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Abstract: In this paper, the authors present an efficient three-dimensional algorithm, based on the fully explicit matrix inversion free finite element version of the Characteristic Based Split (CBS) scheme, and apply it for the first time to the simulation of complex thermo-fluid-dynamic problems in domains containing simultaneously a fluid and a porous layer. The stability analysis recently developed for the two-dimensional version of the algorithm is here extended to the three-dimensional version. Unstructured grids have been successfully employed to solve complex interface problems. The present code produces an effective solution for complex 3D problems, and does not require large computing resources. The advantages deriving from the algorithm’s stability, the use of unstructured meshes and the low computing requirements make the present three-dimensional procedure a powerful and flexible tool for efficient modeling of real life problems. The present 3D code is used to solve both forced and natural convection in partially porous domains. [Copyright &y& Elsevier]