Many laboratory-scale combustors are equipped with viewing windows to allow for characterization of the reactive flow. Additionally, pressure housing is used in this configuration to study confined pressurized flames. Since the flame characteristics are influenced by heat losses, the prediction of wall temperature fields becomes increasingly necessary to account for conjugate heat transfer (CHT) in simulations of reactive flows. For configurations similar to this one, the pressure housing makes the use of such computations difficult in the whole system. It is, therefore, more appropriate to model the external heat transfer beyond the first set of quartz windows. The present study deals with the derivation of such a model, which accounts for convective heat transfer from quartz windows external face cooling system, free convection on the quartz windows 2, quartz windows radiative properties, radiative transfer inside the pressure housing, and heat conduction through the quartz window. The presence of semi-transparent viewing windows demands additional care in describing its effects in combustor heat transfers. Because this presence is not an issue in industrial-scale combustors with opaque enclosures, it remains hitherto unaddressed in laboratory-scale combustors. After validating the model for the selected setup, the sensitivity of several modeling choices is computed. This enables a simpler expression of the external heat transfer model that can be easily implemented in coupled simulations.

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