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DPM Heat and Mass Transfer -- Convective Heating, Evaporation, Boiling, and Radiation

#+CATEGORY: cfd

#+TAGS: DPM heat-transfer evaporation boiling Ranz-Marshall radiation mass-transfer

#+MATURITY: growing

DPM Heat and Mass Transfer :: Complete Reference

Fluent tracks particle temperature and mass changes along the trajectory. The particle energy equation couples convective heat transfer, radiation, and chemical reaction. The mass equation handles evaporation (Law 2), boiling (Law 3), and multicomponent diffusion (Law 8/9). Each law activates based on the particle type and local conditions. This page covers every heat and mass transfer mechanism, the Ranz-Marshall correlation, and the decision logic for which laws activate when.

Particle Energy Equation

The particle temperature equation is:

where:

For inert particles (shisha PM2.5), radiation and reaction are off. The latent term is also zero. Only convection remains.

Convective Heat Transfer -- Ranz-Marshall Correlation

Fluent uses the Ranz-Marshall correlation for the convective heat transfer coefficient:

where:

From this, $h$ is recovered:

Limiting cases:

Regime$Re_p$NuPhysical meaning
Still particle$\to 0$2Pure conduction from a sphere in quiescent fluid
Slow motion$< 1$$\approx 2$Convection is negligible
Moderate slip$1$--$1000$$2 + 0.6\,Re_p^{0.5}\,\text{Pr}^{0.33}$Classical forced-convection regime
High slip$> 1000$$0.6\,Re_p^{0.5}\,\text{Pr}^{0.33}$High-Re limit (conduction term vanishes)

For shisha PM2.5:** $Re_p \sim 10^{-4}$, so $\text{Nu} \approx 2$. The convective coefficient is:

Despite the large $h$, the particle mass is tiny ($m_p \sim \frac{\pi}{6} \rho_p d_p^3 \sim 6 \times 10^{-15}$ kg), so the heating rate $dT_p/dt = h A_p (T - T_p) / (m_p c_p)$ has a very short time constant ($\sim$ milliseconds). The particle reaches thermal equilibrium with the surrounding fluid almost instantly.

Particle heating time constant:

For PM2.5 ($d_p = 1$ \mu m, $\rho_p = 1200$ kg/m^3, $c_p = 1000$ J/(kg.K), $k_f = 0.026$ W/(m.K)):

$\tau_T = \frac{1200 \times 1000 \times (10^{-6})^2}{12 \times 0.026} \approx 3.8 \times 10^{-3}$ s

The particle temperature equilibrates with the fluid in about 4 milliseconds. Over the typical 0.1--1 s residence time in the shisha chamber, the particle is essentially isothermal with the surrounding gas.

When does particle temperature actually matter?

Evaporation -- Law 2

Law 2 governs the evaporation of liquid droplets. The droplet temperature rises until it reaches the boiling point or the local vapor pressure equals the saturation pressure.

Activation condition: Particle type = Droplet; $T_p$ < boiling point; liquid species present.

Mass loss rate:

where:

Energy consumed:

The latent heat of vaporization $L_v$ is drawn from the particle's sensible heat:

This cooling effect slows the particle temperature rise. Evaporating droplets stay near the wet-bulb temperature until the liquid is exhausted.

Applicable to shisha:** No. Shisha PM2.5 particles are inert (solid aerosol, carbonaceous tar). They do not evaporate. Leave Law 2 off.

When activated by mistake:** If you enable droplet evaporation on an inert particle, Fluent ignores the evaporation law. No harm done, but the setup is logically inconsistent.

Boiling -- Law 3

Law 3 governs boiling of liquid droplets once $T_p$ reaches the saturation temperature.

Activation condition: Particle type = Droplet; $T_p \ge T_{\text{sat}}$; liquid species present.

Mass loss rate:

The droplet temperature is held at $T_{\text{sat}}$ during boiling. All incoming heat goes into phase change.

Applicable to shisha:** No. Same reason as Law 2.

Radiation Heat Transfer

The radiative heat exchange is:

where $T_{\text{rad}}$ is the radiation temperature (from the DO, P-1, S2S, or DTRM radiation model).

Applicable to shisha:** Minor. Shisha smoke is at low temperature (50--100 degrees C). Radiative exchange with the surrounding surfaces is negligible compared to convection. Leave off unless the bowl chamber has a strong radiative source (e.g., glowing coal at 600 degrees C).

When to enable radiation:

Multicomponent Evaporation -- Laws 8 and 10

For multicomponent droplets (mixtures of liquids), Fluent solves simultaneous evaporation of each species using a diffusion-based model.

Law 8:** Multicomponent evaporation with finite diffusion inside the droplet. Each species has its own diffusion equation in the radial direction.

Law 10:** Simplified multicomponent evaporation with infinite internal diffusion (uniform composition). The droplet is treated as a lumped-capacitance system for each species.

Applicable to shisha:** No. PM2.5 is inert.

When to use:**

Reaction Heat -- Combusting Particles

Combusting particles release heat from: 1. Devolatilization (Law 1): volatile matter is released (endothermic) 2. Char combustion (Law 4): carbon reacts with O2 (exothermic) 3. Char surface reaction: similar to Law 4 but with different kinetics

The reaction heat appears as $Q_{\text{reaction}}$ in the energy equation. For combusting particles, this term dominates the energy balance and the particle temperature can exceed the gas temperature significantly.

Applicable to shisha:** No. PM2.5 smoke is cool and chemically inert in the shisha chamber (no combustion in the chamber itself; combustion happens on the tobacco below the foil).

Mass Transfer -- Inert Particles Have None

For inert particles:

The only active terms in the energy equation are convection and (optionally) radiation. For the shisha case, track $T_p$ for completeness but expect it to equilibrate with the local gas temperature almost instantly.

Heat Transfer in Fluent -- Panel Setup

In the DPM model panel under "Physical Models":

OptionEffectEnable for shisha?
Heat transferActivates the particle energy equationYes (completeness)
Radiation interactionAdds radiative exchange termNo (negligible)
ReactionActivates combustion heat sourceNo (inert)

When "Heat transfer" is off, the particle temperature is fixed at the injection temperature and does not change along the trajectory. For shisha PM2.5 at moderate temperature differences, this is acceptable if you do not need $T_p$ data.

When "Heat transfer" is on, $T_p$ is integrated alongside position and velocity. The cost is one additional ODE per parcel. Negligible compared to the trajectory integration cost.

Summary -- What Activates for Shisha PM2.5

MechanismActive?Reason
Convection (Ranz-Marshall)YesAlways active for heat transfer
RadiationNoSmoke is cool; radiative exchange negligible
Evaporation (Law 2)NoInert particle; no liquid phase
Boiling (Law 3)NoInert particle; no liquid phase
Multicomponent (Laws 8/10)NoInert particle; single-component
Devolatilization (Law 1)NoNo volatile matter
Combustion (Law 4)NoNo char oxidation
Reaction heatNoNo chemical reaction

The particle temperature equilibrates with the gas in $\sim 4$ ms. The trajectory is unaffected by $T_p$ because drag depends only on fluid properties. Track $T_p$ to enable post-processing of temperature fields, but do not expect it to drive any physics.

See Also