Boiling-induced natural-circulation flow in various engineered cooling channels is modeled and solved by considering the conservation of mass, momentum, and energy in the two-phase mixture, along with the two-phase friction drop and void fraction. The model is applied to estimate the induced mass flow rates through a uniform annular gap and a nonuniform annular gap between the reactor vessel and insulation under the in-vessel corium retention-external reactor vessel cooling conditions, and in the engineered corium cooling system of an ex-vessel core catcher during a severe accident. Dependence of the induced flow rate on various system parameters including the channel gap size, inlet diameter, inlet subcooling, and wall heat flux has been identified numerically. Results of the present study provide useful information for enhancing the design of engineered cooling channels to assure long-term cooling and retention of corium under severe accident conditions.