This paper presents an effective numerical method for predicting the stratified flow in a horizontal circular pipe. The method employs a body-fitted, nonorthogonal grid system to accommodate the pipe wall of circular geometry and the interface of the two fluids at different temperatures, of which the level is variable. The transient behaviors of fluid flow and temperature distribution in the piping are simulated using the finite volume approach. The convection term is approximated by a higher-order bounded scheme named HLPA, which is known as a high-resolution and bounded discretization scheme. The cell-centered, nonstaggered grid arrangement is adopted and the resulting checkerboard pressure oscillation is prevented by the application of modified momentum interpolation scheme. The SIMPLE algorithm is employed for the pressure and velocity coupling. The new way of treating the unsteady conjugate heat transfer problem is presented. The present method has been applied to the stratified flow in the pressurizer surge line of the nuclear reactor, and the results have been discussed. In addition, this study has investigated the effects of level of the interface between the two stratified fluids on the transient evolution of temperature distributions in the piping wall.