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Functionally graded materials have found extensive applications in the aerospace industry and solar energy systems due to their excellent performance in enhancing heat transfer/insulation. Developing corresponding theoretical frameworks for the coupled radiation and conduction heat transfer (CRCHT) is crucial for unlocking their full potential and expanding their applicability in various high-performance and critical applications. Considering the limitations of existing frameworks in addressing CRCHT problems in practical applications, such as the explicit iteration procedure and the linearization assumption, a fully implicit framework as the source value caching function Monte Carlo (SVC-FMC) method is proposed based on the null collision reverse Monte Carlo and the Green's Function Markov Superposition Monte Carlo, which are suitable for solving the radiative transfer equation and the energy equation within non-uniform media. The accuracy of the proposed method is validated with different heat transfer systems. It was observed that the maximum root mean square error during the verification process did not exceed 0.08, thereby demonstrating the efficacy of SVC-FMC in analyzing CRCHT processes involving gradient materials. Results reveal that the material properties that transcend the functional distribution form will augment the strengthening effect of heat transfer/insulation. The scattering characteristics significantly influence the strengthening effect caused by refractive index distribution.

The thermal design of detectors can effectively reduce problems caused by high-power consumption, such as shortened detector life, accuracy reduction, and chip damage. However, the traditional numerical model for the thermal design of detector arrays is difficult to construct and solve accurately, requiring a complex model structure, massive grid division, and considerable computation. In this study, a novel thermal design method, called the unit–array equivalent method (UAEM), is proposed for the thermal design of detector arrays consisting of multiple complex repetitive detector units. The method can simplify the detector unit structure in an array by using an equivalent approach for ensuring model accuracy. The effectiveness of the method is verified through numerical experiments on heat conductivity, surface gas, and surface radiation. Meanwhile, this method is used to study the ALICE Inner Tracking System, and the equivalence and correlation of UAEM are examined. Compared with the model constructed by traditional methods, this method saves 95% of the calculation time. At the same time, the average error between the equivalent model and the experiment is within 0.35 °C. This method solves the contradiction between model accuracy and computation. Thus, an accurate and fast numerical approach for the thermal analysis of detector arrays is provided.