Heat transfer between colliding surfaces and particles

Collisional heat transfer between two contacting curved surfaces is investigated computationally using a finite difference method and analytically using various asymptotic methods. Transformed coordinates that scale with the contact radius and the diffusion length are used for the computations. Hertzian contact theory of elasticity is used to characterize the contact area as a function of time. For an axisymmetric contact area, a two-dimensional self-similar solution for the thermal field during the initial period of contact is obtained, and it serves as an initial condition for the heat transfer simulation throughout the entire duration of collision. A two-dimensional asymptotic heat transfer result is obtained for small Fourier number. For finite Fourier numbers, local analytical solutions are presented to elucidate the nature of the singularity of the thermal field and heat flux near the contact point. From the computationally determined heat transfer during the collision, a closed-form formula is developed to predict the heat transfer as a function of the Fourier number, the thermal diffusivity ratio, and the thermal conductivity ratio of the impacting particles.