Computational fluid dynamics (CFD) plays a crucial role in the design of cooling systems in gas turbine combustors due to the difficulties and costs related to experimental measurements performed in pressurized reactive environments. Despite the massive advances in computational resources in the last years, reactive unsteady and multi-scale simulations of combustor real operating conditions are still computationally expensive. Modern combustors often employ cooling schemes based on effusion technique, which provides uniform protection of the liner from hot gases, combining the heat removal by means of heat sink effect with liner coverage and protection by film cooling. However, a large number of effusion holes results in a relevant increase of computational resources required to perform a CFD simulation capable of correctly predicting the thermal load on the metal walls within the combustor. Moreover, a multi-physics and multi-scale approach is mandatory to properly consider the different characteristic scales of the several heat transfer modes within combustion chambers to achieve a reliable prediction of aerothermal fields within the combustor and wall heat fluxes and temperatures. From this point of view, loosely coupled approaches permit a strong reduction of the calculation time, since each physics is solved through a dedicated solver optimized according to the considered heat transfer mechanism. The object of this work is to highlight the capabilities of a loosely coupled unsteady multi-physics tool (U-THERM3D) developed at the University of Florence within ansys fluent. The coupling strategy will be employed for the numerical analysis of the TECFLAM effusion cooled swirl burner, an academic test rig well representative of the working conditions of a partially premixed combustion chamber equipped with an effusion cooling system, developed by the collaboration of the Universities of Darmstadt, Heidelberg, Karlsruhe, and the DLR. The highly detailed numerical results obtained from the unsteady multi-physics and multi-scale simulation will be compared with experimental data to validate the numerical procedure.