Wake Flow and Heat Transfer Due to a Spherical Viscous Droplet

Abstract

A numerical study on the buoyancy-assisted flow and heat transfer from a liquid spherical droplet falling in fluid medium is made. The investigation is based on the solution of the Navier-Stokes equations together with the energy equation inside and outside the droplet, along with a suitable interface condition. The governing equations for three-dimensional flow and heat transfer are solved through the pressure correction based iterative algorithm, SIMPLE. The Reynolds number for the exterior flow is considered below 300 with the Richardson number in the range 0 ≤ Ri ≤ 1.5. The form of the wake due to the viscous droplet and its influence on heat transfer and drag coefficient are analyzed for a wide range of physical parameters. It is found that by increasing the Reynolds number, the predicted rate of heat transfer is significantly increased for a liquid droplet compared to a solid sphere. The increment of viscosity of the droplet increases the drag experienced by the droplet but reduces the rate of heat transfer. An increase in Richardson number produces an increment in drag coefficient as well as in heat transfer. In order to establish a simplified model for heat transfer due to a viscous droplet, we compared our computed solutions with several empirical correlations for conjugate heat transfer and proposed a model (in absence of buoyancy). We have also investigated the validity of several empirical correlations for the drag coefficient.

The authors acknowledge the financial support received from the Council of Scientific and Industrial Research, Government of India through a project grant.