ME 415 Tutorial2

8/2/2019 ME 415 Tutorial2

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ME 415 Energy Systems

Design Tutorial


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COURSE MATERIAL

This is a classic thermal systems designcourse. It is application intensive and coversflow in pipes and piping systems, pumps and

pumping systems, heat exchangers and heatexchanger design, and thermal systemsimulation.


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APPLICATION THROUGH EXCEL

The ME 415 Add-In offers several uniqueuser-defined functions for application ofcourse material in the Excel environment. As

a result, students are able to solve complexproblems through elimination of cumbersomehand calculations or reading of charts and

graphs.


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APPLICATION THROUGH EXCEL

These user-defined functions are utilized inthe Excel Spreadsheet.

The functions can be invoked by severalmethods.

Call directly from the cell

Requires known function name and argument

constraints (specific units, range sizes, etc.)Call from the user ribbon (Excel 2007)

Provides function descriptions and input boxes


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DIRECT CELL CALL METHOD This method requires the user to highlight

desired cell(s) for output and type=Function Name(Arg1,Arg2,) For example, we desire to know the Nusselt number

for turbulent flow in a tube.This method requiresknowing whatarguments the functionneeds to compute thedesired output.

Direct cell call methodbecomes useful whenuser has gainedexperience with aspecific function or

group of functions.


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USER RIBBON CALL METHOD

This method uses the user ribbon and theInsert Function button located at the top of theExcel 2007 window. Advantages of this method are function lists and

descriptions that provide details on each argumentsrequirements .

Highlight cell(s) for desired output and select theformulas tab on the user-ribbon as seen on

following slide. Then click either Insert-Function button


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USER RIBBON CALL METHOD

From the Insert-Function pop up windowdisplayed on the right, select User Definedfrom the function category list.

Either Insert-Function button

will work


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USER RIBBON CALL METHOD User can select the correct function by scrolling through each

function and its description. Once function is selected, spacesare provided for each argument. Some arguments can be

optional such as the Quiet argument on the NuDTurbTube

function.


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ME 415 ADD-IN FEATURES

The ME 415 Add-In provides tools for severalspecial design calculations. Heat Transfer Fin Efficiency

Heat Exchanger Effectiveness-Number of TransferUnits (NTU) Method

Pump Performance Correction for Viscous Fluids

Hardy-Cross Flow and Hazen-Williams Head Loss

Analysis Friction Factor Calculator (Swamee-Jain and

Churchill)

Nusselt Number


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FIN EFFICIENCY

The function fin_eff uses known fin parametersm, l, ri , and ro. m = SQRT(h/k)

l is total fin length ri is inner radius (circular fins)

ro is outer radius (circular fins)

The function call from the Excel spreadsheet is

=fin_eff(Index,m,l,ri,ro) or=fin_eff_fintype(m,l,ri,ro) which will provide anequivalent result for an Index corresponding tothe same fin type.


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FIN EFFICIENCY

Study of finned surfaces in heat exchangerdesign requires analysis of fin efficiency.

Calculation of fin efficiency can becomecumbersome with complex fin geometries.

With known fin dimensions, the user-definedfunction fin_eff readily calculates finefficiency.

From calculation of fin efficiency, furtheranalysis of finned surface properties such astotal surface effectiveness can be easily

determined.


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FIN EFFICIENCY When using the =fin_eff_fintype function call, the following

function names should be used for each specific fin geometry. Straight Rectangular Fins

=fin_eff_rect(m, l)

Straight Triangular Fins =fin_eff_tri(m, l)

Circular Rectangular Fins =fin_eff_rect_c(m, l, ri, ro)

ri and ro are required arguments here

Rectangular Spines (Circular cross-section) Round Pin Fin =fin_eff_pin_R(m, l)

Rectangular Spines (Square cross-section) Square Pin Fin m = Sqrt(2*h/k/) =fin_eff_pin_S(m,l)

Triangular Spines (Circular Cone cross-section) Cone Pin Fin =fin_eff_pin_C(m,l)


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FIN EFFICIENCY An Index value of 1,2,3,4,5, or 6 should be supplied for the appropriate fin geometry.

1 Straight Rectangular Fins =fin_eff(1,m, l)

2 Straight Triangular Fins =fin_eff2,m, l)

3 Circular Rectangular Fins =fin_eff(3,m, l, ri, ro)

ri and ro are required arguments

4 Rectangular Spines (circular cross-section) Round Pin Fin =fin_eff(4,m, l)

5 - Rectangular Spines (square cross-section) Square Pin Fin m = Sqrt(2*h/k/) =fin_eff(5,m,l)

6Triangular Spines (Circular Cone cross-section)

Cone Pin Fin fin_eff(6,m,l)


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FIN EFFICIENCY

Functionarguments ri

and ro areprovided asoptional.

When Index 3is used for a

circularrectangular

fin, ri and roare required.Otherwise,they shouldnot be

supplied.


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NTU METHOD

The function calls from the Excel spreadsheet are=Hx_eff( Index,NTU,Cmin ,Cmax ,Passes) and=Hx_NTU( Index,eff, Cmin ,Cmax ,Passes).

The function Hx_eff uses known parameters NTU, Cmin,Cmax, and No. of Passes to calculate heat exchanger

effectiveness. NTU=UA/Cmin. Cmin is the smaller of the two capacities Ch and Cc. Cmax is the larger of the two capacities Ch and Cc.

Passes is an optional argument (specific to certain heatexchanger types).

The function Hx_NTU uses known parameterseffectiveness, Cmin, Cmax, and No. of Passes tocalculate NTU.

Where Cmin, Cmax, and Passes are same as above.


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NTU METHOD

Heat exchanger analysis where only inletconditions are known uses the Number ofTransfer Units (NTU) Method to determine

heat exchanger effectiveness.

Effectiveness NTU relations for some heatexchanger types require iterative calculation

which is simplified by user-defined functionsHx_eff and Hx_NTU.


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NTU METHOD

An Index value of 1-8 should be supplied for theappropriate heat exchanger type.

1 Parallel flow: single pass

2 Counterflow: single pass

3 Shell and tube (one shell pass; 2,4,6, etc., tubepasses)

4 Shell and tube (n shell passes; 2n, 4n, 6n, etc.,tube passes) - - Passes argument required

5 Cross flow (both streams unmixed)

6 Cross flow (both streams mixed)

7 Cross flow (stream Cmin unmixed)

8 Cross flow (stream Cmax unmixed)

Index 4 requires input of the No. of passes. All otherindexes should not have No. of passes supplied.


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NTU METHOD The direct cell call method uses

=Hx_eff( Index,NTU,Cmin ,Cmax ,Passes) and=Hx_NTU( Index,eff, Cmin ,Cmax ,Passes).

The user-ribbon call method is shown in the figurebelow.


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VISCOUS PUMP

The function calls from the Excel spreadsheet are=Vis_pump_QHE(QHE_Matrix,Vis) and=Vis_pump_CF(QBE, HBE, Vis).

The function Vis_pump_QHE uses a pre-calculatedQHE matrix and viscosity of the pumping fluid to providecorresponding flow and head values for the high viscosityfluid. The user can then generate (plot) a new pumpcurve with the supplied output.

The function Vis_pump_CF uses known best efficiencypoint (BEP) flow and head values along with the viscosityof the pumping fluid to provide correction factors thatcorrect the pump curve data. The user can multiplythese correction factors with original pump data to findcorresponding flow and head values for the high viscosityfluid.


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VISCOUS PUMP

Because pump performance is greatly affectedby highly viscous fluids, a correction methodmust be used to estimate performance whenmanufacturers data is not available.

These pump corrections can be found fromcharts but is simplified through user-definedfunctions Vis_pump_QHE and Vis_pump_CF.

With the known best efficiency point (BEP) of a

specific pump, the correction factors forefficiency, flow, Head0.6Q, Head0.8Q, Head1.0Q,and Head1.2Qcan be found. Both user-definedfunctions use a BEP to calculate and output thenew data for a high viscosity pumping fluid.


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VISCOUS PUMP

The function Vis_pump_QHE uses a pre-calculated QHE Matrix and known viscosity. The QHE matrix is a 4 x 3 matrix that the user must

generate for input into the Vis_pump_QHE function. From a given pump curve (water), determine the BEP

(highest efficiency). From this point, the user determinesthe flow and head at the pumps best efficiency.

The 4 x 3 matrix is then generated as follows. Q H E (efficiency)

0.6*QBE [email protected] [email protected]*QBE [email protected] [email protected]*QBE [email protected] [email protected]*QBE [email protected] [email protected]

Viscosity (SSU Saybolt Seconds Universal)


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VISCOUS PUMP

Vis_pump_QHE outputs a matrix of cells. Toexecute the function, the user must highlightthe expected output of cells. The output is

the same size as the input QHE matrix (4 x3).

Highlight any open cells in a 4 x 3 matrix.

Call =Vis_pump_QHE( QHE_Mat(4 x 3),Vis).Once all arguments are entered, the keystrokecommand Ctrl+Shift+Enter (Do NOT press OK)must be used to obtain the desired corrected

pump curve data.


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VISCOUS PUMP

The output of the cells is corrected pumpcurve data for the high viscosity fluid.

Ctrl+Shift+Enter(Do not click

OK)


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VISCOUS PUMP

The function Vis_pump_CF uses known BEParguments flow (QBE), head (HBE), and viscosity. Flow (GPM) Head (ft)

Viscosity (SSU Saybolt Seconds Universal) Vis_pump_CF outputs an array of cells. To

execute the function, the user must highlight theexpected array of six cells in any column and call

=Vis_pump_CF( Flow,Head,Vis). Once allarguments are entered, the keystroke commandCtrl+Shift+Enter (Do NOT press OK) must beused to obtain the desired correction factors.


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VISCOUS PUMP

Output array: C CQ CH (0.6 x

QNW)

CH (0.8 xQNW)

CH (1.0 xQNW)

CH (1.2 xQNW)

Ctrl+Shift+Enter(Do NOT click OK)


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VISCOUS PUMP

For flowsequal to orless than100 GPM,correction

factors for0.6, 0.8, 1.0,and 1.2 flowrates will beequal.

Otherwise,correctionfactors willvary.

Final arrayoutput


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HARDY-CROSS ANALYSIS

The function calls from the Excel spreadsheetare =Hardy_Darcy(RngL,RngD,RngQ,RngN,RngE,rho

,vis)

=Darcy(RngL,RngD,RngQ,RngE,rho,vis)

and

=Hardy_Hazen(RngL,RngD,RngQ,RngN,RngC,tol,

k1) =HazenWill(RngL,RngD,RngQ,k1,RngC)

Darcy-Weisbach and Hazen-Williams are twomethods for calculating head loss through

pipes. They use unique parameters to


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HARDY-CROSS ANALYSIS

Hardy-Cross formulation is an iterativemethod for obtaining the steady-state solutionfor any generalized series-parallel flownetwork. It can be systematically applied toany fluid flow network.

While Hardy-Cross flow values can beobtained using solver in Excel, an alternative

method that employs user-defined functionsHardy_Darcy and Hardy_Hazen suppliesthe same solution.


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HARDY-CROSS AND DARCY-WEISBACH

The function Hardy _Darcy uses system geometry,initial guesses for line flow rates, loop-node analysis,pipe roughness, density, and dynamic viscosity todetermine flow through the system.

Corresponding to the number of pipes in the system,the user should supply a range of lengths (RngL),diameters (RngD), initial flow guesses (RngQ), andepsilon values coefficients (RngE). The user alsosupplies a n-connection matrix (RngN), a density,

and a dynamic viscosity. The function call from the Excel spreadsheet is

=Hardy_Darcy(RngL,RngD,RngQ,RngN,RngE,rho,vis).


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The user must input a rho (density)and vis(dynamic viscosity). Typical units for each arelbm/ft

3 and ft2/sec, respectively, when units of Q areft3/sec.

Hardy_Darcy outputs an array of cells. To executethe function, the user must highlight the expectedarray of cells (No. of pipes in system) in any columnand call

=Hardy_Darcy(RngL,RngD,RngQ,RngN,RngE,rho,vis). Once all arguments are entered, thekeystroke command Ctrl+Shift+Enter (Do NOTpress OK) must be used to obtain the desiredHardy flow values.


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Ctrl+Shift+Enter(Do not click

OK)


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The final array output Hardy _Darcy flowvalues are shown above. Darcy-Weisbachhead lossvalues through each pipe canthen be found with these known flow rates.

Final arrayoutput


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The user-defined function Darcy uses thesame system geometry and the calculatedHardy_Darcy flow values to find the headloss through each pipe.

The function call from the Excel spreadsheetis =Darcy(RngL,RngD,RngQ,RngE,rho,vis).

Since the Darcy function also uses rangeinputs, the keystroke commandCtrl+Shift+Enter must again be used toobtain the expected array Darcy head loss

values.


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RngQ usesnew

Hardy_Darcyflow values


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HARDY-CROSS AND HAZEN-WILLIAMS

The function Hardy _Hazen uses system geometry,initial guesses for line flow rates, and loop-nodeanalysis to determine flow through the system.

Corresponding to the number of pipes in the system,

the user should supply a range of lengths (RngL),diameters (RngD), initial flow guesses (RngQ),and Hazen-Williams coefficients (RngC). The useralso supplies a n-connection matrix (RngN), atolerance value (tol), and a K1 value (k1).

The function call from the Excel spreadsheet is=Hardy_Hazen(RngL,RngD,RngQ,RngN,RngC,tol,k1).


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Typical values for tol and k1 are .0001 and4.727 respectively when units of Q are ft3/sec.

Hardy_Hazen outputs an array of cells. Toexecute the function, the user must highlight the

expected array of cells (No. of pipes in system)in any column and call=Hardy(RngL,RngD,RngQ,RngN,RngC,tol,k1). Once all arguments are entered, the keystroke

command Ctrl+Shift+Enter (Do NOT pressOK) must be used to obtain the desired Hardyflow values.

HARDY CROSS AND HAZEN WILLIAMS


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Ctrl+Shift+Enter(Do NOT click OK)


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The final array output Hardy_Hazenflow values are shown above. Hazen-Williams head lossvalues througheach pipe can then be found with theseknown flow rates.

Final arrayoutput


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The user-defined function HazenWill uses thesame system geometry and the calculatedHardy_Hazen flow values to find the head lossthrough each pipe.

The function call from the Excel spreadsheet is=HazenWill(RngL,RngD,RngQ,k1,RngC). k1 is 4.727 when units for Q are ft3/sec

Since HazenWill also uses range inputs, thekeystroke command Ctrl+Shift+Enter mustagain be used to obtain the expected arrayHazen-Williams head loss values.

HARDY CROSS AND HAZEN WILLIAMS


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RngQ usesnew

Hardy_Hazenflow values


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FRICTION FACTOR

The function calls from the Excel spreadsheetare =fric_Swamee(Eps_Dia, ReD)

=fric_Churchill(Eps_Dia, ReD)Eps_Dia is the relative roughness = /DReD is the Reynolds number = *V*D/

Swamee-Jain and Churchill are two methods

for calculating friction factors, a valuenecessary for calculating head loss throughpiping. Each function must be used withcaution, as they each represent friction factors

for different flow regions.


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FRICTION FACTOR

The Swamee-Jain friction factor calculation isappropriate for use only in a region of turbulentflow. For piping flows

Turbulent region ReD

> 2300Darcy-Weisbach is used for ReD


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FRICTION FACTOR

Since Reynolds number 4000, either

fric_Churchill or fric_Swamee can be used


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NUSSELT NUMBERS

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)


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NUSSELT NUMBERS

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 todecide 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


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NUSSELT: FLAT PLATE, LOCAL

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 - Prandtl number, Pr = Cp / k = / Rexc - Critical Reynolds number. Reynolds number at

transition point from laminar to turbulent. If Re < Rexc, thenlaminar calculation. Otherwise, the calculation is for turbulentflow. 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


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NUSSELT: FLAT PLATE, MEAN 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 - Prandtl number, Pr = Cp / k = /

Rexc Critical Reynolds number. Reynolds number attransition point from laminar to turbulent. If Re < Rexc, thenlaminar calculation. Otherwise, the calculation is for a mix oflaminar and turbulent. If omitted, Recx = 5 X 105

Ranges For laminar, Pr 0.6 For mixed, ReL 10

8, 0.6 Pr 60

TurbulentLaminar

x Ts

V, T Rex, c


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NUSSELT: 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 - Prandtl number, Pr = Cp / k = /

Range ReDPr 0.2


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NUSSELT: 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 - Prandtl 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


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NUSSELT: 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 / Pr - Prandtl number, Pr = Cp / k = / St_D - Transverse spacing / Diameter, St / D Sl_D - Longitudinal spacing / Diameter, Sl / D

Aligned - True or 1 for Aligned tubes, False or 0 for Staggered tubes. Aligned ifomitted. 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 = V St / (SD-D)

Ranges Pr 0.7 2000 ReD, max 40,000

AlignedStaggered

Rows Rows

St

SlSl

St

SD


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NUSSELT: BANK OF TUBES, ZUKAUSKAS

NuDBarZTubes(Re, Pr, Prs, St_Sl, Aligned, Nl, Quiet)

Returns the average Nusselt number for crossflow over a bank of tubesbased on a new correlation by Zukauskas Inputs based on the film temperature, Tf = (Ts+T)/2

Re - Reynolds number, ReD, max = Vmax D / Pr - Prandtl number, Pr = Cp / k = / Prs - Prandtl number calculated for the average of the inlet and outlet

temperatures St_Sl - Transverse spacing / Longitudinal 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 = V St / (SD-D)

Ranges

0.7 Pr 500 1000 ReD max 2 X 10

6

Aligned

Staggered

Rows Rows

St

SlS

l

St

SD


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NUSSELT: LAMINAR FLOW IN A TUBE NuBarLamTube(Re, Pr, D_L, Thermal, mu_mus, Quiet)

Returns the average Nusselt number for laminar flow through a circulartube 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 - Prandtl number, Pr = Cp / k = / D_L - Diameter / Length, D / L

Thermal - True or 1 for Thermal entry length, False or 0 for combined entrylength. 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 approximationfor 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


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NUSSELT: 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 - Prandtl number, Pr = Cp / k = /

Range 0.5 Pr 2000 3000 ReD 5 X 10

6

L/D 10


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NUSSELT: 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 / Pr - Prandtl 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 = ReDX Pr 100

For uniform surface heat flux 3.6 X 103 ReD 9.05 X 10

5

102 PeD 104

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