Three dimensional (3D) buoyancy driven fluid flow, heat and mass transfer through a vertical board with structures of randomly packed fibers are simulated by a non-dimensional lattice Boltzmann method (NDLBM). The two outside walls in the board transverse direction are fixed with opposing constant temperature and species concentration. The outside walls in the longitudinal directions are adiabatic. Varying board porosities, fiber diameters, and board thicknesses are generated by a controllable structure generation scheme (CSGS). The NDLBM simulations with D3Q27 grids show 3D velocity, temperature and concentration fields in the mesoscopic scale. The effects of board porosity, fiber diameter, and board thickness are quantified. The results show that the trends of macroscopic Nusselt, Sherwood, and Biot numbers with macroscopic porosity are similar to previous 2D random structure simulations, but the 3D fiber structures are more effective for both heat and mass transfer compared to 2D random structures with equivalent governing parameters. The difference in transfer properties is attributed to mesoscopic flow patterns. The mesoscopic 3D spiral flow is due to the 3D vortex generated by local fiber boundaries. The stagnation points of the 3D spiral structures usually appear at relative higher local porosity positions. The 3D spirals enhance the pore scale heat mass transfer.