The inert heating or cooling laws (Laws 1 and 6) are applied
when the particle temperature is less than the vaporization temperature
that you define, 
, and after the volatile fraction, 
, of a particle has been consumed. These conditions
may be written as
Law 1:
 | (12–68) |
Law 6:
 | (12–69) |
where 
is the particle temperature, 
is the initial mass
of the particle, and 
is its current mass.
Law 1 is applied until the temperature of the particle/droplet
reaches the vaporization temperature. At this point a non-inert particle/droplet
may proceed to obey one of the mass-transfer laws (2, 3, 4, and/or
5), returning to Law 6 when the volatile portion of the particle/droplet
has been consumed. (Note that the vaporization temperature, 
, is an arbitrary
modeling constant used to define the onset of the vaporization/boiling/volatilization
laws.)
When using Law 1 or Law 6, Ansys Fluent uses a simple heat balance
to relate the particle temperature, 
, to the
convective heat transfer and the absorption/emission of radiation
at the particle surface:
 | (12–70) |
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where | |
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Equation 12–70 assumes that there is negligible internal resistance to heat transfer, that is, the particle is at uniform temperature throughout.
is the incident radiation in W/
:
 | (12–71) |
where 
is the radiation intensity and 
is the solid angle.
Radiation heat transfer to the particle is included only if you have enabled the P-1 or discrete ordinates radiation heat transfer to particles using the Particle Radiation Interaction option in the Discrete Phase Model Dialog Box.
Equation 12–70 is integrated in time using an approximate, linearized form that assumes that the particle temperature changes slowly from one time value to the next:
 | (12–72) |
As the particle trajectory is computed, Ansys Fluent integrates Equation 12–72 to obtain the particle temperature at the next time value, yielding
 | (12–73) |
where 
is the integration time step
and
 | (12–74) |
and
 | (12–75) |
Ansys Fluent can also solve Equation 12–72 in conjunction with the equivalent mass transfer equation using a stiff coupled solver. See Including Coupled Heat-Mass Solution Effects on the Particles in the User's Guide for details.
The heat transfer coefficient, 
, is evaluated using the correlation
of Ranz and Marshall [542], [543]:
 | (12–76) |
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Pr = Prandtl number of the continuous
phase ( |
For inert and combusting particles, the following heat exchange coefficient correlations are available in Ansys Fluent:
Constant HTC
In this method, the volumetric heat transfer coefficient is specified as a constant value.
Nusselt number
In this method, the heat transfer coefficient is computed using the user specified Nusselt number
as follows:
(12–77)
Tomiyama model
See Tomiyama Model for details.
Ranz-Marshall model (default)
The model uses Equation 12–76 to evaluate the heat transfer coefficient.
Hughmark model
See Hughmark Model for details.
Gunn model (DDPM only)
See Gunn Model for details.
For more information on how to use these models, see Heat Transfer Coefficient in the Fluent User's Guide.
Finally, the heat lost or gained by the particle as it traverses each computational cell appears as a source or sink of heat in subsequent calculations of the continuous phase energy equation. During Laws 1 and 6, particles/droplets do not exchange mass with the continuous phase and do not participate in any chemical reaction.