Engineering & Science
Wakao-Kaguei Packed-Bed Sherwood & Nusselt Correlation (Catalyst & Adsorption)
Calculate external particle-to-fluid mass and heat transfer in packed catalytic and adsorption beds via Wakao & Kaguei’s correlation Sh = 2 + 1.1 * Re_p^0.6 * Sc^(1/3) and Nu = 2 + 1.1 * Re_p^0.6 * Pr^(1/3).
Why packed catalyst pellets transfer mass nearly TWICE as fast as isolated spheres at the same Re_p!
Tortuous interstitial jets between touching catalyst pellets or activated-carbon beads thin external boundary layers far more aggressively than uniform free-stream flow around an isolated sphere (where Ranz-Marshall scales as 0.6 * Re_d^0.5)! After correcting historical axial-dispersion artifacts across dozens of packed-column datasets, Noriaki Wakao and Seiichiro Kaguei (Heat and Mass Transfer in Packed Beds, 1982) established the authoritative correlation for 3 <= Re_p <= 10,000: Sh = 2 + 1.1 * Re_p^0.6 * Sc^(1/3) and Nu = 2 + 1.1 * Re_p^0.6 * Pr^(1/3), where particle Reynolds number Re_p = ρ * u_superficial * d_p / μ!
Compare liquid-phase carbon adsorption (Re_p = 180, aqueous organic solute Sc = 650) with gas-phase catalytic preheating (Re_p = 180, air Pr = 0.71): high liquid Schmidt number drives Sh up to 216.88, while gas-phase Nu equals 24.13!
| Packed-Bed Transport Mode (Re_p = 180) | Sc or Pr | Wakao-Kaguei Sh or Nu | Comparison vs Isolated Sphere (0.6*Re^0.5) |
|---|---|---|---|
| Liquid Adsorption Column (Sc = 650) | Sc = 650 | Sh = 216.88 | 3.07× higher than isolated sphere (71.7)! |
| Gas-Phase Catalyst Bed (Pr = 0.71) | Pr = 0.71 | Nu = 24.13 | 2.63× higher than isolated sphere (9.18)! |
| Out-of-Domain Negative Re_p or Sc <= 0 | Invalid | "Invalid Packed-Bed Inputs" | Physical Domain Guard |
Wakao-Kaguei Packed-Bed Mass-Transfer Sherwood Number (Sh)
Evaluates 2 + 1.1 * (Re_p ^ 0.6) * (Sc ^ (1/3)) from superficial particle Reynolds number B2 and fluid Schmidt number B3.
=IF(OR(B2 < 0, B3 <= 0), "Invalid Packed-Bed Inputs", ROUND(2 + 1.1 * (B2 ^ 0.6) * (B3 ^ (1 / 3)), 2))Wakao-Kaguei Packed-Bed Heat-Transfer Nusselt Number (Nu)
Evaluates 2 + 1.1 * (Re_p ^ 0.6) * (Pr ^ (1/3)) using fluid Prandtl number B4.
=IF(OR(B2 < 0, B4 <= 0), "Invalid Packed-Bed Inputs", ROUND(2 + 1.1 * (B2 ^ 0.6) * (B4 ^ (1 / 3)), 2))Try the example
Use the original values or change them to test your understanding.