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Typical Heat Exchange EquipmentEnergy balances
Heat flux and heat transfer coefficientsTemperature difference
Overall heat transfer coefficientHeat Exchanger Analysis
Heat transfer across a solid wall separating two liquids –latent heat (phase change) or sensible heat (∆T without phase change).
All such operations need heat transfer by conduction and convection
Simple tubular condenser
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If vapour entering is single component (not a mixture), not superheated, and the condensate not sub cooled then shell side temp. is constant
T - point temperature difference (T1-inlet, T2 - outlet)
Terminal point temperature differences = approaches
Temperature range or range, Tcb – Tca
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Counterflow or countercurrent flow
Tha – Temperature of hot fluid entering
Thb – Temperature of hot fluid leaving
Tca – Temperature of cold fluid entering Tca – Temperature of cold fluid leaving
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Approaches : T1 = Tha – Tca T2 = Thb - Tcb
Warm fluid range = Tha - Thb Cold fluid range = Tcb - Tca Parallel flow – Fluids enter same end & flow out
same end
Parallel flow: rarely used for single pass Thb >> Tca & Tha >> Tcb
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H/E mechanical, potential & kinetic energies << enthalpy, hence for each fluid stream:
m ( Hb – Ha ) = Q
q = Q/A
If the shell side fluid is hotter or colder than the ambient temperature then undesired heat loss/gain could result so lagging (insulation) is necessary. 6
For the warm fluid, enthalpy balance: mh (Hhb – Hha) = Qh
heat lost = heat gained : Qc = - Qh
Overall enthalpy balance mc (Hcb - Hca ) = mh ( Hha – Hhb ) = Q mh Cph( Tha – Thb ) =mc Cpc(Tcb - Tca ) = Q
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For condensers with phase change: mh λ = mc Cpc(Tcb - Tca ) = Q
assuming no superheated vapour, no subcooled condensate
Otherwise : mh [λ +Cph( Th – Thb )] =mc Cpc(Tcb - Tca )
HEAT FLUX = Rate of heat transfer per unit area [Wm-2], [Btuhr-1ft-2] 8
Important to specify whether internal or external surface areas being used (choice is arbitrary but order of magnitude different)
Heat flux across solid layers proportional to driving force T
Q/A = ∆T/R also true for liquid layers H/E driving force : Th -Tc
hot fluid avg. temp cold fluid avg. temp
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∆T, hence heat flux, varies along length of H/E dQ/dA = U∆T = U(Th – Tc) Proportionality factor U, (overall heat
transfer coefficient) [Wm-2 oC-1] For external tube area A = Ao , U = Uo
For internal tube area A = Ai , U = Ui
Uo= Ai = Di
Ui Ao Do
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Uo = dAi = Di
Ui dAo Do
For plate type H/E the areas for both sides are the same so there would be only one value for U.
Q = UA∆T Q = ∆T U A The value of U is important for designing any
cooling or heating system
Inner diameter
Outter diameter
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Assuming no accumulation of heat in the media:
Q = h1 A ∆ T1 Q = h2 A∆T2 Q = h3 A ∆ T3
∆T1 = Q/h1 A ∆T2 = Q/ h2 A ∆ T3 = Q/ h3 A ∆T1 + ∆T2 + ∆ T3 = Q( 1 + 1 + 1)
A ( h1 h2 h3 )
∆T1 + ∆T2 + ∆T3 = ∆ T (Total temperature difference)
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∆T = Q ( 1 + 1 + 1) but Q = ∆ T
A ( h1 h2 h3 ) U A
I = 1 + 1 + 1 U h1 h2 h3
Reciprocals of the heat transfer coefficients = resistances and are additive
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In some cases the areas are not the same: A1, A2, A3
∆T1+ ∆T2 + ∆ T3 = Q ( 1 + 1 + 1 ) (A1 h1 A2 h2 A3 h3) Using one of the areas as the basis then U will
vary according to that area (say A1) Q = U1 A1 ∆ T or ∆T = Q
U1 A 1 = 1 + A1 1 + A1 1
U h1 A2 h2 A3 h314
The U value depends on Heat transfer mechanism
Fluid dynamics of both fluids
Properties of the H/E construction materials
Geometry of fluid paths
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Deposits & scale cause performance deterioration after a period of operation
Deposits from the flow streams increase thermal resistance and decrease heat transfer rate
Fouling factor or fouling resistance used to measure the overall effect of deposits on the heat transfer
Most common fouling is accumulation of solid deposits from the fluid onto the heating surfaces
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Corrosion and chemical fouling also affect heat transfer
Glass coating and plastic pipes used to reduce chemical fouling
Algae growth in warm fluids lead to biological fouling
Chemical treatment is used to reduce biological fouling
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Fouling factor is zero for new, clean heat exchangers, Rf =0
Rf depends operating temperature,fluid velocity and duration of service
Fluid R f , m2 oCw-1
Distilled water, sea water, T>50oC 0.0002
Distilled water, sea water, T<50oC 0.0001
Fuel Oil 0.0009
Steam (oil free) 0.0001
Refrigerants (liquid) 0.0002
Refrigerants (vapour) 0.0004
Alcohol vapours 0.000118
Fouling factors must be obtained experimentally from the U values for both clean and dirty heat exchangers
Eg. Sea Water at 125.0 oC is used in a heat exchanger with fouling factor, Rf=0.0002 m2 oC/W. What is the percent reduction in the heat exchanger’s U value if in the clean state U=1961 W/m2 oC?
cleandirtyf UU
R11
WCmUU
R o
cleandirtyf /0002.0
11 2
%64.271001961
14191961%1419
099.7
1
099.70005099.00002.1961
10002.0
1
reductionU
U
dirty
dirty
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Application determines hardware and configuration
Double pipe, tube in tube or concentric tube H/E is the simplest form & as the name implies consisting of two concentric tubes.
Compact H/E are designed where there is strict limitations regarding weight and volume so as to give large heat transfer area per unit volume. The area density (ratio of area to volume) β> 700 m2 m-3.
Examples are car radiators (β=600 m2 m-3) and glass ceramic gas turbine H/E (β=15000 m2 m-3)
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The most common type of H/E used in industrial applications.
Tube count can reach several hundreds with baffles.
Classifies by tube passes as, one shell pass and two tube passes, or two shell passes and four tube passes.
Fouling can be severe and the H/E must be taken out of service periodically to labourously clean the tubes.
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Corrugated parallel plates facing each other and held firmly together by head frames with hot and cold fluids flowing between alternate plates.
Gap between plates 1.3-1.5 mm with large surface area to volume ratio.
Increasing demand for heat transfer can be met by simply increasing the number of plates.
Application prevalent in the diary and brewing industries with stainless steel the popular material of construction with rubber seal gaskets.
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High degree of turbulence even at low flow rates
Very high heat transfer coefficients typical
Heat transfer Water U
Per plate Flow rate Value
W/K gal/h kW/m2K
1580 550 3.70
2110 850 4.94
2640 1250 6.13
Easy to dismantle and clean
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Sheets of metal are coiled to enclose a spiral annulus in the construction in this H/E with the advantage of good fouling characteristics and ease of cleaning.
Application confined to fluids with high solids concentration.
Velocities as high as 2.1 m/s and U values of 2.8 kW/m2K are achievable.
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SHEs are usually relatively small in size.
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H/Es are usually selected to satisfy a particular temperature range or to predict outlet temperatures under conditions of known flow rates.
Two methods are normally used to analyze H/E performance:
LMTD method
NTU method31
Counterflow or countercurrent flowTha
Th vs q
Tc vs qThb
Tca
ΔT1
Q QT
ΔT2
Tcb
ΔT1
ΔT2
ΔT vs q
ΔT
Assumptions:
i) Overall coefficient is constant
ii) The specific heats of the hot & cold fluids are constant
iii) Heat loss to the surroundings is negligible
iv) The flows are steady and either counter current or parallel (not both)
Te
mp
era
ture
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Based on the assumptions the temperatures of the hot and cold streams are expected to vary linearly with the heat rate.
Similarly ΔT will vary linearly with q resulting in a line of constant gradient
ΔT1 & ΔT2 are the temperature approaches then the gradient of the ΔT vs. q line is given by:
TQ
TT
dQ
Td 12
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1
2
12
1
2
12
12
1
2
0
12
12
lnln
ln
:
)tan(
2
1
TTTT
LMTDLMTDUA
TTTT
UAQ
AQ
TTU
T
T
dAQ
TTU
T
Td
exchangerheattheofareaentiretheovergIntegratin
UtconsQ
TT
TdAU
Td
TUAdQTUA
dQbut
TTT
TT
A
T
T
T
T
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When ΔT1 ~ ΔT2 ΔLMTD ~ ΔTavg
With condensing fluids ΔLMTD is the same for all types of flow patterns
For non-condensing fluids in counter current flow pattern:
ΔT2 = warm end approach ΔT1 = cold end approach
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For variable U values:
Where U1, U2 are the U values at the ends of the H/E
Other researchers proposed other methods of determining a representative temperature change across the H/E. According to Underwood:
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12
2112
lnTUTUTUTU
AQ TT
3
1
231
13
1
21)( TTTm
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A heat exchanger is required to cool 20.0 kg/s of water from 360.0 K to 340.0 K using 25.0 kg/s of water at 300.0 K. If the overall heat transfer coefficient is constant at 2.0 kW/m2K what is the required surface area using;
(a) counter current concentric tube heat exchanger
(b) co-current concentric tube heat exchanger
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For multi pass H/E flow pattern is counter current in some tubes (passes) and parallel flow in others
Finding the actual temperature difference would be very difficult due to complex flow patterns
Underwood and Bowman et al introduced use of a correction factor based on graphical methods of modifying the ΔLMTD.
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Depending on equipment geometry and inlet and outlet temperatures a correction factor may be applied to the counter current flow ΔLMTD to compensate for the complex flow.
ΔTm =F*ΔLMTD CF
F<1 For cross flow & multi-pass shell & tube H/Es F=1 Limiting value corresponds to counter flow H/Es Charts of F vs P & R
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sideshell
tubesideP
P
Cm
Tt
TTR
tT
ttP
mC
.
.
12
21
11
12 1 – inlet2 – outlet
T – Shellsidet = Tubeside
Determination of F requires the inlet and outlet temperatures of both the hot and cold fluids.
0 < P < 1 0 < R < infinity
Phase change Tube sidePhase change shell side
(boiling/condensation)
F = 1
For condensers or boilers F = 1 regardless of the configuration of the heat exchanger 40
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1. Water at the rate of 68.0 kg/min is heated from 35 oC to 75.0 oC by an oil having a specific heat capacity of 1.9 kJ/kg oC. The fluids are used in a counter current flow double pipe heat exchanger and the oil enters at 110.0 oC and leaves at 75.0 oC. Using 320.0 W/m2 oC for the overall heat transfer coefficient calculate the heat exchanger area.
2. If instead of a double pipe heat exchanger we use a shell and tube heat exchanger with water making one shell pass and the oil making two tube passes what would be the required area using the same U value?
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