# 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 (m^{2})/m^{3} of space is maximum for a compact heat ex-changer .

#### (ii)Heat Transfer area density

#### The surface area in m^{2}/m^{3} 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/m**^{2 }K.

^{2 }K.

#### 1/UA =1/h_{i}A_{i}+f_{i +} ln (r_{2}/r_{1})/2πkL +1/h_{o}A_{o} + f_{o}

#### Where f_{i and } f_{o are fouling resistances on the inner and outer surfaces.}

**CALCULATION OF U**

**(i) ****On the basis of A**_{i}

_{i}

**(ii) ****On the basis of A**_{o}

_{o}

#### CALCULATE resistances 1/h_{i}A_{i} and 1/h_{o}A_{o}. Find which resistance is greater. Greater of the two becomes the basis of calculating U.

#### Overall heat transfer coefficient based on outer area

#### 1/U_{o} =r_{o}/r_{i} h_{i} + 1/h_{o} +( r_{o}/r_{i}) f_{i} +(r_{0} /k) ln (r_{2}/r_{1}) + f_{o}

#### Overall heat transfer coefficient based on inner area

#### 1/U_{i} =1/h_{i} +( r_{i}/r_{0}) (1/h_{o)} + f_{i} +(r_{i} /k) ln (r_{o}/r_{i}) + ( r_{i}/r_{0}) f_{o}

#### If the tube is very **thin,** then with no fouling

#### 1/U= 1/h_{i} +1/h_{o}

#### CALCULATION OF h_{i} and ho for finding U

**CALCULATION OF h**_{i}

_{i}

#### Find Reynolds number in the tube. Find laminar or turbulent flow. Apply corresponding Nusselt Number equation to find h_{i}

#### (a) For laminar flow in a tube Nu = 1.32(∆T/d)^{0.25}

#### (b) For turbulent flow in the tube Nu = 0.023 Re^{0.8} Pr ^{0.4}

**(c**) For turbulent two phase flow in a tube

#### Nu = 0.023 (k_{L}/D)Re^{0.8}Pr^{0.4} 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} (ρ_{L} /ρ_{V})^{0.5} (µ_{g}/µ_{L})^{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 h**_{o}

_{o}

#### I. Sensible heat exchange on the outside of the tube or FOR A SINGLE PHASE HT

#### (a) Laminar flow over horizontal plate

#### Nu= h_{o}D_{0}/k_{f} = 0.54 (Gr Pr)^{0.25}

#### (b) Turbulent flow over horizontal plate

#### Nu= h_{o}D_{0}/k_{f} = 0.14 (Gr Pr)^{0.33}

#### (c) Laminar flow over a vertical plate

#### Nu= h_{o}D_{0}/k_{f} = 0.59 (Gr Pr)^{0.25}

#### (d) Turbulent flow over a vertical plate

#### Nu= h_{o}D_{0}/k_{f} = 0.10 (Gr Pr)^{0.33}

**II. ** **Where phase change takes place on the outside of the tube Or ****For two phase HT **

#### h_{NBHTC} =0.00122[(k_{L}^{0.79} c_{pl}^{0.45 }ρ_{L}^{0.49})/ (σ^{0.19}µ_{L}^{0.79}h_{fg} ρ_{V}^{0.79})] ΔT_{ex }^{0.24} Δp _{sat }^{0.75}

#### Where h_{NBHTC} is Nucleate boiling H T coefficient Or two phase heat transfer coefficient

#### ΔT_{ex} = T_{sur} –T_{sat}

#### Δp_{sat} = p_{sur} –p_{sat}

#### (iii)**Calculation of h**_{o}**in case of condensation**

_{o}

#### (a) Laminar film condensation on a vertical plate

#### Average HT coefficient from NUSSELT EQUATION

**h**_{o} = h_{av} = 0.943 [ k^{3}ρ^{2}g h_{fg}/ (μ L (T_{sat}—T_{sur}))]^{0.25}

_{o}

**(b**) Turbulent film condensation on a vertical plate

#### Film heat transfer coefficient

**h**_{o} =h_{av} = 0.0077(Re)^{0.4} [ k^{3}ρ^{2}g / (μ^{2}]^{1/3}

_{o}

#### After finding h_{i} and h_{o}, 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^{.}=U_{dirty} 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^{.}c_{p})_{min }= U A/ C _{min}

^{.}

#### value of (m^{.}c_{p})_{hot }=C_{hot}

^{.}

#### (m^{.}c_{p})_{cold}=C_{cold}

^{.}

#### 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}

^{. }

_{actual }/q

^{. }

_{max}

**q**^{. }_{max} = C _{min}(T _{max} – T _{min})= C _{min}(T _{hot in} – T _{cold in})

^{. }

_{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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