Summary

Over the last twenty years, with the progressive miniaturization trend of engineering systems, there has been a continuous increase of the rates with which heat is dissipated per unit area in electronic equipment. Among the many technologies under constant evaluation and development for cooling of high heat fluxes, such as two-phase thermosyphons, heat pipes and forced convection boiling in microchannels, spray cooling is one of the most promising due to the high heat transfer coefficients involved. The technique consists of atomizing a working fluid through a nozzle (or a nozzle array) directed to ward the surface to be cooled. Depending on the operating conditions, a thin liquid film can cover completely the heated surface and various regimes of boiling heat transfer can be present. These conditions provide high values for the heat transfer coefficient, which enables the removal of the large heat transfer rates with a small superheating of the heater wall. This work presents a theoretical analysis of the cooling process with a single spray perpendicular to an upward-facing flat plate heater. The mathematical model for determining the phase velocities, temperatures and droplet concentration per unit volume in the spray is based on a two-fluid quasi two-dimensional differential formulation which considers the variation of velocities in the radial direction via Gaussian distributions. A criterion for the existence of a continuous film on the heated surface is presented based on the relation between the droplet lifetime on the heated surface and the frequency with which it reaches the heated surface. When the operating conditions are such that a continuous liquid film is formed, a mathematical model is proposed to determine the variation of the film thickness as a function of the radial distance from the spray center line. This model is based on mass and momentum balances, taking into account the momentum transfer to the film by the drops which impact on its free surface. A universal log-law velocity profile is assumed in the liquid film. Boiling heat transfer in the thin film is computed based on a superposition model using the thin liquid film boiling correlation of Nishikawa. The model is verified against experimental data obtained by several authors for working fluids such as water, FC-72 and R-134a, with an average agreement of ± 30%for the average heat transfer coefficient. A mathematical model was also developed for heat transfer in the discontinuous liquid film regime based on the theory advanced by Aoki for the evaporation of a single droplet impacting on a surface. The proposed calculation method combines the Aoki model for the fraction of the surface covered by the drops with a model for the single-phase forced convection heat transfer in the fraction of the surface in direct contact with the vapor.

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