Numerical modeling of the non-isothermal liquid droplet impact on a hot solid substrate

The heat transfer from a solid phase to an impinging non-isothermal liquid droplet is studied numerically. A new approach based on an arbitrary Lagrangian–Eulerian (ALE) finite element method for solving the incompressible Navier–Stokes equations in the liquid and the energy equation within the solid and the liquid is presented. The novelty of the method consists in using the ALE-formulation also in the solid phase to guarantee matching grids along the liquid–solid interface. Moreover, a new technique is developed to compute the heat flux without differentiating the numerical solution. The free surface and the liquid–solid interface of the droplet are represented by a moving mesh which can handle jumps in the material parameter and a temperature dependent surface tension. Further, the application of the Laplace–Beltrami operator technique for the curvature approximation allows a natural inclusion of the contact angle. Numerical simulation for varying Reynold, Weber, Peclét and Biot numbers are performed to demonstrate the capabilities of the new approach.