To solve the temperature at the fluid-solid interface in conjugate heat transfer simulations, a partitioned yet non-iterative scheme with desirable accuracy has been developed. It takes into account the involved complex effects, for example, heterogeneous solid structure, moving interface, and phase change.The fluid and solid phases are discretized by standard Cartesian and unstructured tetrahedron meshes, respectively. At each time step the moving fluid-solid interface is tracked with the level-set function. The non-iterative solution is achieved by formulating a linear system formed from the discretized interface elements, each of which, either triangular or quadrilateral, is assigned with a respective control volume constructed from adjacent grid points in both fluid and solid phases. The temperature gradient operator is treated by the node-based Green-Gauss formula for better robustness if the interface geometry (or mesh) is highly skewed. Numerical results demonstrate the second-order accuracy with satisfactory robustness even on highly skewed interfaces.

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