Computing Particle Temperature
Select the Compute Particle Temperature check box in the physics interface Advanced Settings section to define an auxiliary dependent variable for particle temperature. The particle temperature Tp (SI unit: K) is then computed along each particle trajectory by integrating the first-order equation
(5-16)
where
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mp (SI unit: kg) is the particle mass,
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Cp (SI unit: J/(kg·K)) is the particle specific heat capacity,
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t (SI unit: s) is the time, and
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Q (SI unit: W) is the total heat source at the particle surface.
The particle temperature is treated as a single value for each particle, not as a temperature distribution throughout the particle’s volume. Therefore, the temperature computation is only valid when the temperature throughout the particle can be considered uniform; that is, the heat transfer resistance within the particle is negligibly small compared to the heat transfer resistance at the surface of the particle. This is typically true for small particles with high thermal conductivity.
Convective Heat Losses
Use the Convective Heat Losses feature to apply convective heat transfer at the surface of the particles. This feature creates the following contribution to the total heat source in Equation 5-16:
where
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h (SI unit: W/(m2·K)) is the heat transfer coefficient,
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Ap (SI unit: m2) is the particle surface area, and
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T (SI unit: K) is the temperature of the surrounding fluid at the particle’s position.
The Biot number Bi (dimensionless) can be used to determine whether the particle temperature can be treated as a uniform value. The Biot number is defined as
where LC (SI unit: m) is a characteristic length, typically the ratio of particle volume to particle surface area, and kp (SI unit: W/(m·K)) is the particle thermal conductivity. If the Biot number is very small, much less than unity, then the conductive heat transfer within the particle takes place on a much shorter time scale than convective heat transfer at the surface of the particle, so the particle temperature can be treated as a uniform value.
Radiative Heat Losses
Use the Radiative Heat Losses feature to make the particles undergo radiative heat exchange with their surroundings. This feature creates the following contribution to the total heat source in Equation 5-16:
where
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εp (dimensionless) is the particle emissivity,
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σ = 5.670373 × 10-8 W/(m2·K4) is the Stefan-Boltzmann constant,
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Ap (SI unit: m2) is the particle surface area, and
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T (SI unit: K) is the temperature of the enclosure or ambient surroundings.
User-defined Heat Source
Use the Heat Source feature to create a user-defined heat source for the particles. This feature creates a user-defined contribution to the total heat source Q in Equation 5-16.