Based on the geometrical structure and operation condition of test prototype of medical isotope reactor, the three-dimensional physical and mathematical models on the natural convection and bubbly driven two-phase convective heat transfer in the pool with internal heat source and with horizontal and vertical tube heat exchanger immerged were proposed, and the corresponding numerical simulation was performed. The computed heart transfer coefficients for different internal heat source and bubble flow rate were gained and compared with the detected ones by employing the analogy theory and dimension analysis, the empirical criteria correlations of Nusselt number of two phase heat transfer for the horizontal and vertical heat transfer exchanger was derived and compared with each other, which was provided with theoretical reference for the selection of the heat exchanger tube layout