Direct and inverse convection models on the slot-ventilated enclosure flows with unknown wall heating fluxes

Slot-ventilated enclosure flows occurr in many engineering problems, including microelectronic cooling, cardiovascular blood flow, airborne transmission, built ventilation, etc. Inverse models on such slot-ventilated flows have consistently been observed, straightforwardly representing that boundary wall conditions are missing or unknown, whereas temperatures at certain internal points could be known as priors. In present work, the direct and inverse models on the slot-ventilated enclosure flows were established successively. For direct flow problems, enclosure flows covering from forced convection dominated flow to natural convection dominated flow are fully simulated, varying some dominant parameters, Richardson number, Reynolds number, and the functional forms of the imposed boundary heat flux. In subsequent inverse convection modeling within a mixed convection domain, multiple unknown heat fluxes and their profiles were creatively identified using the adjoint methodology, in which direct, sensitivity, and adjoint problems were formulated and solved jointly by finite volume method. The impacts of Reynolds number, Richardson number, flux functional forms, and measurement errors on the accuracy of inverse solutions have been thoroughly examined. Inverse solutions accuracy becomes poor as the field flow is dominated by mechanical ventilation, and their accuracy further deteriorates as the noise levels increase. The results demonstrate that the current inverse problem approach could yield highly accurate estimations for multiple arbitrary unknown heat flux functions within the enclosure, without any priori information. This versatile approach was applicable to a range of mixed convection control or reconstruction problems, offering substantial contributions to electronic cooling design and the optimization of enclosed air environments.