This study uses the porous medium approach to develop the scaling law for investigating fluid flow and heat transfer behavior of different scaled cuboid and cylindrical packed beds filled with monosized pebbles. Dimensionless flow and thermal similarity parameters are derived from the nondimensional forms of the Navier−Stokes equation with Darcy-Forchheimer terms and the local thermal nonequilibrium (LTNE) energy equations for adiabatic and convective heat loss boundary conditions at the sidewalls. A library is developed to improve the accuracy of numerical solvers in the open-source OpenFOAM software to account for local variations in the porosity of packed beds. Leveraging the library, both unsteady and steady-state numerical models are constructed using OpenFOAM. These models are used to investigate the impact of scaling on flow and temperature distributions in packed beds for a range of heat generation rates and mass flow conditions. The scale analysis results reveal consistent nondimensional pressure drops and dimensionless outlet temperature for the scaled prototypes at different Reynolds numbers and nondimensional heat generation rates. Further, it is found that the scaling law effectively maintains the consistency in uniformity in flow characteristics and heat transfer for various scaled prototypes. The applicability of transient and steady-state scaling parameters is elucidated by considering two prominent applications in fusion reactors and thermal energy storage systems. Using the scaling law, the pressure drop of a scaled-down packed pebble bed reactor reported in the literature is predicted and compared with the VDI (Verein Deutscher Ingenieure) heat atlas correlation, demonstrating its broader applicability in engineering and industrial applications.