HEAT EXCHANGER CLASS NOTES FOR MECHANICAL ENGINEERING
HEAT EXCHANGER CLASS
NOTES FOR MECHANICAL
ENGINEERING
Heat exchanger transfers heat between
two fluids separated by a solid wall in
between. Cools the hot fluid. Heats the
cold fluid. There are many types of heat
exchangers. Different heat exchangers
are used in different applications.
Heat exchanger exchanges heat between
two fluids with a solid wall in between.
One fluid is heated while the other
fluid is cooled. There are two methods
of analysis. These are LMTD and NTU
methods. LMTD is used where inlet
and outlet temperatures of the two
fluids are known.
Definition of a heat exchanger
It is a device for heat transfer between two fluids.
Recuperator
It is a device to transfer heat between two fluids which do not mix.
Compact heat exchanger
(i) A heat ex-changer which transfers maximum heat per unit volume of space.
Or
Surface area in (m2)/m3 of space is maximum for a compact heat ex-changer .
(ii)Heat Transfer area density
The surface area in m2/m3 of space is heat transfer area density.
TYPES OF HEAT EX-CHANGERS
Four basis of classification
(i) On the basis of flow
(a) Parallel flow: Initial q. is very high but then decreases, not used presently.
(b) Counter flow: q. is high throughout, area required is less, more efficient, universally used.
(c) Cross flow: where one fluid changes state namely condenser/evaporator. These are quiet common.
Fig. Types of Heat Exchagers
(ii) On the basis of function these perform
(a) Condenser
(b) Evaporator
(c) Boiler
(d) Preheater
(e) Super-heater
(iii) On the basis of construction
(a) Double pipe HEX
(b) Shell and coil HEX
(c) Shell and tube HEX: maximum in use because of easy de-scaling.
Fig. Shell & Tube Heat Exchanger (Counter Flow)
(d) Multiple shell pass/multiple tube pass HEX
It is a type of cross flow heat ex-changers to increase heat transfer. It is very common in condensers and evaporators.
(iv) On the basis of operating principle
(a) Mixing type: Cooling towers, Jet condensers, Direct contact heat water feeders, desert coolers
(b) Non mixing type: Radiators, pre- heater economizer and pre-heater
Practical Applications of Heat Exchangers
Radiators
Inter-coolers in multi-compressors
Air preheaters
Economizers
Super-heaters
Waste water heat recovery system
Oil coolers in transformers
Condensers and evaporators in refrigerating units
HEAT EXCHANGER-OVERALL HEAT TRANSFER COEFFICIENT
DEFINITION
Overall heat transfer coefficient is a single coefficient for convection, conduction and convection taking place simultaneously. Its symbol is ‘U’. Its units are W/m2 K.
1/UA =1/hiAi+fi + ln (r2/r1)/2πkL +1/hoAo + fo
Where fi and fo are fouling resistances on the inner and outer surfaces.
CALCULATION OF U
(i) On the basis of Ai
(ii) On the basis of Ao
CALCULATE resistances 1/hiAi and 1/hoAo. Find which resistance is greater. Greater of the two becomes the basis of calculating U.
Overall heat transfer coefficient based on outer area
1/Uo =ro/ri hi + 1/ho +( ro/ri) fi +(r0 /k) ln (r2/r1) + fo
Overall heat transfer coefficient based on inner area
1/Ui =1/hi +( ri/r0) (1/ho) + fi +(ri /k) ln (ro/ri) + ( ri/r0) fo
If the tube is very thin, then with no fouling
1/U= 1/hi +1/ho
CALCULATION OF hi and ho for finding U
CALCULATION OF hi
Find Reynolds number in the tube. Find laminar or turbulent flow. Apply corresponding Nusselt Number equation to find hi
(a) For laminar flow in a tube Nu = 1.32(∆T/d)0.25
(b) For turbulent flow in the tube Nu = 0.023 Re0.8 Pr 0.4
(c) For turbulent two phase flow in a tube
Nu = 0.023 (kL/D)Re0.8Pr0.4 F
Factor F is correction factor for two phase flow
Case 1 F =1 for 1/χ > 0.1
Case 2 F= 2.35(1/χ + 0.213) for 1/χ < 0.1
Where χ is Martinelli-Nelson Parameter
1/χ = (x/ (1-x))0.9 (ρL /ρV)0.5 (µg/µL)0.1
NOTE: Original Dittus-Boelter Equation is for liquid phase flow only. For a two phase flow, it uses a correction factor ‘F’.
CALCULATION OF ho
I. Sensible heat exchange on the outside of the tube or FOR A SINGLE PHASE HT
(a) Laminar flow over horizontal plate
Nu= hoD0/kf = 0.54 (Gr Pr)0.25
(b) Turbulent flow over horizontal plate
Nu= hoD0/kf = 0.14 (Gr Pr)0.33
(c) Laminar flow over a vertical plate
Nu= hoD0/kf = 0.59 (Gr Pr)0.25
(d) Turbulent flow over a vertical plate
Nu= hoD0/kf = 0.10 (Gr Pr)0.33
II. Where phase change takes place on the outside of the tube Or For two phase HT
hNBHTC =0.00122[(kL0.79 cpl0.45 ρL0.49)/ (σ0.19µL0.79hfg ρV0.79)] ΔTex 0.24 Δp sat 0.75
Where hNBHTC is Nucleate boiling H T coefficient Or two phase heat transfer coefficient
ΔTex = Tsur –Tsat
Δpsat = psur –psat
(iii)Calculation of hoin case of condensation
(a) Laminar film condensation on a vertical plate
Average HT coefficient from NUSSELT EQUATION
ho = hav = 0.943 [ k3ρ2g hfg/ (μ L (Tsat—Tsur))]0.25
(b) Turbulent film condensation on a vertical plate
Film heat transfer coefficient
ho =hav = 0.0077(Re)0.4 [ k3ρ2g / (μ2]1/3
After finding hi and ho, U can be calculated
AT EXCHANGER ANALYSIS
There are two methods.
(a) LMTD METHOD
(i) when all the four temperatures are known.
q.=U A LMTD
(ii) When fouling is to be considered
q.=Udirty A LMTD
where f=1/U dirty –1/U clean
Values of f and U clean are given in standard tables.
(i) ANALYSIS OF MULTIPASS HEAT EXCHANGERS
For multi-pass shell/multi-pass tube / multi-pass both in shell and tube
/ cross flow HEX
q.=(UA LMTD counter flow) F
Factor F is read from charts having F along y-axis
Parameter P along x-axis
Curves for various values of parameter Z.
Parameter P =Temp range of tube fluid/max. temp diff in HE
Parameter Z = Temp range of shell fluid/Temp range of tube fluid
Values of F <0.75 should be read from graphs since graphs are not accurate for F<0.75.
Then, use complex mathematical equations to find ‘F’.
Low value of F means more area of heat ex-changer.
(b)NTU METHOD
Use this method when LMTD is not known. When the four temperatures are not given.
NTU = Number of transfer units (dimensionless) which represents the size of heat exchanger. NTU measures the effectiveness of the heat exchanger. It is a fictitious term.
NTU= U A/ (m.cp)min = U A/ C min
value of (m.cp)hot =Chot
(m.cp)cold=Ccold
Where C min is smaller of C hot and C cold
C = C min/C max
where C is heat capacity ratio
EFFECTIVENESS
Effectiveness Є = q. actual /q. max
q. max = C min(T max – T min)= C min(T hot in – T cold in)
(i) Effectiveness for parallel flow heat exchanger
Є = (1 –e—NTU(1+C))/(1+C)
(ii) Effectiveness for counter flow heat exchanger
Є = (1 –e—NTU(1–C))/(1–C e—NTU(1—C))
where C = C min/C max
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