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Research Papers: Conduction

# Heat Transfer Between Colliding Surfaces and Particles

[+] Author and Article Information
Like Li, Renwei Mei, James F. Klausner, David W. Hahn

Department of Mechanical and Aerospace Engineering,  University of Florida, Gainesville, FL 32611likelichina@ufl.edu

J. Heat Transfer 134(1), 011301 (Nov 18, 2011) (12 pages) doi:10.1115/1.4004874 History: Received December 01, 2010; Revised August 08, 2011; Published November 18, 2011; Online November 18, 2011

## Abstract

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.

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## Figures

Figure 1

Variation of the contact area during collision

Figure 2

Computational domain and boundary conditions at z = 0

Figure 3

Temperature contours on the surface of particle 1 based on the self-similar solution at small time (t*≪1) at (a) Fo = 0.02, (b) Fo = 0.1, (c) Fo = 1.0, and (d) Fo = 10.0

Figure 4

Dimensionless heat flux across the contact area at small time (t*≪1) based on self-similar solutions

Figure 5

(a) Local solution of (θ − 0.5)/(wρ1 / 2 ) around the singularity point at (ξ, η) = (1, 0) and (b) The value of w in the local solution of θ around the singularity point at (ξ, η) = (1, 0)

Figure 6

Local transient temperature profiles at (ξ > 1, η = 0) when Fo = 1

Figure 7

Compasion of numerical result and analytical fit for fi (η) in Eq. 58

Figure 8

Variation of the dimensionless heat flux integral qw*(t*) over the contact area at Fo = 0

Figure 9

Variation of the multiplier A*/t* in Eqs. 30,31

Figure 10

Variations of the dimensionless heat flow rate Q·*(t*) at Fo = 0; the self-similar solution is Q·*(t*) = 0.2820948A*/t*.

Figure 11

Comparison of the dimensionless heat flux integral qw*(t*) at different Fourier numbers

Figure 12

Heat flux q*(t*,ξ) in the contact area at various times for Fo = 1

Figure 13

Temperature variations along ξ-direction(η = 0) at various times for Fo = 1

Figure 14

Heat transfer as a function of the impact Fourier number (particles of the same material)

Figure 15

Correction factor comparison between computation and the approximate expression at (a) k2 /k1  = 1.0, (b) k2 /k1  = 0.1, and (c) k2 /k1  = 10.0

Figure 16

Isothermals on the surface of particle 1 at Fo = 50 when (a) t*  = 0.5, (b) t*  = 0.75, and (c) t*  = 0.95

## Errata

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