Heat Transfer From Vertical/Inclined Boundaries of Heat-Generating Boiling Pools

A model for heat transfer from the sides of a volume heated boiling pool is proposed. Because of the density difference caused by volume boiling and by thermal expansion due to the temperature difference between the bulk fluid and the fluid near the wall, the lighter liquid and vapor bubbles cause movement of the bulk fluid in the upward direction. The rising liquid between the bubbles finds a return path along the walls or sides of the pool and forms a boundary layer which may be laminar in its initial length followed by transition to turbulent depending, of course, on the conditions prevailing at the entry to the sides and in the bulk of the pool. The analysis for the laminar case provides the definition of equivalent Grashof number for the combined two-phase and thermal expansion driven natural convection along the sides of pool. The turbulent boundary layer is analyzed by assuming a two-layer model in which the inner layer is characterized by viscous and conduction terms and the outer by mean convection terms. The similarity analysis of the governing equations yields universal profiles for temperature and velocity and the scaling laws for the inner and outer layers. An asymptotic matching of the temperature profile in the overlap region leads to a heat transfer law which correlates the available experimental data on volume heated boiling pools exceedingly well.