12.16.3. Heat Exchange

The heat transfer from the discrete phase to the continuous phase is computed in Ansys Fluent by examining the change in thermal energy of a particle as it passes through each control volume in the Ansys Fluent model. In the absence of a chemical reaction (that is, for all particle laws except Law 5) the heat exchange is computed as

(12–508)

where
	= initial mass flow rate of the particle injection (kg/s)
	= initial mass of the particle (kg)
	= mass of the particle on cell entry (kg)
	= mass of the particle on cell exit (kg)
	= heat capacity of the particle (J/kg-K)
	= heat of pyrolysis as volatiles are evolved (J/kg)
	= temperature of the particle on cell entry (K)
	= temperature of the particle on cell exit (K)
	= reference temperature for enthalpy (K)
	= latent heat at reference conditions (J/kg)

The latent heat at the reference conditions for droplet particles is computed as the difference of the liquid and gas standard formation enthalpies, and can be related to the latent heat at the boiling point as follows:

(12–509)

where
	= heat capacity of gas product species (J/kg-K)
	= boiling point temperature (K)
	= latent heat at the boiling point temperature (J/kg)

For the volatile part of the combusting particles, some constraints are applied to ensure that the enthalpy source terms do not depend on the particle history. The formulation should be consistent with the mixing of two gas streams, one consisting of the fluid and the other consisting of the volatiles. Hence is derived by applying a correction to , which accounts for different heat capacities in the particle and gaseous phase:

(12–510)

where
	= particle initial temperature (K)