Spray cooling efficiency plays a critical role in the heat dissipation process from the external surface of industrial low-carbon cement rotary coolers. This study numerically investigated the thermal performance of high-temperature zones by examining four spray parameters: spray angle, nozzle distance, spray height, and mass flow rate. Multi-objective optimization design (MOD) was subsequently performed using response surface methodology (RSM). RSM reveals spray angle as the most significant parameter affecting heat transfer. With temperature uniformity as a constraint, MOD yields the following optimal parameters: 89° spray angle, 380 mm nozzle distance, and 663.5 mm spray height. This configuration achieves an average surface temperature of 814.33 K and a heat flux of 131,588.3 W/m². The optimized spray parameters ensure high heat flux and uniform surface temperature while enlarging the heat transfer area and strengthening the synergistic heat transfer between dual nozzles. This approach provides a reliable technical pathway for efficient thermal management in industrial rotary cooler exteriors.

The accurate reconstruction of the internal temperature field in rotary kilns is critical for optimizing the clinker calcination process and ensuring energy efficiency. In this study, a rapid and high-fidelity surrogate modeling framework is proposed, utilizing snapshot ensembles generated by full-order Computational Fluid Dynamics (CFD) simulations to reconstruct the temperature field of the axial center section. The framework incorporates a symmetric Autoencoder (AE) coupled with a TabPFN network as its core components. Capitalizing on the kiln’s strong axial symmetry, this reduction–regression system efficiently maps the high-dimensional nonlinear thermodynamic topology of the central section into a compact low-dimensional latent manifold via AE, while utilizing TabPFN to establish a robust mapping between operating boundary conditions and these latent features. By leveraging the In-Context Learning (ICL) mechanism for prior-data fitting, TabPFN effectively overcomes the data scarcity inherent in high-cost CFD sampling. Predictive results demonstrate that the model achieves a coefficient of determination (R²) of 0.897 for latent feature regression, outperforming traditional algorithms by 6.53%. In terms of field reconstruction on the test set, the model yields an average temperature error of 15.31 K. Notably, 93.83% of the nodal errors are confined within a narrow range of 0–50 K, and the reconstructed distributions exhibit high consistency with the CFD benchmarks. Furthermore, compared to the hours required for full-scale simulations, the inference time is reduced to 0.45 s, representing a speedup of four orders of magnitude. Consequently, the predictive system demonstrates excellent accuracy and efficiency, serving as an effective substitute for traditional models to realize online monitoring and intelligent optimization.

In a calcined clay rotary cooler, the flow behavior and heat transfer characteristics of the granular bed are key factors determining the cooling efficiency. In this study, an Euler–Euler multiphase model coupled with the kinetic theory of granular flow (KTGF) was used to simulate the granular bed flow and heat transfer in a rotating drum of a rotary cooler. Unlike conventional large-particle beds, the 11 μm calcined clay particles interact more strongly with the gas phase, resulting in stratification and fluidization in the fine-particle bed. The effects of rotational speed, baffle configuration, and number of baffles on the flow and heat transfer behavior of the calcined clay granular bed were investigated. The results show that L-shaped baffles provide superior cooling, achieving a granular bed temperature and heat transfer coefficient (HTC) of 656.88 K and 151.15 W/(m²·K), respectively. At 2 rpm, the maximum temperature decrement and HTC increment are 5.73 K and 46.30 W/(m²·K), whereas excessive rotational speeds intensify bed fluidization. Additionally, increasing the number of L-shaped baffles has limited influence on expanding the fluidized region. With 12 L-shaped baffles, the temperature decrement peaks at 2.86 K and the HTC increment reaches a relatively high 33.27 W/(m²·K). This study provides a theoretical basis for the design and optimization of industrial-scale rotary cooling equipment for fine-particle beds.