Dynamics of a Vaporizing Droplet in Laminar Entry Region of a Straight Channel

A theory is developed for two-phase flow wherein droplets suspended in a gas stream penetrate the hydrodynamic boundary layer in the laminar entry region of a straight channel with isothermal walls. A fraction of the droplets is captured by the boundary layer due to isotropic turbulence superimposed at the edge of the the boundary layer. Transverse motion of the droplet is under the influence of Stokes’ drag, buoyancy, gravity and inertia forces. Axial motion of the droplets is with the local gas velocity without slip. Droplet trajectories are determined by the numerical integration of the equations of motion employing the fourth order Runge-Kutta technique. Using these results, a two region model is developed for determining the convective heat transfer conductance augmented by droplet vaporization. Momentum and heat transfer results are presented for air/water-droplet system containing 10μ–50μ droplets under typical conditions encountered in dry cooling towers.