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HeatFlux Command

The HeatFlux command applies heat fluxes to surfaces near particles (which are expected to be on the surface) in MPM calculations. It applies a flux to all particles selected by a ParticleBC block.

HeatFlux (mode),(face),(style),(value),<(time)>

where the parameters depend on the type of heat flux being applied. The two types of flux boundary conditions, which depend on (mode), are as follows.

Externally Applied Heat Flux

This condition applies a surface flux in heat flux units for transport rate of heat per unit area. A positive value is flux into the material while a negative value is flux out of the material. The parameters are:

Coupled Heat Flux

This version calculates the heat flux from a function of the particle temperature. The parameters are:

Two uses of this flux condition are to implement convective and/or radiative boundary conditions. In convective cooling or heating, the function could be

function = h*(T0 - t)

where h is heat transfer coefficient (in heat flux units/K), T0 is a reservoir temperature, and t is used for surface particle temperature. In radiative cooling or heating, the flux function could be the Stefan-Boltzman law:

function = σ*ε*(T04 - t4)

where σ = 5.6704e-8 W/(m^2 K^4) is the Stefan-Boltzman constant and ε (<1) is the emissivity. In these functions, the physical terms should be replaced by their numerical values. If desired, however, they could also be functions themselves, such as to have h be a function of t or surface particle temperature. They cannot, however, depend on time, because t is used here for particle temperature instead of time.