Migration and heat transfer modeling of a neutrally buoyant melting particle in Poiseuille flow

A computational model is developed to simulate the hydrodynamic and heat transfer behavior of a melting cylindrical solid particle in plane Poiseuille flow between horizontal parallel plates. The two-dimensional transient conservation equations for mass, momentum, and energy are solved using a finite-volume scheme implemented on a deforming mesh, accounting for the rotation and non-uniform melting of the particle. An arbitrary Lagrangian-Eulerian (ALE) method is employed to directly track the moving and deforming solid-liquid interface during the particle migration and phase change. The developed model was validated by comparison with the previously reported numerical results for migration of a non-melting neutrally buoyant cylindrical particle in plane Poiseuille flow with heat transfer. The effects of flow Reynolds (Re), Grashof (Gr), and Stefan (Ste) numbers, as well as the initial position of the melting particle across the channel on the particle trajectory, melting rate, and average Nusselt (Nu) number were investigated. It was found that the melting rate increased by increasing Gr and Ste and decreased by increasing Re. The Nu did not change more than 20% with increasing Re number from 100 to 1000, but increased significantly by increasing Gr. It was also observed that by increasing Re, the particle migrates toward the channel center because of the stronger Magnus effect. Increasing Gr, on the other hand, pushes the particle to the bottom wall due to the stronger downward flow adjacent to the particle induced by buoyancy-driven convection (natural convection).