# The Heat Conduction Model

Heat Conduction calculates the heat flux between particle-particle and particle-geometry contacts. This model must be used with Update Temperature particle body force to complete the calculation. The Temperature Update particle body force allows the inclusion of an external heat source and is where each particle temperature is calculated based on the heat flux calculated in the contact model and a given external heat flux.

The calculated heat flux is applied to particles only. You can assign the geometry as a heat source. However, the geometry temperature will never change whereas the particle temperature will update based on the calculated heat flux.

For dilute phase simulations, convective heat transfer is dominant and conduction between the particles or wall can be neglected. However, for dense phase, contacts between particles are significant such that conductive heat transfer must be taken into account. A single phase DEM simulation on heat transfer in granular flow in rotating vessels provides a simple approach in modeling inter-particle heat transfer. This model is based on the work of Chaudhuri (Chaudhuri, Muzzio and Tomassone 2006).

The heat flux between the particles is defined as:

where the contact area is incorporated in the heat transfer coefficient _{c} and is defined as:

where F_{N} is the normal force, r* the geometric mean of the particles radii from the Hertz’s elastic contact theory and E* is the effective Young’s modulus for the two particles. The bracketed term on the RHS of the equation models the contact area between particles. This contact model must be used along with the Temperature Update body force model.

(c) 2023 Altair Engineering Inc. All Rights Reserved.