Engineering & Science
Sieder-Tate Laminar Tube Nusselt Number With Wall-Viscosity Correction
Calculate the Sieder-Tate developing laminar tube Nusselt number Nu_D = 1.86 * (Re * Pr * (D / L))^(1/3) * (mu_b / mu_w)^0.14 to capture viscous lube-oil heating enhancement vs. cold-wall boundary thickening.
Account for steep bulk-to-wall oil viscosity gradients inside shell-and-tube exchangers!
Constant-property Nusselt correlations fail badly for viscous hydrocarbon oils, syrups, and polymer melts because liquid viscosity plunges exponentially with temperature! During tube-wall HEATING, hot low-viscosity oil right against the wall (mu_w << mu_b) accelerates the velocity gradient and boosts heat transfer; during tube-wall COOLING, cold sluggish oil coats the inner wall (mu_w >> mu_b) and chokes heat transfer!
E. N. Sieder and G. E. Tate (1936) captured both developing thermal-entry convection (Graetz number Gz = Re * Pr * (D / L)) and radial viscosity distortion via the famous (mu_b / mu_w)^0.14 wall-viscosity ratio: Nu_D = 1.86 * (Re * Pr * (D / L))^(1/3) * (mu_b / mu_w)^0.14! For laminar lube oil (Re = 1,200, Pr = 85, tube diameter D = 0.025 m, length L = 3.0 m -> Gz = 850): steam-heating a cold oil stream (mu_b = 0.180 Pa*s, hot wall mu_w = 0.045 Pa*s -> ratio = 4.0) boosts Nu_D to 21.39, whereas cooling hot oil against a chilled wall (mu_b = 0.045, cold wall mu_w = 0.180 -> ratio = 0.25) drops Nu_D by 32% to 14.51!
| Heat Exchanger Duty (Re = 1200, Pr = 85, D = 25 mm, L = 3 m) | Viscosity Ratio mub / muw | Correction (mub/muw)^0.14 | Sieder-Tate NuD |
|---|---|---|---|
| Heating Viscous Oil (mub = 0.18, muw = 0.045) | 4.00 | 1.214 (+21.4% Boost) | 21.39 |
| Cooling Viscous Oil (mub = 0.045, muw = 0.18) | 0.25 | 0.824 (-17.6% Penalty) | 14.51 |
| Invalid Pipe Geometry or Viscosity <= 0 | Guarded Input Error | N/A | "Invalid Sieder-Tate Inputs" |
Sieder-Tate Laminar Tube Nusselt Number Nu_D
Evaluates 1.86 * (Re * Pr * (D / L))^(1/3) * (mu_b / mu_w)^0.14 for laminar tube flow (Re < 2300).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0, B6 <= 0, B7 <= 0), "Invalid Sieder-Tate Inputs", ROUND(1.86 * ((B2 * B3 * (B4 / B5)) ^ (1 / 3)) * ((B6 / B7) ^ 0.14), 2))Dimensionless Graetz Thermal-Entry Number Gz = Re * Pr * (D / L)
Verifies developing thermal boundary layer applicability (Sieder-Tate requires Gz >= ~10 so Nu_D exceeds asymptotic 3.66).
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Sieder-Tate Inputs", ROUND(B2 * B3 * (B4 / B5), 1))Try the example
Use the original values or change them to test your understanding.