated and used to determine the radiation view factor. The variance of the algorithm in relation to mesh resolution and sample size is tested against published exact solutions. The radiative flux is divided into absorbed and reflected bands using hemispherical reflectance spectra measured within the 250–15,000 nm wavelength range, enabling the model to predict the thermal build-up of coatings with very different radiative properties. Results show that the transient temperature distribution of spectrally selective surface coatings within an NIR furnace can be modelled, with good agreement observed between experimental and simulated data. The model shows the expected relationship between colour and absorption, with darker coatings displaying greater absorption and heating rates than lighter coatings. Surprisingly, colours which appear similar to one another can display different heating rates, a result of their varied infrared reflectance properties.