Excel in ME Nusselt 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.

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)

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∞

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

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

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

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

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

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 ≤ 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 ≤ (m/ms) ≤ 9.75

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

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