Excel in MEExcel in MENusselt numbersNusselt numbers

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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.

k

LhNu

k

LhNuNuBar

FunctionsOptional 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)

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 / – Pr - Parndtl number, Pr = cp / k = / – 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

TurbulentLaminar

x Ts

V, T∞

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 / – Pr - Parndtl number, Pr = cp / k = / – 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

TurbulentLaminar

x Ts

V, T∞ Rex, c

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 /

– Pr - Parndtl number, Pr = cp / k = /

• Range– ReD Pr ≥ 0.2

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 s

– Re - Reynolds number, ReD = V D /

– Pr - Parndtl number, Pr = cp / k = /

– mu_mus - / s; viscosity ratio calculated from T∞ and Ts at the surface

• Range– 0.71 ≤ Pr ≤ 380

– 3.5 ≤ ReD ≤ 7.6 X 104

• 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 / – Pr - Parndtl number, Pr = cp / k = / – 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

Bank of Tubes

AlignedStaggered

Rows Rows

St

SlSl

St

SD

• 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 / – Pr - Parndtl number, Pr = cp / k = / – 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

Bank of Tubes, Zukauskas

AlignedStaggered

Rows Rows

St

SlSl

St

SD

• 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 s

– Re - Reynolds number, ReD = V D / – Pr - Parndtl number, Pr = cp / k = / – 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 - / s; viscosity ratio calculated from Tm and Ts at the surface; only needed for combined entry with Pr ≤ 5. 0 if omitted

• Ranges for combined entry– Pr ≥ 0.6; For Pr ≥ 5, the answer is calculated with the thermal entry formula– 0.0044 ≤ (/s) ≤ 9.75

Laminar Flow in a Tube

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 /

– Pr - Parndtl number, Pr = cp / k = /

• Range– 0.5 ≤ Pr ≤ 2000

– 3000 ≤ ReD ≤ 5 X 106

– L/D ≥ 10

• 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 / – Pr - Parndtl number, Pr = cp / k = / – 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

Liquid metal flow through a tube