**4. Conclusion**

The numerical method based on the BEM is presented for solving the coupled set of partial differential equations, which describe the fluid flow and heat transfer in porous medium domain. The mathematical model is based on the Navier-Stokes equations, which are averaged over the representative elementary volume. The proposed numerical algorithm solves the velocity-vorticity formulation of the governing equations. The numerical scheme is split into the single-domain BEM, which solves the kinematic equation for unknown boundary vorticity values and sub-domain BEM for domain velocity, vorticity, and temperature values.

The numerical algorithm is tested on an example of natural convection phenomena in porous media domain for a 2D as well as 3D geometry. Porous media are fully saturated with pure fluid or water-based nanofluid with addition of Cu nanoparticles. Obtained numerical results were validated with available benchmark solutions.

The natural convection phenomena strongly depend on the parameters, e.g., Rayleigh number and Darcy number. Addition of nanoparticles to a base fluid enhances the heat transfer through porous media, when conduction is the dominant heat transfer mechanism. On the other hand, in convection dominated regime, the addition of nanoparticles reduces the magnitude of convective motion.

The good agreement of the results with the published ones confirms the efficiency of the BEMbased methods as a powerful alternative to the existing numerical methods.
