Models for heat transport in granular interactions

radius heat model

Parameters: \(k_s\)

Example:

pair_style granular
pair_coeff * * hertz 1000.0 50.0 tangential mindlin 1000.0 1.0 0.4 heat radius 0.1

For heat radius, the heat \(Q\) conducted between two particles is given by

\[Q = 2 k_{s} a \Delta T\]

where \(\Delta T\) is the difference in the two particles’ temperature, \(k_{s}\) is a non-negative numeric value for the conductivity (in units of power/(length*temperature)), and \(a\) is the radius of the contact and depends on the normal force model. This is the model proposed by Vargas and McCarthy.

area heat model

Parameters: \(h_s\)

Example:

pair_style granular
pair_coeff * * hertz 1000.0 50.0 tangential mindlin 1000.0 1.0 0.4 heat area 0.1

For heat area, the heat \(Q\) conducted between two particles is given by

\[Q = h_{s} A \Delta T\]

where \(\Delta T\) is the difference in the two particles’ temperature, \(h_{s}\) is a non-negative numeric value for the heat transfer coefficient (in units of power/(area*temperature)), and \(A=\pi a^2\) is the area of the contact and depends on the normal force model.