Heat Conduction Model

The Heat Conduction contact model calculates the heat flux based on the relative temperatures and the particle overlap.

This model 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. The Geometry temperature does not change whereas the particle temperature will be updated 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 (H&A) Chaudhuri (Chaudhuri, Muzzio, and Tomassone 2006).

The heat flux between the particles is defined as:

Q p 1 p 2 = h c Δ T p 1 p 2 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa aaleaacaWGWbGaaGymaiaadchacaaIYaaabeaakiabg2da9iaadIga daWgaaWcbaGaam4yaaqabaGccqqHuoarcaWGubGaamiCamaaBaaale aacaaIXaaabeaakiaadchadaWgaaWcbaGaaGOmaaqabaaaaa@4375@

Where the contact area is incorporated in the heat transfer coefficient c and is defined as:
h c = 4 k p 1 k p 2 k p 1 + k p 2 3 F N r * 4 E * 1 3 MathType@MTEF@5@5@+= feaahyart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAamaaBa aaleaacaWGJbaabeaakiabg2da9maalaaabaGaaGinaiaadUgadaWg aaWcbaGaamiCaiaaigdaaeqaaOGaam4AamaaBaaaleaacaWGWbGaaG OmaaqabaaakeaacaWGRbWaaSbaaSqaaiaadchacaaIXaaabeaakiab gUcaRiaadUgadaWgaaWcbaGaamiCaiaaikdaaeqaaaaakmaadmaaba WaaSaaaeaacaaIZaGaamOramaaBaaaleaacaWGobaabeaakiaadkha daahaaWcbeqaaiaacQcaaaaakeaacaaI0aGaamyramaaCaaaleqaba GaaiOkaaaaaaaakiaawUfacaGLDbaadaahaaWcbeqaamaalaaabaGa aGymaaqaaiaaiodaaaaaaaaa@50A1@
 Where FN 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 indicates the contact area between particles.
Note: You must use this contact model along with the Temperature Update Body Force model.