Chapter 2

Ramazani, Heat Exchangers 1

Dr. Ahmad RAMAZANI S.A.Associate Professor

Sharif University of Technologyانتقال حرارت کاربردی

احمد رمضانی سعادت آبادی

Autumn, 1385 (2006)

Applied Heat Transfer Part Two

Heat Exchangers


Topics of This chapter

Introduction of Heat Exchangers (HEXs)The Overall Heat Transfer CoefficientFouling FactorTypes of Heat ExchangersThe Log Mean Temperature Difference (LMTD) MethodEffectiveness-number heat transfer unit (NTU) Method

Effectiveness and Heat Transfer RateCompact Heat Exchangers

Analysis for Variable Properties• Heat Exchanger design Consideration


Heat Exchanger Types

• What is a heat exchanger ? An equipment that permits to transfer heat from a hot fluid to a cold one without any direct contact of fluidsHeat exchangers, can be seen in quotidian life, as well as different industries.

Almost all Chemical And Petrochemical Plants, Air Conditioning Systems, Power production, Waste Heat recovery, Automobile Radiator, Central Heating System Radiator, Electronic Parts, ….


• Heat Exchanger can be categorized according to Flow arrangement and Type of Construction

• Parallel flow (fig. a) and Counter-flow (fig. b) in concentric tubes (double-pipe)

Concentric Tubes: a) parallel flow; b) Counter flow

Heat Exchanger Types


• Finned and unfinned tubular heat exchanger with cross flow

Cross flow heat exchangers a) finned; b) unfinned

Heat Exchanger Types (Con.)


• Shell-and-tube heat exchanger with one shell pass and one tube pass (Cross counter flow mode of operation)



• Other types of Shell-and-tube heat exchanger

One shell pass and two tube passes

Two shell passes and four tube passes









Compact heat exchanger coresHeat Exchanger Types (Con.)


Heat Exchanger Types (Con.)Core of a plate Compact heat exchanger with counter flow from Aluminum, AKG America Corp.


• Heat Exchanger with fins on Surface, General Motors Corp., Lockport, NY



Heat Exchanger Types (Con.)• Heat exchanger with fins


• Fins deposited on tubes internal surface for increasing heat transfer



• Heat transfer area density (m2/m3) for different types of heat exchangers



The Overall Heat Transfer Coefficient

The Overall heat transfer coefficient for walls


The Overall Heat Transfer Coefficient (con.) The Overall heat transfer coefficient for Duble-pipe (HEXs)(U can be determined from Total Thermal resistance to heat transfer between two fluid)


The Overall Heat Transfer Coefficient (Con.) Table 10.1. Approximate Values of Overall Heat-transfer Coefficient


The Overall Heat Transfer Coefficient, Example 1.

EXAMPLE 10.1. OVERALL HEAT.TRANSFER COEFFICIENT FOR PIPE IN AIR.Hot water at 98•C flows through a 2-in schedule 40 horizontal steel pipe [k = 54 W/m.oC] and is exposed to atmospheric air at 20•C. The water velocity is 25 cm/s .Calculate the overall heat-transfer coefficient (U) for this situation, based on the outer area of pipe.Solution. From Appendix A (P. 653) the dimensions of 2-in schedule 40 pipe areID = 2.067 in = 0.0525 mOD = 2.375 in = 0.06033 mThe heat-transfer coefficient for the water flow on the inside of the pipe is determinedfrom the flow conditions with properties evaluated at the bulk temperature. The free-convection heat-transfer coefficient on the outside of the pipe depends on the temperature difference between the surface and ambient air. This temperature difference depends on the overall energy balance. First, we evaluate hi and then formulate an iterative procedure to determine ho.The properties of water at 98oC are

p = 960 kg/m3 µ = 2.82*10^-4 kg/m.sk = 0.68 W/m.oC Pr = 1.76


The Reynolds number is

and since turbulent flow is encountered, we may use Eq. (64)

For unit length of the pipe the thermal resistance of the steel is

The Overall Heat Transfer Coefficient , Example 1. (Con.)

446801082.2

)025.0)(25.0)(960(Re 4 =×

== −µρud


The Overall Heat Transfer Coefficient, Example 1. (Con.)


The Overall Heat Transfer Coefficient, Example 1. (Con.)


The Overall Heat Transfer Coefficient, Example 2.EXAMPLE 10-2. OVERALL HEAT-TRANSFER COEFFICIENT FOR PIPE IN STEAM.The pipe and hot-water system of Example 10-1 is exposed to steam at 1 atm and 100oC. Calculate the overall heat-transfer coefficient for this situation based on the outer area of pipe.Solution. We have already determined the inside convection heat-transfer coefficient in Example 10.1 as

hi = 1961 W/m2 . oCThe convection coefficient for condensation on the outside of the pipe is obtained by using Eq. (9-12),

where To is the outside pipe-surface temperature. The water film properties are,


The Overall Heat Transfer Coefficient, Example 2.


The Overall Heat Transfer Coefficient, Example 2 (Con).


The Overall Heat Transfer Coefficient, Example 2 (Con).


The Overall Heat Transfer Coefficient(Fouling Factor)

•After a period of operation, heat transfer surfaces of HEXs may become

Coated with various deposits present in the flow systems

CorrodedOr, in general, deteriorated because of use

Resulting in decreased performance because of additional resistance(s) to heat flow

•The overall effect of this deterioration is represented by a Fouling Factor Rf

cleandirtyf UU

R 11−=


The Overall Heat Transfer Coefficient(Fouling Factor Con.)


The Overall Heat Transfer Coefficient Example 3. (Fouling Factor Con.)

From previous example hclean= 1961 W/m2. oCand so from above equation we can obtain hi


Liquid Temperature Profile in Counterflow HEXs

Liquid Temperature profile in a Counter-flow double pipe HEXs (Oil is hot fluid in tube and water is cold one in shell)


Liquid Temperature Profile in Cross-flow HEXs

Fluid Temperature profile in a Cross-flow Heat Exchangers (Steam is hot fluid and water is the cold one, Steam condense on the tube at a constant temperature)


The Log Mean Temperature Difference (LMTD) Method

HEX across difference raturemean tempe Suitable=∆

∆=

mTmTUAQ

Fluid Temperature Profile in Double Pipe Heat Exchangers

Counter FlowParallel Flow


Heat balance on an element of HEX

Mixing two above relations

The Log Mean Temperature Difference (LMTD) Calculation


The Log Mean Temperature Difference (LMTD) Calculation (Con.)

Heat exchanges at length an element of HEXs

Putting values of mhCh and mcCc in relation obtained for ln of temperatures differences


The Log Mean Temperature Difference (LMTD) Calculation (Con.)


Correction Factors for LMTD Method

Fig. 10.8. Correction Factor for HEX with one Shell and two, four, or any multiple of tube passes


Correction Factors for LMTD Method (Con.)

Fig. 10.9. Correction Factor for HEX with Two Shell and four, eight, or any multiple of tube passes



Fig. 10.10. Correction Factor for Single-pass Cross-flow HEXs, both fluid unmixed



Fig. 10.11. Correction Factor for Single -pass Cross-flow HEXs, one fluid mixed, the other unmixed


Use of the LMTD for calculation exchanger performance.

• EXAMPLE. 10-4. CALCULATION OF HEAT EXCHANGER SIZE FROM KNOWN TEMPERATURE.

• Water at the rate of 68 kg/min is heated from 35 to 75OC by an oil having a specific heat of 1.9 kJ/kg.oC. The fluids are used in counterflow double pipe heat exchanger, and the oil enters the exchanger at 110oC and leaves at 75oC. The overall heat-transfer coefficient is 320 W/m2.oC. Calculate the heat exchanger area.

• Solution. The total heat transfer is determined from the energy absorbed by the water


Use of the LMTD method for calculation exchanger performance. (Con.)

• Since all the fluid temperatures are known, the LMTD can be calculated by using the temperature scheme in Fig. 10-7b:


Use of the LMTD for calculation HEXs performance. (Con.)


Use of the LMTD for calculation exchanger performance. (Con.)

So, Using Fig. 10.8. Correction factor is F=0.81


Use of the LMTD for calculation exchanger performance.

CFT

CmTCmTTCmTCmq

Ooh

hh

cchhhhccc

33.3360)1)(15000(

)100130)(1)(30000(==

−=∆

∆=∆⇒∆=∆=

&

&&&

Example 10.6. Design of Shell and tube HEXs:Water at the rate of 30000lbm/h [3.783 kg/s] is heated from 100 to 130oF [37.78 to 54.440C] in a shell-and tube heat exchanger. On the shell side one pass is used withwater as the heating fluid, 15,000 1b.m [1.892 kg/s], entering the exchanger at 200 oF [93.33oC]. The overall heat-transfer coefficient is 250 Btu/h . ft2. oF [1419 W/m2 . oC], and the average water velocity in the 3/4in [1.905-cm] diameter tubes is 1.2 ft/s[ 0.366 m/s]. Because of space limitations the tube length must not be longer than 8 ft [2.438 m]. Calculate the number of tubes per passes, and the length of the tubes. consistent with this restriction.Solution: We first assume one tube pass and check to see if it satisfies the conditions of this problem. The exit temperature of the hot water is calculated from








Effectiveness-NTU Method


Effectiveness-NTU Method (Con.)Energy balance for a) parallel flow b) Counterflow Shell-tube HEXs


Effectiveness-NTU Method (Con.)






Example: Application of Effectiveness-NTU Method

P. 578

P. 573


Example: Application of Effectiveness-NTU Method (Con.)

Effectiveness can be calculated using Eq. 10.21, P.573, to be




Example: Application of Effectiveness-NTU Method

Fig. 10.15



105Btu/h][1.38kW 34.40)55.1544.29)(1006)(887.2(

×=−=∆= ccc TCmq &

The heat transfer is then



q=

hhh TCmq ∆= & and ;

Fig. 10.15


Example: Application of Effectiveness-NTU Method (Con.)We should assume values for the water flow rate until we could match the performance of HEX according to Fig. 10. 15 or table 10. 3.The selected iterations to approach to correct values are as follow:

CT

m

Cm

O

exitw

h

hh

68.19645

10034.422.82

y accordingl is re temperatuexit water The

/h]lb [1221 kg/s 0.154 4180645 and

CW/645about as rate flow- water theestimate thusWe

4

,

m

o

=×

−=

==

=

&

&


Boilers and Condenser (HEXs)


Compact Heat Exchangers

These heat exchangers are best for gasesand low h cases


Compact Heat ExchangersFor these types of heat exchangers driving mathematical relation can be

difficult, however some correlation are presented to able us to calculate heat transfer and Pressure drop values for them.

These correlations are based on Stanton and Reynolds dimensionless numbers Which are written based on the mass velocities in the minimum flow cross-sectional area and hydraulic diameter stated in

Mass Velocity

f is friction inside the tubes and v1 and v2 are specific volume at entrance and exit and vm is its average at HEXs

Ratio of the free-flow = area to frontal area





St P

r2/3

or

f

Fig. 10.20. Heat transfer and friction factor for finned circular-tube HEX


Example: Compact Heat Exchangers


Analysis for Variable Properties


Analysis for Variable Properties (Con.)

(10-34)

(10-33)

Where,


Analysis for Variable Properties (Con.)

Solution Method: The numerical-analysis procedure is clear when the inlet temperatures and flows given:

1) Choose a convenient value of ∆Aj for the analysis.2) Calculate the value of U for the inlet conditions and

through the initial ∆A increment.3) Calculate the value of Q for this increment From Eq.

(10-32).4) Calculate the values of Th, Tc, and Th - Tc, for the next

increment, using Eqs 10.31 and 10.345)Repeat the foregoing steps until all increment in ∆A are

employedRamazani, Heat Exchangers 78

Analysis for Variable Properties (Example)



Fig. 10.16. A rock-bed thermal-energy storage unit schematic









Stored energy with time for the rock-bed thermal-energy storage unit of figure 10.16


Heat-Exchanger Design Considerations


Heat-Exchanger Design Considerations

Chapter 2

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