When two particles of different temperatures approach each other they start to exchange heat due to radiation, heat conduction through the fluid where the particles are immersed, heat convection in the the fluid and heat conduction as they touch each other. In addition heat can be generated during contact due to friction between the particles and dissipation as they deform.
But let us focus only on heat conduction between two particles whose temperatures are as shown in the figure:
The amount of heat transferred between the particles depends obviously on various factors: the temperature difference, the size of the contact area and contact duration. In reference [1] we can find a relation for the case where the collision between the particles is purely elastic (i.e. no losses and as the particles deform they later return to their initial shape). Also we assume that the particles do not rotate or slide during contact, so just a collision along the normal to plane of contact:
(in [1] there are more details; they are also repeated in [3])
But can we also look up other relations? Yes, for instance in ref. [2] you can find a relation for heat conduction for an elasto-plastic collision. In addition you can have a look at our own paper (see [3]), where we investigated so-called viscoelastic collisions (collisions where particles may also dissipate some energy as they deform).
Questions? Please contact: Pawel.Kosinski (_at_) ift.uib.no
[1] Sun, J., Chen, M. M.: (1988) A theoretical analysis of heat transfer due to particle impact. International Journal of Heat and Mass Transfer 31, 969-975
[2] Ben-Ammar, F., Kaviany, M., Barber, J. R.: (1992) Heat transfer during impact. International Journal of Heat and Mass Transfer 35, 1495-1506
[3] Kosinski, P., Balakin, B.V., Middha, P., Hoffmann, A.C.: (2013) Heat conduction during collisions of cohesive and viscoelastic particles, International Journal of Heat and Mass Transfer 58, pp. 107-116, doi:10.1016/j.ijheatmasstransfer.2012.11.011 preprint