A model based on one-dimensional heat conduction and classical homogeneous nucleation has been applied to study the boiling explosion phenomena during high heat flux pulse heating of water. In this model, a characteristic liquid cluster at the liquid boundary is taken into consideration and the boiling explosion condition is defined by considering the energy balance in that cluster. The model describes that the boiling explosion corresponds to a particular stage of liquid heating at which the energy consumption in the cluster due to bubble nucleation and growth exceeds the energy deposition to the cluster by external heating. By applying this model, the occurrence of the boiling explosion condition in water at atmospheric pressure has been determined for a wide range of boundary heat fluxes (15-1000 MW/m2) at various liquid initial temperatures (293 K-373 K). The effects of the boundary heat flux and the liquid initial temperature on various boiling explosion characteristics such as the liquid temperature and the time of the boiling explosion, heat flux across the liquid vapor interface, number of bubbles generated per unit area at the boiling explosion etc. are determined and discussed in context with other relevant information. The boiling explosion time as obtained in the present model is found to be in good agreement with that reported by other researchers for identical liquid heating conditions. With the consideration of a characteristic time period of 1 millisecond for the occurrence of the boiling explosion, the present study corresponds to a limiting boundary heat flux of about 15 MW/m2 for water at atmospheric pressure.