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Excel in ME

Excel in ME. Nusselt numbers. Loading an Add-in. Download Nusselt.xla from www.me.ua.edu/excelinme Click Browse button to find and load Nusselt.xla. Functions. Functions return the local (Nu) or average (NuBar) Nusselt number

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Excel in ME

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  1. Excel in ME Nusselt numbers

  2. Loading an Add-in • Download Nusselt.xla from www.me.ua.edu/excelinme • Click Browse button to find and load Nusselt.xla

  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. 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. V, T∞ Turbulent Laminar x Ts 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

  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 Rex, c V, T∞ 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. Staggered Aligned SD St St Sl Sl Rows Rows 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

  10. Staggered Aligned SD St St Sl Sl Rows Rows 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

  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 ≤ 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

  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 = ReDX Pr ≥ 100 • For uniform surface heat flux • 3.6 X 103 ≤ ReD ≤ 9.05 X 105 • 102 ≤ PeD ≤ 104

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