In advanced water cooled reactors, an annular gap exists between pressure tube and calandria tube. The gap is closed from top but is open from bottom. Due to differential temperature between pressure tube and calandria tube, air flow is induced by natural convection. This leads to heat transfer from pressure tube to calandria tube. The quantification of the heat transfer between pressure tube and calandria tube is numerically carried out with the help of the CFD code PHOENICS. Validation of the CFD code with experimental results and some established computational work from the literature has been done in order to verify the accuracy of the code. The natural convection phenomenon in the annular gap is then simulated. The velocity and temperature fields obtained from the CFD simulation are used to compute local and average heat transfer coefficients. Heat transfer coefficients for various pressure tube temperatures are computed. The effect of water on the heat transfer in the annular gas is also studied.