Engineering & Science
Hausen Laminar Thermal Entry-Length Formula: Graetz Number & Pipe Nusselt
Calculate length-averaged laminar tube Nusselt number Nu_D = 3.66 + 0.0668*Gz / (1 + 0.04*Gz^(2/3)) from Graetz number Gz = (D/L)*Re*Pr for constant wall temperature.
Why assuming Nu_D = 3.66 severely underpredicts heat transfer in short viscous-liquid tubes!
In laminar pipe flow (Re_D < 2,300) of high-Prandtl oils, glycols, or pharmaceutical syrups, the thermal boundary layer requires L_th ≈ 0.05 * D * Re * Pr to merge at the centerline! Across short heat-exchanger tubes where Graetz number Gz = (D / L) * Re_D * Pr remains large, Helmuth Hausen’s (1943) empirical correlation Nu_D = 3.66 + (0.0668 * Gz) / (1 + 0.04 * Gz^(2/3)) captures the thin entrance thermal boundary layer and smoothly approaches 3.66 as L -> ∞ (Gz -> 0)!
For a D = 0.025 m tube of length L = 1.5 m carrying laminar water/glycol at Re_D = 1,600 and Pr = 5.8, Graetz number is Gz = 154.67 and length-averaged Nusselt jumps to Nu_D = 8.460 (2.31× the fully developed 3.66 limit!), rising further to Nu_D = 12.783 in a compact L = 0.5 m Manifold!
| Tube Length L (D = 0.025 m, Re = 1,600, Pr = 5.8) | Graetz Number Gz = (D/L)RePr | Hausen Average Nu_D | Enhancement Over 3.66 |
|---|---|---|---|
| L = 1.5 m (Standard Shell Pass) | 154.67 | 8.460 | 2.31× fully developed |
| L = 0.5 m (Short Compact Core) | 464.00 | 12.783 | 3.49× entrance boost |
| Turbulent or Invalid (Re >= 2300 or D <= 0) | Out of Laminar Regime | "Outside Laminar Pipe Regime" | Flow-Regime Guard |
Hausen Length-Averaged Laminar Pipe Nusselt Number Nu_D
Evaluates 3.66 + (0.0668 * Gz) / (1 + 0.04 * Gz^(2/3)) from tube diameter B2 (m), tube length B3 (m), laminar Reynolds number B4 (0 < Re < 2300), and Prandtl number B5.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B4 >= 2300, B5 <= 0), "Outside Laminar Pipe Regime", ROUND(3.66 + (0.0668 * ((B2 / B3) * B4 * B5)) / (1 + 0.04 * (((B2 / B3) * B4 * B5) ^ (2 / 3))), 3))Dimensionless Graetz Number Gz = (D / L) * Re_D * Pr
Computes the reciprocal dimensionless thermal length governing entrance boundary-layer development.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B4 >= 2300, B5 <= 0), "Outside Laminar Pipe Regime", ROUND((B2 / B3) * B4 * B5, 2))Try the example
Use the original values or change them to test your understanding.