This study uses a two-dimensional discrete-element simulation to determine the effective thermal conductivity and self-diffusivity-quantities that depend on the random motions of particles within a granular material flow. The simulations are performed for solid fractions from 0.015 to 0.68 and for different Biot-Fourier numbers. The assumptions used in the simulations are consistent with dense-gas kinetic theory;hence, the simulation results are shown to compare well with the self-diffusivity based on kinetic theory predictions. For the heat transfer problem, the analysis differs from classic kinetic theory since the particles can exchange heat with the surrounding fluid. For Biot-Fourier numbers much less than I, the effective conductivity from the simulations coincides with kinetic theory predictions. As the Biot-Fourier number increases above 0.1, the results deviate considerably from the classic analysis, but can be predicted using a modified kinetic theory approach. The simulation is a powerful technique, which can be extended to problems that are not consistent with kinetic theory assumptions.