The current research work describes the flow and thermal analysis inside the circular flow region of an annular heat pipe with a working fluid, using computational fluid dynamics (CFD) simulation. A two-phase flow involving simultaneous evaporation and condensation phenomena in a concentric annular heat pipe (CAHP) is modeled. To simulate the interaction between these phases, the volume of fluid (VOF) technique is used. The temperature profile predicted using computational fluid dynamics (CFD) in the CAHP was compared with previously obtained experimental results. Two-dimensional and three-dimensional simulations were carried out, in order to verify the usefulness of 3D modeling. Our goal was to compute the flow characteristics, temperature distribution, and velocity field inside the CAHP. Depending on the shape of the annular heat pipe, the thermal performance can be improved through the optimal design of components, such as the inner width of the annular heat pipe, the location of the condensation part, and the amount of working fluid. To evaluate the thermal performance of a CAHP, a numerical simulation of a 50 mm long stainless steel CAHP (1.1 and 1.3 in diameter ratio and fixed inner tube diameter (78 mm)) was done, which was identical to the experimental system. In the simulated analysis results, similar results to the experiment were obtained, and it was confirmed that the heat dissipation was higher than that of the existing conventional heat pipe, where the heat transfer performance was improved when the asymmetric area was cooled. Moreover, the simulation results were validated using the experimental results. The 3-D simulation shows good agreement with the experimental results to a reasonable degree.