In this work, fully explicit numerical solutions for heat and fluid flow in cylindrical domains, completely or partially filled with a fluid saturated porous medium, are presented. Laminar natural convection in a vertical porous annulus and in a vertical annulus with a centrally located heat generating rod, and laminar forced convection in a pipe partially filled with a porous medium are numerically simulated. Novel stability conditions are carried out for the fully explicit Artificial Compressibility (AC) version of the Characteristic Based Split (CBS) algorithm, in order to effectively solve the above problems. The results presented in this paper are validated against experimental and numerical results available from the literature.