A three‐dimensional, two‐phase computational model for simulating boiling‐enhanced mixed convection in free‐surface flows is presented. The associated constitutive models for the thermophysical and transport properties are described. A computational model incorporating the discrete‐element analysis was used to simulate the multi‐dimensional, two‐phase flow around a heated chip in a test tank filled with Freon‐(R113). Two and three‐dimensional simulations of both natural convection and nucleate boiling heat transfer regimes are presented. The velocity field, the temperature distribution, and the vapour concentration profiles are evaluated and discussed. The simulated heat fluxes are compared with the available experimental data. While the heat fluxes from the two‐dimensional simulation agree with the fluxes calculated for the three‐dimensional case, the flow in the tank is essentially three‐dimensional. The results show that there are secondary flows which cannot be captured by a two‐dimensional model. The heat flux in the boiling heat transfer regime is only about ten times larger than that in the natural convection regime due to the small vapour concentration in tank.