Homogeneous Boiling Explosion Condition: From an Energy Point of View

When a liquid undergoes boiling by homogeneous nucleation during non-equilibrium heating is very important as the characteristics of the system before and after the occurrence of homogeneous boiling explosion is significantly different. In the present study, we studied homogeneous boiling explosion condition from an energy point of view: how much energy is required to boil the liquid by homogeneous nucleation from a given initial temperature. As a representative one, water heating at atmospheric pressure has been considered under three different heating conditions namely; i) linear heating at the boundary ii) high heat flux pulse heating and iii) liquid contact with high temperature surface. The analytical formulations for cumulative energy distribution in the liquid under various liquid heating conditions have been derived and the cumulative energy density within the liquid are calculated. It has been found that the instantaneous cumulative energy density very near to the liquid boundary is several times higher than that corresponding to the thermal penetration depth for all liquid heating cases. The present study shows that, the cumulative energy density at the boiling explosion over a characteristic liquid cluster being equal to the size of a critical embryo is independent of the heating parameter and for a given initial condition, it has been found to be almost constant for all liquid heating conditions. However, the cumulative energy density at the boiling explosion decreases as the liquid initial temperature increases for all liquid heating cases. The obtained results are compared with other numerical results reported in the literature for water subjected to uniform volumetric heating at atmospheric pressure.