Mathematical modeling of heat and mass transfer in hot gas spray systems

A mathematical model is developed to study simultaneous heat and mass transfer in hot gas spray systems. The model is obtained by writing mass, energy, and momentum balances for both continuous and discontinuous phases. Governing equations along with suitable correlations for heat and mass transfer coefficients have been solved numerically. In order to develop a realistic model for such complicated systems, a droplet size distribution was implemented in the model instead of using an average size. A steady state spray-cooling problem is analyzed to illustrate the applicability of the model. To validate the mathematical model for this case, necessary data was collected and measured in commercial cement plants. A good agreement between plant data and the model was noticed in general, and results obtained from the model indicate that size distribution of water droplets and physical dimensions of the spray-cooling system are important parameters. This model is very useful in determining the so-called "critical operation condition" at which sludge formation at the bottom of spray-cooling systems will happen. The predicted parameters in spray-cooling systems both for droplet phase and gas phase aptly illustrate the ability of the model to treat the complex phenomena associated with two-phase flows.