1. Excel in ME
Nusselt numbers

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3. Functions
Functions return the local (Nu) or average (NuBar) Nusselt number
The functions are reliable only over certain ranges. An answer will be returned, but it is up to the user to decide if it is adequate.
A warning will appear for values outside the reliable range for the function.
Quiet - Each function has an optional Quiet input. True or 1 will turn off the warnings. False if omitted.

4. Optional Inputs in italics
Functions
Optional Inputs in italics
NuxPlate(Re, Pr, Rexc, Quiet)
NuBarPlate(Re, Pr, Rexc, Quiet)
NuDBarCyl(Re, Pr, Quiet)
NuDBarSphere(Re, Pr, mu_mus, Quiet)
NuDBarTubes(Re, Pr, St_D, Sl_D, Aligned, Nl, Quiet)
NuDBarZTubes(Re, Pr, Prs, St_Sl, Aligned, Nl, Quiet)
NuDBarLamTube(Re, Pr, D_L, Thermal, mu_mus, Quiet)
NuDTurbTube(Re, Pr, Quiet)
NuDLiqMetals (Re, Pr, UniformT, Quiet)

5. Flat Plate, Local Nusselt Number
NuxPlate(Re, Pr, Rexc, Quiet)
Returns the local Nusselt number at x
Inputs based on the film temperature, Tf = (Ts+T∞)/2
Re - Reynolds number, Rex = V x / n
Pr - Parndtl number, Pr = cp m / k = n / a
Rexc - Critical reynolds number. Reynolds number at transition point from laminar to turbulent. If Re < Rexc, then laminar calculation. Otherwise, the calculation is for turbulent flow. If omitted, Recx = 5 X 105
Ranges
For laminar, Pr ≥ 0.6
For turbulent, Rex ≤ 108, 0.6 ≤ Pr ≤ 60
Turbulent
Laminar x Ts
V, T∞

6. Flat Plate, Mean Nusselt Number
NuBarPlate(Re, Pr, Rexc, Quiet)
Returns the average Nusselt number from 0 to x
Inputs based on the film temperature, Tf = (Ts+T∞)/2
Re - Reynolds number, Rex = V x / n
Pr - Parndtl number, Pr = cp m / k = n / a
Rexc - Critical reynolds number. Reynolds number at transition point from laminar to turbulent. If Re < Rexc, then laminar calculation. Otherwise, the calculation is for a mix of laminar and turbulent. If omitted, Recx = 5 X 105
Ranges
For laminar, Pr ≥ 0.6
For mixed, ReL ≤ 108, 0.6 ≤ Pr ≤ 60
V, T∞
Rex, c
Turbulent
Laminar x Ts

7. Cylinder in crossflow NuDBarCyl(Re, Pr, Quiet)
Returns the average Nusselt number for crossflow over a cylinder
Inputs based on the film temperature, Tf = (Ts+T∞)/2
Re - Reynolds number, ReD = V D / n
Pr - Parndtl number, Pr = cp m / k = n / a
Range
ReD Pr ≥ 0.2

8. Sphere NuDBarSphere(Re, Pr, mu_mus, Quiet)
Returns the average Nusselt number for flow over a sphere
Inputs based on the ambient fluid temperature, T∞, except ms
Re - Reynolds number, ReD = V D / n
Pr - Parndtl number, Pr = cp m / k = n / a
mu_mus - m / ms; viscosity ratio calculated from T∞ and Ts at the surface
Range
0.71 ≤ Pr ≤ 380
3.5 ≤ ReD ≤ 7.6 X 104

9. Bank of Tubes NuDBarTubes(Re, Pr, St_D, Sl_D, Aligned, Nl, Quiet)
Returns the average Nusselt number for crossflow over a bank of tubes
Inputs based on the film temperature, Tf = (Ts+T∞)/2
Re - Reynolds number, ReD, max = Vmax D / n
Pr - Parndtl number, Pr = cp m / k = n / a
St_D - Transverse spacing / Diameter, St / D
Sl_D - Longitudianl spacing / Diameter, Sl / D
Aligned - True or 1 for Aligned tubes, False or 0 for Staggered tubes. Aligned if omitted.
Nl - Number of rows, if less than 10. Allows for correction factor if there are less than 10 rows. If omitted, Nl ≥ 10
Vmax
Aligned - Vmax = St V / (St-D)
Staggered
if 2 SD > St +D, same as aligned
else Vmax = ½ V St / (SD-D)
Ranges
Pr ≥ 0.7
2000 ≤ ReD, max ≤ 40,000
Aligned
Staggered
Rows St Sl SD

10. Bank of Tubes, Zukauskas
NuDBarZTubes(Re, Pr, Prs, St_Sl, Aligned, Nl, Quiet)
Returns the average Nusselt number for crossflow over a bank of tubes based on a new correlation by Zukauskas
Inputs based on the film temperature, Tf = (Ts+T∞)/2
Re - Reynolds number, ReD, max = Vmax D / n
Pr - Parndtl number, Pr = cp m / k = n / a
Prs - Parndtl number calculated for the average of the inlet and outlet temperatures
St_Sl - Transverse spacing / Longitudianl spacing, St / Sl
Aligned - True or 1 for Aligned tubes, False or 0 for Staggered tubes. Aligned if omitted.
Nl - Number of rows, if less than 20. Allows for correction factor if there are less than 20 rows. If omitted, Nl ≥ 20
Vmax
Aligned - Vmax = St V / (St-D)
Staggered
if 2 SD > St +D, same as aligned
else Vmax = ½ V St / (SD-D)
Ranges
0.7 ≤ Pr ≤ 500
1000 ≤ ReD, max ≤ 2 X 106
Aligned
Staggered
Rows St Sl SD

11. Laminar Flow in a Tube
NuBarLamTube(Re, Pr, D_L, Thermal, mu_mus, Quiet)
Returns the average Nusselt number for laminar flow through a circular tube
Function based on uniform surface temperature
Inputs based on the mean of the inlet and outlet temperatures, Tm = (Ti+To)/2, except ms
Re - Reynolds number, ReD = V D / n
Pr - Parndtl number, Pr = cp m / k = n / a
D_L - Diameter / Length, D / L
Thermal - True or 1 for Thermal entry length, False or 0 for combined entry length. True if omitted.
Thermal entry assumes a fully developed velocity profile. For instance, if the tube is preceded by a section where there is no heat transfer. Also gives a good approximation for large Prandtl number fluids, like oil.
Combined entry has both the velocity and thermal profiles developing simultaneously.
mu_mus - m / ms; viscosity ratio calculated from Tm and Ts at the surface; only needed for combined entry with Pr ≤ if omitted
Ranges for combined entry
Pr ≥ 0.6; For Pr ≥ 5, the answer is calculated with the thermal entry formula
≤ (m/ms) ≤ 9.75

12. Turbulent Flow in a Tube
NuDTurbTube(Re, Pr, Quiet)
Returns the Nusselt number for turbulent flow through a circular tube
Inputs based on the mean of the inlet and outlet temperatures, Tm = (Ti+To)/2
Re - Reynolds number, ReD = V D / n
Pr - Parndtl number, Pr = cp m / k = n / a
Range
0.5 ≤ Pr ≤ 2000
3000 ≤ ReD ≤ 5 X 106
L/D ≥ 10

13. Liquid metal flow through a tube
NuDLiqMetals (Re, Pr, UniformT, Quiet)
Returns the Nusselt number for liquid metal flow through a circular tube
Other correlations do not apply to liquid metals
(3 X 10-3 ≤ Pr ≤ 5 X 10-2)
Inputs based on the mean of the inlet and outlet temperatures, Tm = (Ti+To)/2
Re - Reynolds number, ReD = V D / n
Pr - Parndtl number, Pr = cp m / k = n / a
UniformT - True or 1 for uniform surface temperature, False or 0 for uniform heat flux at surface. True if omitted.
Ranges
For uniform surface temperature
Peclet number, PeD = ReD X Pr ≥ 100
For uniform surface heat flux
3.6 X 103 ≤ ReD ≤ 9.05 X 105
102 ≤ PeD ≤ 104