The heat transfer coefficient of the curved surface reflects the external cooling capacity of the reactor pressure vessel under serious accident. This topic used Ansys fluent software 14.5 as simulation tool, mesh generation of the flow area is carried out after the geometric model of the lower head, and then the heat transfer coefficient of the curved surface is numerically simulated. In this paper, the heat transfer coefficient formulas are fitted according to the laminar and turbulent flow, and the influence of the cavity on the heat transfer coefficient is discussed. Calculation results show that, for single-phase flow both laminar and turbulent flow, the heat transfer coefficients increase with the increase of Re, and increase with the increase of Pr, decrease with the increase of theta; According to the comparison of the heat transfer coefficients under different radii of curved surfaces, reducing the radius is beneficial to increase the heat transfer capability; In subcooled boiling flow, the void fraction is less than 21%, the heat transfer coefficient increases with the increases of the void fraction, the void fraction is conducive to heat transfer; but when the void fraction is higher than 21%, it is opposite.