# Conjugate Heat Transfer Advancements and Applications in Aerospace Engine Technology
## 1 Introduction  
Advancements in aviation technology have resulted in a substantial increase in the inlet temperatures of next-generation aero-engine high-pressure turbines, which now range between 2100 K and 2200 K and continue to climb. These temperatures significantly surpass the melting points of current high-performance turbine blade materials, posing significant challenges to the longevity and safety of these components. To achieve more accurate predictions of the temperature distribution closer to experimentally obtained values of gas turbine blades, one must concentrate on conjugating the boundary condition at the fluid-solid interface through coupled heat transfer analysis. Such a coupled field study is termed as conjugate heat transfer (CHT) [1]. Over the past decade, conjugate heat transfer has emerged as a pivotal tool for elucidating the thermal exchange mechanisms within air-cooled turbines. Pioneering work by [PERSON] et al. [2] harnessed this method to simulate the low-temperature air cooling of Mark II blades, which featured ten cylindrical cooling passages. Their findings revealed a commendable concordance with empirical observations, validating the efficacy of their computational approach. Expanding upon this foundation, [PERSON] et al. [3] leveraged the same computational paradigm to scrutinize the thermodynamic performance of a singular cooling cavity proximate to the blade tip, alongside a pair of slit ejectors situated along the leading-edge stagnation line of a film-cooled guide vane. [PERSON] et al. [4] undertook an exhaustive comparative analysis, juxtaposing the cooling efficacy of turbine blades crafted from high-conductivity superalloys against those composed of lower-conductivity ceramics. Their investigations underscored the intricate interplay between material thermal properties and heat dissipation strategies and poignantly illustrated the convoluted nature of heat transfer within solid structures during the film cooling of turbine blades, highlighting the profound impact of film coverage on thermal transport dynamics. Complementing these studies, [PERSON] et al. [5] conducted a meticulous numerical examination of both conjugate and non-conjugate heat transfer phenomena within NASA-C3X planar cascades. Their research was primarily centered on delineating the influence of phase transitions on heat transfer processes. In parallel, [PERSON] et al. [6; 7] executed a sophisticated conjugate heat transfer simulation within the transonic regime of the MT1 HP stage, yielding results that exhibited a striking alignment with empirical data. Most recently, [PERSON] et al. [8] have advanced the state-of-the-art by integrating experimental data with a sophisticated conjugate heat transfer model to predict the spatial distribution of blade temperature, static pressure, and convective heat transfer coefficients for a NASA-C3X turbine blade adorned with ten cylindrical cooling channels. Their work encompassed simulations under five distinct turbulence models, culminating in a comprehensive comparison with empirical findings. This combination of computational modeling and empirical validation represents a significant stride forward in our understanding of the thermal management within advanced turbine systems. [PERSON] et al. [9] employed Large Eddy Simulations (LESs) to investigate the internal cooling channels of a turbine blade at a Reynolds number of 40,000 and a blockage ratio of 0.3. Their findings highlighted the critical role of thermal boundary conditions in augmenting heat transfer within the channel. Local simulations indicated that transitioning from a decoupled condition to a coupled thermal condition markedly alters the heat transfer outcomes, culminating in a variation of up to 80%. Notably, the enhancement factor exceeds 50% in regions behind the turbulator, where a substantial recirculation zone amplifies the heat transfer efficacy. Consequently, for an accurate assessment of the heat transfer enhancement on the blade walls, conjugate heat transfer computations are imperative.