Finite element modeling of the transient heat conduction between colliding particles

Finite element method (FEM) is employed to simulate the transient heat conduction during the collision between spherical particles. The total collision time is divided into many small time steps. At each time step, the contact area is evaluated by the Hertz's theory of elastic collision and based on this information, a grid system is generated for FEM computation to determine the temperature distribution in a particle and the heat exchange between particles. The total heat exchange is the sum of the heat exchange at all time steps. The FEM approach and computer code are verified by the good agreement between the numerical and analytical solutions for a well-established case. It is then used to simulate the transient heat transfer process during particle collision. It is shown that the heat exchange is affected by variables related to collision conditions and material properties. The results are qualitatively consistent with those obtained analytically based on the semi-infinite-media assumption. However, the analytical model overestimates the heat exchange, particularly when the Fourier number is high. A modified equation is proposed to overcome this problem based on the present FEM results. The equation is particularly suited for the newly developed particle scale modeling of the heat transfer of multiparticle systems.