Baslc Gomponents of Shell and Tube HeatExchangels

There are various components to a shell and tube heatexchanger, but the following are the essential ones:1. Tubes2. Baffles3. Tie rods4. Tubesheets

Tubes

There are basically two types-finned tubes and baretubes. Finned tubes have external fins mounted by vari-ous mechanical means. The necessity of having externalfins mounted on tubes is to provide more heat transferarea and thus more heat influx to the tube fluid. Finnedtubes are most common where there is a gasJiquid orgas-gas transfer of heat with the gas always being exter-nal to the tubes. Typical applications of finned tubes arewaste heat recovery exchangers, waste heat boilers, gasturbine regenerators, and air-cooled exchangers. Exam-ples of some finned tube designs are shown later.

Plain or bare tubes are the most common in shell andtube design. These tubes come in two basic types-solidwall construction and duplex construction. The duplexdesign consists ofa tube within a tube in which the outertube is mechanically drawn over the inner tube. Thesolid wall tube is what the name implies, a simple tube ofsolid wall construction. Tubing is available in almost asmany materials as piping and is available in standardgauge sizes listed in Table 7-3, along with diamerers andsection properties.

In applying the U-tube exchanger design, tubes mustbe bent 180'. Thble 7-4 lists the recommended minimumbend radii.

Baffles

Baffles serve several functions and consequently thedesign of each is dependent on its purpose. Baffles canact as:

l Structural supports for the tubes.2. Dampers against vibration.3. Devices 1o control and direct flow Datterns of the

shell-side liquid.

Baffles as Tube Structural Supports. Like piping,tubes behave as structural beams and consequently willdevelop excessive deflection, or sag, if left unsupported.Baffles act as the structural supports in the shell and tubeexchanger. Another structural function of baffles is toadd stiffness to the tubes so that each tube. in effect. is

The Mechanical Design of Shell-and-Tube Heat Exchangers 1o7

constrained at each baffle. Thus, the hole in the baffle,being larger by varying amounts than the outside tube di-ameter, acts as a limit stop for the tube. In piping me-chanics (see Chapter 2) a limit stop is a restraint that lim-its the amount of pipe (in this case, tube) movement tothe distance between the hole diameter and the outsidediameter of the tube. In other words, the tube can trans-late in the lateral direction perpendicular to the tube axisonly by the amount of clearance between the tube ODand the hole diameter. Translation is mentioned insteadof rotation because even though the tube rotates, it is in-significant. Thus, the baffle hole acts as a limit stop andprevents lateral buckling of the tubes when they are in-duced to thermal expansion by temperature differentials.In this sense the tubes are much stiffer and stronger thanthey would be without the baffle supports. The conse-quences of strengthened tubes affect the integrity of tubejoint connections in the tubesheets and this will be dis-cussed shortly. We see from this discussion that the baf-fle plates act as both structural supports and as buckiingstabilizers.

Baftles as Tube Vibralion Dampers. Figure 7-6shows baffles of circular rings with rods that run verti-cally in the first two rings and horizontally in the secondtwo rings, thus damping vibration much in the same wayas helical vortex strakes on stacks (Chapter 5). The rodsbreak up forming vortices that induce vibrations, a phe-nomenon discussed in Chapters 4 and 5 called vortexshedding. The rods also reduce turbulence to below res-onant levels of the natural frequency of the tubes andthey reduce fluid elastic vibration.

Baffles Conlrol and Direct the Flow Pattern of theShell-Side Fluid. There are various types of baffles thatdirect and/or control the flow ofthe shell side fluid. Fie-ures 7-l and 7-2 are examples of baffles guiding or d'i-recting the flow in the vertical direction. Fig]ure 7-7shows baffles diverting flow in the horizontal direction.The flow direction is a function of the orientation of thebaffles and their respective geometries and is dependentupon process requirements. The arrangement in Figure7-7 is said to be vertically cut and the arrangements inFigures 7-l and 7-2 arc said to be horizontally cut.

Often, process conditions require the shell-side fluidto flow horizontally, parallel to the longitudinal axis ofthe exchanger. This arrangement, called a longitudinalbaffle, is shown in Figure 7-8. Figure 7-8a shows a two-pass shell-side arrangement and Figure 7-8b shows afour-pass shell-side arrangement. The baffles control theflow in the sense that both the direction and flow rate aredependent on orientation and number of passes, respec-tively. With the same inlet flow rate, the fluid velocity

108 Mechanical Design of Process Systems

Table 7-3Characteristics of Tubing [21

Tubeo.D. B.W.C.

Gage Sq.Inch

Sq. tt.

LenAtlr

Sq. Ft.

lengrtl

WGisht

len8thSteel

Tubot.D.

Ssctlon o.D.

t.D. 5q. Inch

Y.tt

yt%%Yl

h

v,

%%

%vs%%

xt/.

',|

%

%1A

I

III

II

I

tt/tt%t%1t/tlYatYlty.t%t)At\t\ttwt\ttkzz22

2224

2?

t82022?4

l82022

t2l3l4l5l617l8l920

l0II\2l3l4l5

t7l820

El0

t2l3l4l5

l820

1E

l0IIt2l3l4t6IE20

l0\2l4l6

ltt2

l4

.028

.022

.018

.016

.049

.035.028.022

.065-049.035.028

.109

.095

.0E3

.072

.065

.05E

.049

.042

.035

.134

.t20

.109

.095.063.0t2.055.056.049.035

.165

.134

.t20

.109

.095

.083

.072

.065_049.035

.180

.165

.134

.t20

.109

.095

.083

.065,049.035

.134

.i09

.0E3

.065

.120

.t09

.095

.0E3

.0295

.0333

.0360

.0313

.0603

.0731

.0799

.0850

.1075.1269.t452.1546

.1301.14E6.1655.1817.1924.2035.218t-2298.2419

.1E25

.2043

.2223

.2463

.2679

.2884.3019.3157.3339.3632

.3525

.4?AE

.4536

.4803

.51t3

.5463.5755.5945.6390.6793

.6221.6648.7574.8012.8365_8825_9229.9852

'\.042

1.094

Ll921.2911.398t.471

2.4332.4942-5132.642

.0655.0655.0655.0555

.0962.09E2.0982_0982

.1309

.1309

.1309.1309

.1636

.1636

.1636.1636.1636.1636.t636

.1963

.1963

.1953

.1963.1963.1963.1963.t963.1953.1963

.2618_2618.2618,2618_2518.2618.2618.2618.26t8.2618

.3272

.32t2

.3272

.3272

.3212_3?t2.3272.3272.3212.327?

_3927.3927.3927.3921

.5236

.5236

.5236

.0508_0539.0560.0570

.0725

.0798

.0835

.0E57

.0969.1052.l t26.l162

.1066

.1139

.t202

.1259

.1296

.1333

.1380

.14t6_1453

.1262

.1335.1393.1466.1529.t587.1623_1660.\107.1780

.1754

.19t6.19902041

.2t21

.2183_2241_z?t8.2361.2435

.2330_2409_25t I.2644.?t02.2715.2E36.2932

.3089

.3225.3356.3492.3587

_4606.1665.4739_4801

_066.054.045.040

,lil.t27.104.083

.302

.236

.171

.l4I

.602

.537

.479

.425

.388

.350

.303

.262

.221

.884.809.748.666.592.520.4t6.428.367.269

L46?1.2t1Lt291.037.9lE.813.714.649.496.360

2.0571.921I.59E1,4481.329Ln31,033_823.629.456

1.955l.6lE1258.996

2,4102.201t.9341.6s9

.194

.26

.2t4

.218

.277_305.319.331

.370

.402

.430

.407

.435

.459.461.495.509.521.541_555

.482.510.532.560.5E4.606.620.634.652.680

.670-132.760.782.610.634.856.870.902.930

.890

.920

.9821.0101.a321.0601.0E41.1201.t52Ll80

1.232t.2E?1.334l_370

1_760t.1821.8101.834

.00012

.00011

.00009

.00008

.00068

.00055.00045.00036

.0022

.0018

.00t4

.0012

.0061.0057.0053.0049.0045.0042.0037.0033.0028

.0129

.0122

.0116

.0107

.0098

.0089

.0083

.0076

.0067

.0051)

.0392

.0350.0321.0307.0280.0253.0227.0210.01660t24

.0E90_0847.0741.0666.4612.0579.0521.0426,0334.0247

.1354.1159.0931.0755

.3144

.2904

.2586

.2300

.00098

.00083

.00071

.00064

,0036.0029.0025.0020

.00E5

.@72_0056.0046

.019i

.0163

.0170

.0155

.0145

.0131

.0118

.0105

.0091

.0344.0326.0309.0285.0262.0238.0221.0203.0178.0134

.0784.0700.0654.0615.0559.0507.0455.0419.0332.0241

_\425.1355.u86.1100.1027.0926.0833.06E2.0534.0395

.1806,1546.t241_1008

.3141.2904.2586.2300

.9792

.0810

.0E?4

.0829

_l164.12t3.\227.\248

.1556

.1606

.1649

.167r

.1864

.1903

.1938

.1971

.I993

.2016

.2043

.2068

.2089

.2229.2267.2299.2340-23/6.24t0.2433-2455.2484.2532

.3009.3098.3140.3V4.3211.3255.3291.3314.3366.341{

.3836.3880.3974.4018.4052.4097.1136.4196_4250.4291

_4853.4933.50tE.5079

.6660_6697.6144,6784

46525656

94lt4125134

198227241

2322582833003V340358377

285319347384416450471{92521567

550555708749E04852898921997

1060

9701037ll8212501305I31lI440I537l5?6t707

186020142l6l2299

3795389040144t2l

1.289t.2t4l.16ELI46

1.3541.2331.176l133

1.3511.241L1631.126

1.5361.43i1.35212991.2631.228l_1861.155L125

1.556t.4111.4101.339t.284l.?3Et.2t01.183Ll501.103

1.4931.3661.3161.2791.2351.199t.1671.1491.t091.075

1.4041.359'\.2731.238t.2t ILl79I.153t.ll61.0E5L059

1.2181-1701.1211.095

1.136l.\22Ll05t.090

.0195

.0159

.0t31

.0!t7

.0502

.0374

.0305-0244

.(]EE6_0694.0511.0415

.t7l

.158

.l4l

.125

.ll4.103.089.0t7.065

.260

.238

.220

.196_174.153.140.t26.l0E.079

.430

.364

.332

.305

.?10

.239_210.191.146_106

.605

.565_470_426.391.315.304.212.185_134

.575

.476

.370.293

.709

.647.559.500

l.0i1.09l t3l.I4

The Mechanical Design of Shell-and-Tube Heat Exchangers 109

Table 7-4Minimum Tube Bend Radii l4l

Tube Outside Dia. (in.) Bend Radius (in.) Center-to-Center Oistance (in.)

Duplex, all sizes*Plain:5/s

I*For bends this sharp, the tube wall on the outer circumference of the tube ma\ thin down lt/z to 2 gauge rhicknesses. dependin| on condition and specifictube materiaL Morc genercus ndii \9ill reduce this thinning. TEMA presents a formula for calculating the minimum wall thickness.

Figure 7-7. Baffles can divert flow horizontally. (Courtesy ofHowell Training Company.)

3 times Tube O.D.t3/te

1

131t6

6 times Tube OD15/s

22z/s

Figure 7-6. Although complex, this design eliminates tube vi-bration. To use this configuration, one must be cognizant ofpressure data [5]. (Courtesy of Heat Transfer Engineering,Hemisphere Publishing Corporation, New York, Washington,D.C.)

Figure 7-8. Longitudinal baffles direct flow in the axial di-rection. (Courtesy of Howell Training Company.)

VAPOR IN LET

FLUID IN LET

FLUIO OUTLET

CONDENSATE OUTLET

1 10 Mechanical Design of Process Systems

increases as the flow area decreases, that is, the velocityincreases with an increase in the number of oasses.

The control of flow in exchangers is accomplished aswell with orifice baffles. Figure 7-9 shows an annularorifice baffle. To utilize this type of design a very cleanshell-side fluid is required, since the fluid must flow inthe annular space between the tube outside diameter andthe hole in the baffle forming the orifice. The flow at theorifice is very turbulent and the pressure drop through anorifice-baffle arrangement is very high. Consequently,these baffles are not used often in industry. Also, sincethe orifice baffle requires a very clean fluid, non-New-tonian fluids are completely ruled out. We will see laterin the chapter that the plate fin type of exchanger is supe-rior to the shell and tube design for many clean services.The reason for the shell and tube desisn to be dominantis because of the wider variery of fliids it can handleversus any other design.

Other baffle arrangements are possible with varyingbaffle shapes and orientations. Figure 7-10 shows baf-fles in disc and doughnut shapes, which disperse theflow in a radial direction. Baffles can be cut to allow forhorizontal or vertical flow in varying amounts as shownin Figure 7-11.

Tie Rods

These are structural rods that run oarallel to the ex-changer tubes through the outer perimeter of the baffles.fastened to the tubesheets such that they space and sup-port the baffles. Tie rods, being attached to the baffleplates, also prevent them from vibrating and damagingthe tubes. Table 7-5 lists what TEMA recommends as aminimum number of tie rods and rod diameters for a setof shell diameters.

Tubesheets

These are the structured plates in which the tubes areconnected at each end ofthe exchanger. Tubesheets comein two basic types-single and double. Double tube-sheets consist of two tubesheets mounted together at eachend of the tubes with a clearance between the two sheets.The reason for using two tubesheets at each end is to re-duce the possibility of a leak of the tube-side fluid. Dou-ble tubesheets are quite common with highly toxic ser-vices, where a leak cannot be tolerated.

Single tubesheets are much more common than doubletubesheets because ofprocess applications and economy.Typical tube-tubesheet connections are shown in Figure1 1a

Of great immediate concern in tubesheet design is theloading induced by the tubes thermal movement, which

Figure 7-9. Annular orifices between tube outside surface andhole in baffle plate [6].

Figure 7-10. Doughnut and disc type baffles [6].

Table 7-5TEMA Tie Rod Standards (in.)

"c" & "8"Exchanger

Tie RodDlameter

8-15r6-2728-3334-4849-60

Nominal "R" Exchanger"R" Exchanger Tie RodShellDiameter Dlameter

irinlmumNumber

of Tie Rods3/z

3/t

tlztlz

3/a

tlzrlztlz

4oo8

10

% Cul Bd!.d on Diomehr

lA) VeflicolCul Eoltle

Ihis Areo Cll Ool to Arlor Vopor Passog..Siz€ of Cul Set by Combiiolions ol HeolTroisf€r Co€llici€nt oid Pressure Drop.

This Areo Reooead lron Soiil€ lo Allo* lorLiquid D,oinoqa,Sire Sel to Slil Erp€cl.d Fkr

o, : :: when Cc < ktlrz\Ku f r_ | ,,-,,-,1

o. = : ll - llllJ I when C" > k#rt I lLc I

The Mechanical Design of Shell-and-Tube Heat Exchangers 111

is a definite problem in fixed tubesheet exchangers.TEMA gives two equations for determining the compres-sive stress induced on tubesheets for all three types ofexchangers-Classes R, C, and B:

(7 -r)

(7-2)Soltb {iidor, Voror Possoq. Areo

Figure 7-11. Baffle details [4].

Applied Process Design for Chemicol ond

Flush lol/l6"to l/4'

Beoded or Belled

5/16' Minimu ml/8" Minimum

: minimum yield stress oftube material ofdesignremperalure

: radius of gyration of tube: 0.25[d3 + (d" - 2t,)2]0 50, in.: tube wall thickness, in.= equivalent effective unsupported length of the

tube. in.: unsupported tube span, in.

Petrochemicol Plonts

rl Bollh Cll Mun be Horironlor,Ihe. S€dionlind0ding Tubes)Should be Rrhoved rh.ncoidensed liquid rhr is High.

oy

t

trki

Tube Shee

ClodTobe Sheet

Ferrule,some0s tnner

Tube Woll

We ld ed Dupler Tube

Beoded or EelledThis Tube Moy olso be InslolledPloin End (No Ferrule)or FlqredWith or Withoul Ferrule,

I p-tre'' Uinirr.,Usuolly l/4"

ssq+$\ usn"

Typicol Grooved Detoil

Figure 7-12. Typical tubesheet-tube connections [4].

where C" = [rf,:i"

or lor 0.oininq olrer lfoshout.sir. ro SuilFlor.Ihis b l'lol Becohriended tortloriron16l Condenseri.

I8) tlorkonlol C!l 8!ftle

nne I

Ploin

8= l5'Avirose

Flored

112 Mechanical Design of Process Systems

for unsupported tube lengths between twotubesheetsfor unsupported tube lengths between atubesheet and a bafflefor unsupported tube lengths between twobaffles

Et : modulus of elasticity of tube material at meantube metal temperature, psi

4 : outside diameter of tubes, in.oc : allowable tube compressive stress, psi, for the

tubes at the outer periphery of the tube bundle

Equation 7-1 is based on Euler's columl equation andEquation 7-2 is based on the short column formula de-veloped by Professor J. B. Johnson during the nineteenthcentury.

Other TEMA formulations are summarized in the fol-lowing sections. The reader is urged to be familiar withthe TEMA standard and follow its guidelines in design-ing a shell and tube heat exchanger.

TEMA Formulations

Baffles and Support Plates

Natural Frequencies ot Straight Tubes on MultipleEqual Spans

3.36C

where f" : tube natural frequency, HzC : mode constant from Thble 7-6I : span length, in.

E = modulus of elasricity. psiI = moment of inertia, in.a (Table 7-3)

W : Wr + Wn + MWr", lbs/ftWt : weight of empty tube (Table 7-3)Wq : weight of fluid inside tube 0.00545 p1d1,W6o : weight of fluid displaced by tube 0.00545

p"d"'?

M : added mass coefficient from Table 7-6p : fluid density, lbs/ft3d : diameter of tube, in

subscripts:i : insideo : outside

r{o'['o

Allowable Tube Compressive Stress-Periphery ofBundle. The allowable tube compressive stress, psi, forthe tubes at the periphery of the bundle is given by:

-28a,:ffi when C. s kf/ror

-r -. Is"=\l r - (kur)l

whenc >kur- 21 2C"l

/:*where C" = l/ ^'Vsr

Table 7-oMode Constant-C [21

No.ofSpans

Extreme Ends Supported

Fr-l-'-l*,.1|--___l/T-7\--lzf-R

Extreme Ends ClamDed

,l-r+rExtreme Ends Clamped-Supported

r-fr-fr

lst Mode 2nd Mode lst Mode 2nd Mode lst Mode znd Mode

I234567a9

to

31.7331.733r.73

31.73

31,7331.73

126.9449.59&.5237.O234.9934.3233.6733.O233.02

72.3649.5940,5237.O234.9934.3233.6733.0233.0233.02

198.3472.3659.5649.5944.r940.5238.4037.O2

34.99

49.5937.O234.32

32.3731.7331.73

160.6663.9949.5942.7039.1037.O235.6634.9934.3233.67

KT:

yield stress, psi, oftube material at design metaltemperature used.radius of gyration of tube

0.25 .vu +la" - 2tJ1, in. (Table 7-3)

equivalent unsupported buckling length of thetube, inches. Use the largest value consideringunsupported tube spans.unsupported tube span, in.

0.6 for unsupported spans between two tube-sheets.

0,8 for unsupported spans between a tubesheetand a baffle.

1.0 for unsupported spans between two baf-fles.

The Mechanical Desien of Shell-and-T[be Heat Exchansers 113

quency, assuming simple supports and for the first modeonly, may be calculated as follows:

2.74C"

= U-tube natural frequency, Hz: mode constant for U-bend: bend radius, in.

Note: For other than simple support conditions the calculatedfrequency may be estimated by multiplying the abovevalue for f,, by the appropriate ratio of mode constantsfrom Thble 7-6 using single span values.

ASME Tube Joint Load Grlteria

The ASME Secrion VItr Division I Dressure vesselcode lists formularions in evaluating tube forces exertedon tubesheets. Referring to Figure 7-13 and Table 7-7the formulas for the maximum tube force are as follows:

For joint types a, b, c, d, e:

F, : A,o,11f,

For joint types f, g, h, i, j, k:

(7-3)

R2

where fnu

R

Note: The value of S" shall not exceed the Code allowabletensile stress of the tube material at desisn metal tem-perature used.

Effect ot Longitudinal Tube Stress

where fnp : tube natural frequency in stressed condition, HzP = axial force, lbs (positive for tensile, negative

for compressive)

Natural Frequencies of Straight Tubes on UnequalMultiple Spans

f" : 10.83 t'z

For a tube on multiple unequal spans with the extremeends fixed and simply supported at the intermediate sup-ports, ki can be obtained by solving the following char-acteristic determinant for an n span system.

Natural Frequencies of U-Tubes. It must be recog-nized that each tube is a continuous beam that has a sin-gle fundamental frequency. This frequency may belargely governed by the lowest "stand alone" frequencyof either the longest straight span or the U-bend. It issuggested that both be calculated and that the lower valuebe used, keeping in mind the approximate and somewhatconservative nature of the result. The straight span fre-quency may be determined from Thble 7-6 using the ap-propriate mode constant. The U-bend out-of-plane fre-

F, : A,o"11f,f"f,

where Ft :

oall :f=

f. (no tesg =

f, (teso :

(7-4)

maximum tube joint force, lb1cross-sectional metal area of tube, in.2ASME maximum allowable stress. psijoint reliability factormaximum value without test given inTable 7-'7maximum value with test as specified inthe ASME Section VIII Division 1

code, per section UA-002

Figre 7-14 shows how the tube joint load varies forvarious tube gauges of various process conditions. Natu-rally, as the tube wall increases, the tube stiffens and,consequently, the force exerted by the tube on the tube-sheet joint increases. The engineer should evaluate thetube loads with the various process conditions possibleand use the worst for determining the maximum tubejoint force, as shown in Figure 7-14. The TEMA stan-dard gives the formulations to determine the tube iointlorces and the user is referred to this standard for theseexpressrons.

The buckling of exchanger tubes can be a problem ifthermal expansion is not properly accounted for in de-

Dt2

'Er.,j

114 Mechanical Design of Process Systems

Table 7-7Reliability Factors, f, [71

Type Joint Descriptions Notes l. (tesr) f, (no test)(1)(7X8)

(1X2)(1X3)(1X6)

(1X7X8)(1X4)(s)

(7)( l )(4)(s)

(7)(l)(4)(5)

(7)(l)(4xs)(l)(4x5)(l)(4)(5)

abcd

f

c

h

Ijk

Welded only, a> 1.4rWelded only, tsa<L.4tBrazed, examinedBrazed, not fully examinableRolled, welded, a> l.4tRolled, two or more grooves,

and welded, a< l.4rRolled, single-groove, and

welded, a < 1.4rRolled, no grooves, and

and welded, a < 1.4rRolled, two or more groovesRolled, single grooveRolled, no grooves

1.000.701.000.501.00

0.95

0.85

0.700.900.800.60

0.800.550.800.400.80

o.75

0.65

0.500.700.650.50

Notes:(l) The use of f. Ceso factor requires qualification in accordance with UA-003 and UA-004.(2) For welds where a is less than t, fi (no test) - 0. Tubes with Type (b) joints where a<t may be considered as acting as stays and contributing to the

strength of the tubesheet only when the joint is tested in accordance with UA 003 and UA-o(X.(3) A value of 1 00 for f, (test) or .80 for f, (no test) can be applied only to joints in which visual examination assures that the brazing filler metal has

penetrated the entire joint [see UB-14(a)] and the depth of penetration is not less than three times the nominal thickness of the tube wall.(4) When the ralio of OD. to LD., using nominal tube dimensioos, is less than 1.05 or geater than l-410, qualification in accordance with UA403 and

UA-oO1 is required.(5) The nominal pitch used in the desigo of tubesheets for roller expanded joints shall not be less than the following:

P = d" + 0.165 (d" + 2r)

= nominal pitch (center-to-center distance of adjacent tube holes), in.= tube o.D_, in.= nominal thickness of average wall tube, in.

except that:(a) nominal pitch shalt not be less than 4 + 2t unless the joint is qualified in accordance with UA-003 and UA-004; and(b) 96% of the ligaments between tube holes throughout the thickrcss of the rnachined tubesheet shall not be less than 0.85 (P-4). Ligaments whichdo not meet this requirement shall be evaluated and €orrections made as may be necessary.

(6) A value of .50 for f, (test) or .40 for f, (no t€so shall be used for joinls in which visual examination will not provide proof that the brazing filler metalhas penetrated the entire joint Isee US-14(b)1.

(7) The value of f. (no test) applies only to material combinations as provided for under Section IX. For material combinations not provided for underSection IX, f. must be determined by test in accordance with UA-003 and LIA-0O4.

(8) For joint types involving more than one fastening method, the sequence used in the joint descriptions does not necessarily indicate the order in which the

oDerations are Derformed.

I

sign. One such formulation to predict the critical buck-ling load is as follows:

P., - , " q'' ,, t0.5216r t7-51

I L** l'\Ns + t/

where L,u6" : total length of tubei between tubesheetsNB : number of baffles

Equation 7-5 is based on the Euler column formula. Insituations where there are several baffles, such that theeffective length, L", divided by the radius of gyration, k,is between 30 and 120, exclusive, then the Johnson short

column equation is more accurate. For a tube to be con-sidered as a series of short columns constrained by fixedends, one must be certain that the baffles constrainingthe tubes allow practically no translational or rotationalmovement. The stiffness of the baffle plate should beanalyzed, as small translational and rotational tubemovement allowed by the baffle plate could considera-bly alter the buckling characteristics of the tube. Theevaluation of a baffle plate containing several tubes canbe a somewhat detailed analysis, and it may be faster toconsider the tube as a continuous beam in determiningbuckling characteristics.

For further details on the mechanical design of ex-changers, the reader is referred to TEMA. We will dis-cuss tube vibrations shortly.

PBOCESS EVALUATION OF SHELL ANDTUBE EXCHAI{GERS

We are concerned here only with any particular heatexchanger and determining whether it can transfer heatenergy as required. How the unit affects process condi-tions of the entire system is not our concern here, be-cause we are interested only in the proper performanceof the unit. Evaluating the exchanger in relation to theprocess system is the primary concern of the chemicalengineer. The thermal evaluation of the exchanger is onearea where chemical and mechanical engineering over-lap; just as in Chapters 2 and 4 we saw how civil and

The Mechanical Desien of Shell-and-Tube Heat Exchansers t15

mechanical engineering coincide. Thus, the mechanicalengineer must be cognizant of process evaluation of heatexchangers in order to design these units.

A thermal evaluation of shell and tube heat exchansersconcerns primarily two modes of heat transfer-conJuc-tion and convection.

In Chapter 3 we considered heat transfer through pip-ing and vessel components as well as jacketed systems.As described in Chapter 3, the basic expressions used inconveetion are as follows:q : rhcpat

q : UA(LMTD)

(3-24)

(3-26)

{1t

Some ecceptable weld geometriea

t2l

where t is not less lhan l.4t

(61 l7l (81

Figure 7-13. Joint types [7]. (Courtesy of ASME.)