A unified immersed boundary method for conjugate heat transfer with stable interface temperature treatment

This study presents a unified immersed boundary method for simulating conjugate heat transfer (CHT) in systems with complex geometries and large contrasts in thermal conductivity. The method applies a compressible Navier-Stokes formulation across both fluid and solid regions, thereby eliminating the need for separate solvers or coupling schemes. A locally one-dimensional (LOD) interface model is proposed to compute interface temperatures using conductivity- and distance-weighted averaging, ensuring energy conservation and numerical stability at fluid–solid interfaces. The proposed framework is validated through natural convection and rotating flow benchmarks, showing good agreement with reference solutions and clear grid convergence behavior. In particular, the method remains stable and accurate for cases involving large thermal conductivity ratios (up to ks/kf = 50). The framework is further applied to a realistic rotating fan–heat sink configuration with different material conductivities, demonstrating its capability to handle complex geometries, moving boundaries, and strong thermal property contrasts. These results confirm that the proposed unified approach provides a robust and efficient solution for engineering-scale CHT problems and is well suited for high-performance computing environments.