Heat Transfer

Heat transfer causes physical particles (droplets, bubble, solid particles) to heat or to cool according to the temperature of their environment. When the phases are one-way coupled, the continuous phase does not change temperature, even when the particles do. In two-way coupled cases, the heat transfer contributes to both the continuous phase and the dispersed phase, but with different signs so the net heat transfer flux is zero.

For a single particle, the heat transfer is defined as:

where $h_{\mathrm{coef}}$ is the heat transfer coefficient, $A$ is the area of the particle, and $T_p$ and $T$ are the particle and background temperatures, respectively.

In a continuous approach such as dispersed multiphase (in contrast to a discrete approach such as Lagrangian multiphase), the heat transfer can be expressed as:

where:

• ${\overline{Q}}_{\mathrm{cd}}$ is the averaged heat flux between the dispersed and the continuous phase. It is defined as positive for heat flowing from the particles to the background.
• ${\overline{h}}_{\mathrm{coef},d}$ the averaged heat transfer coefficient of the dispersed phase
• $T_d,T$ are the temperatures of the dispersed and the continuous phase, respectively

Ranz-Marshall

The heat transfer coefficient is computed in terms of the Nusselt number:

where $k$ is the thermal conductivity, $D$ is the diameter of the dispersed phase, and ${\mathrm{Nu}}_p$ is the particle Nusselt number.

The Nusselt number correlates as:

where ${\mathrm{Re}}_p$ is the particle Reynolds number and $\mathrm{Pr}$ is the Prandlt number.