The presented work concerned a computation of two-dimensional heat transfer by laminar natural convection in a heat pipe cross section. The cylindrical annular space was categorized into two cases, in the first case the space was filled with a Newtonian fluid and the second case filled with a fluid-saturated porous medium. The mathematical model was described by continuity, momentum and energy equations in the cylindrical coordinates system using Boussinesq’s approximation and Brinkman’s equation. The numerical simulation was carried out using Comsol Multiphysics software. The effects of Rayleigh number, aspect ratio and permeability on the temperature and the velocity fields were examined and results obtained were validated and found to be qualitatively in a good agreement with those in the literature.