Lecture 11 heat exchangers, Lecture notes of Heat and Mass Transfer

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Heat Exchangers

What are heat exchangers for?

• Heat exchangers are practical devices used to transfer

energy from one fluid to another

• To get fluid streams to the right temperature for the next

process

• reactions often require feeds at high temp.

• To condense vapours
• To evaporate liquids
• To recover heat to use elsewhere
• To reject low-grade heat
• To drive a power cycle

Main Categories Of

Exchanger

Wall separating streams Direct contact

• Most heat exchangers have two streams, hot and cold, but some have more than two

Heat exchangers

Recuperators Regenerators

Wall separating streams Wall separating streams Direct contacts

Recuperators/Regenerators

• Recuperative:

Has separate flow paths for each fluid which flow simultaneously through the exchanger transferring the streams

• Regenerative

heat between

Has a single flow path which the hot and cold fluids alternately pass through.

Shell and Tube

• Typical shell and tube exchanger as used in the

process industry

Shell-Side Flow

Configurations

T 2

t 1

T 1

t 2

T ParallelFlow 1

T 2

t (^1) t 2

Position

Temperature

T 2

t 2

T 1

t 1

T CounterFlow 1

T 2

Temperaturet^2 t 1

Position

Basic flow arrangement in

tube in tube flow

Counterflow NoteTh,out can be < Tc,out

Parallel flow T 's (^) ' cannot cross

Energy balance (counterflow) on element shown



 

    

   

 





   

c c h h

h c

c c

c h h

h

h c

h h h c c c

m c m c

d T T dQ

m c

dT dQ m c

dT dQ

dQ UdAT T

c

m

dQ m c dT m c dT

 





 







  

1 1

Nowfrom(1)

( 2 )

RateEquation

specificheat

massflow rateof fluid

( 1 )

• Remember – 1 and 2 are ends, not fluids
• Same formula for parallel flow (but ΔT’s are different) •Counterflow has highest LMTD, for given T’s therefore smallest area for Q.

LMTDisLogMeanTemperature Difference

LMTD

ln /

2

1

Substituteform andput

2 1

2 1

2 2 2

1 1 1

c

Q UA

T T

Q UA T T

T T T END

T T T END h c

h c



 

  

  

  

  

  







Condenser Evaporator

• The LMTD formulas developed earlier are no longer adequate for multipass heat exchangers. Normal practice is to calculate the LMTD for counter flow, LMTD (^) cf , and to apply a correction factor, FT, such that

Δθ eff = FT ⋅ LMTD (^) CF

• The correction factors, FT, can be found theoretically and presented in analytical form. The equation given below has been shown to be accurate for any arrangement having 2, 4, 6, .....,2n tube passes per shell pass to within 2%.

, forR 1

Effectiveness : 1 /

1 /  

 (^) shell

shell N

N

R X

X

P

  ^

  

 





 

    

    



 

  

  

2 P R 1 R 1

R 1 ln^2 P R^1 R^1

1 R P

R 1 ln^1 P

F

2

2

2

T

 

, for R 1

N P N 1

P

P

shell o shell

o 

1 1

2 1 o (^) T t

t t P 

  (^1)

1 

   o

o P

X P R

2 1

Capacity ratio^12 t t

T T R 

  T,t = Shell / tube side;^ 1, 2 = inlet / outlet