Transcript Excel in ME

Excel in ME
Nusselt numbers
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Functions
• Functions return the local (Nu) or average (NuBar)
Nusselt number
hL
Nu 
k
h L
NuBar  Nu 
k
• 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.
Functions
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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
V, T∞
Turbulent
Laminar
x
Ts
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∞
Laminar
x
Turbulent
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
–
–
–
–
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• 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
Staggered
Aligned
SD
St
St
Sl
Rows
Rows
Sl
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
Staggered
Aligned
– 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
SD
St
St
Sl
Rows
Rows
Sl
Laminar Flow in a Tube
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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
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–
–
–
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