Rayleigh-B?nard convection in cylindrical cells was examined in order to gather pertinent data regarding the thicknesses of viscous and thermal boundary layers and how they vary with the Rayleigh number. The effects of turbulence can be observed when a layer of fluid is enclosed by a container with a cold top plate and hot bottom plate, and as the temperature difference between the two horizontal plates increases. This temperature difference is proportional to a dimensionless parameter known as the Rayleigh number Ra. Turbulence and the chaotic changes in the fluid are due to the buoyancy forces that cause warmer air to rise and cooler air to fall. The significant temperature difference between the two plates induces plumes and thin boundary layers as well as a large scale circulation. The Prandtl number Pr equals the ratio of the kinematic viscosity to the thermal diffusivity and characterizes the fluid. The occurrence of turbulence within a cylindrical cell filled with fluid was numerically simulated. For Pr=0.7, Ra was varied between a range of 1x10<sup>5</sup> < Ra < 5x10<sup>7</sup>. For Pr=0.4, Ra was varied between a range of 1x10<sup>5</sup> < Ra < 2x10<sup>8</sup>. Using data generated by taking the horizontal slices of the simulated cell, boundary layer thicknesses were measured. The boundary thicknesses obtained were then plotted against the corresponding Ra and the log of both variables was taken to examine how the thicknesses scale with Ra. The resulting thermal and viscous boundary layer scalings were fairly consistent with experimental values. Also the boundary layer profiles generally fit the theoretical profiles.