M5 Heat Transfer in Fluidized Beds

1 Range of Existence of Fluidization and Bed Expansion

In order to fluidize a particulate solid by an upward-flowing gas or liquid, the fluid velocity u (i.e., the volumetric flowrate divided by the total cross-section) must be in the range between the minimum fluidization velocity, u _mf, and the terminal velocity, u _t:

$$u_{{\rm{mf}}} > u > u_{\rm{t}}.$$

((1))

The two limits in Eq. (1) define the range of existence of a fluidized bed. The limiting velocities are obtained from force (or momentum) balances as

$${{u_{{\rm{mf}}} d} \over \nu } \equiv {\rm{Re}}_{{\rm{mf}}} = {\rm{Re}}_{{\rm{mf}}} ({\rm{Ar}},\psi _{{\rm{mf}}} ),$$

((2))

$${{u_{\rm{t}} d} \over \nu } \equiv {\rm{Re}}_{\rm{t}} = {\rm{Re}}_{\rm{t}} ({\rm{Ar}}),$$

((3))

where ψ _mf is the bed voidage at minimum fluidization (practically often between 0.4 and 0.7) and Ar is the Archimedes number ${\rm{Ar}} \equiv gd^3 \rho (\rho _{\rm{P}} - \rho )/\eta ^2$. For spherical monosized particles Eq. (2) becomes

$${\rm{Re}}_{{\rm{mf}...