Lattice Boltzmann model for thermal behavior of a droplet on the solid surface

• Lee's model was used to simulate droplet impinging dynamics on the solid surface.
• In order to consider the thermal effects, passive scalar model has been used.
• The Boussinesq approximation was used to couple the thermal and hydrodynamic effects.
• The thermal effect of Prandtl number ratio between two phases was discussed.

In this work, a thermal lattice Boltzmann model is applied to simulate thermal behavior of a droplet on the solid surface. For this reason Lee's model which uses the Cahn–Hilliard diffuse interface theory, is utilized to capture the droplet interface. Also contact angle between solid, liquid and gas phases has been considered in simulations. To take into account the thermal effects, passive scalar model is conjugated with the Lee's method. Since in this model the solution of temperature distribution is independent of flow field, application of the Boussinesq approximation couples the energy and momentum equations. Numerical results for two thermal boundary conditions; constant wall temperature and constant heat flux on the wall, are presented and results have been compared with previous numerical results. Results show that by increasing the Prandtl number ratio between droplet and its surrounding, thermal diffusion within the droplet will be delayed and this causes reduction in the droplet average temperature. Also it was shown that the wall heat flux is concentrated around the droplet, while that in the gas phase is negligible.