In this work the dynamics of liquid crystal ordering in a cylindrical geometry are considered. We study a system with liquid crystalline properties that exhibits translational symmetry along the cylinder axis and, therefore, the problem is effectively two-dimensional. The orientation of liquid crystals is described by a tensorial order parameter and the dynamics are governed by a balance between the dissipation and the rate of change of free energy, which includes the elastic, thermotropic and surface energy terms. The evolution of the +2 defect differentiating first into two +1 disclinations and subsequently into four +1/2 defects is analysed. Different boundary conditions, namely strong and weak or no anchoring, have been considered and the critical value for the anchoring strength, at which +1/2 defects are very close to escaping through the boundary but still remain there at equilibrium, has been identified.