cbe 150a – transport spring semester 2014 temperature driving force concentric pipe heat...

CBE 150A – Transport Spring Semester 2014

Temperature Driving Force Concentric Pipe Heat Exchangers


Concentric Pipe Heat Exchange

Goals:

By the end of today’s lecture, you should be able to:

Write the heat transfer rate equation and the fluid enthalpy balances for

concentric pipe heat exchangers.

Describe the temperature profiles and calculate the true mean ∆T for

parallel and countercurrent flow exchangers.

Use the heat transfer rate equation and the fluid enthalpy balances to

make design calculations for concentric pipe heat exchangers.


Concentric pipe (double pipe) heat exchangers

Heat exchangers are used to transfer heat from a hot fluid to a cold fluid.

Concentric pipe heat exchangers are the simplest and most easily analyzed configuration.


Consider a typical concentric pipe heat exchanger:

Temperature Driving Force - Tlm Q = UA Tlm

T = hot side fluid t = cold side fluid

T1

t2

t1 T2


Assumptions:

(1) Ui is constant

(2) (Cp)hot and (Cp)cold are constant

(3) heat loss to the surroundings is negligible

(4) flow is steady state and parallel

The overall heat transfer coefficient (U) does change with temperature, but the change is gradual. Thus, this assumption will hold for moderate temperature

ranges.

Temperature driving force derivation


)()(

)(

)()(

)(

12

12

ttCpm

CpmTT

ttCpmTTCpm

dtCpmdTCpmdQ

dAdLD

dLDtTUdQ

hot

cold

coldcoldhothot

coldcoldcoldhothothot

i

icoldhot

Differential form of the steady-state heat balance:

1

2

3

4

5


112

212

11111

12

12

1)()(

)()(

1)()(

)()(

ln

1)()(

1

)(

)ln(1

1)()(

)()()(

)()(

)()(

tCpmCpm

tCpmCpm

T

tCpmCpm

tCpmCpm

T

CpmCpmCpm

UA

tbabtba

dt

tCpmCpm

tCpmCpm

T

dt

Cpm

dLDU

dLDtttmCp

mCpTUdtCpmdQ

hot

cold

hot

cold

hot

cold

hot

cold

hot

coldcold

hot

cold

hot

coldcold

i

ihot

coldcold

6

7

8

Using Eqns 1 and 3 and substituting Eqn 5 for T:

Using solution for general form of integral and integrating between 0 and L and t1 and t2 yields:


)()(

ln)()()(

ln1)(

)(1

)(

ln

1)()(

1

)(

12

12

21

1221

12

12

21

12

21

12

21

tt

QCpm

tT

tT

tTtT

tt

Cpm

UA

tT

tT

ttTTCpm

UA

tT

tT

CpmCpmCpm

UA

cold

cold

cold

hot

coldcold

9

10

11

12

Expand and simplify:

Substitute for (mCp) terms using Eqn 4:


Thus, the true mean T for a parallel flow concentric pipe heat exchanger is the log-mean temperature difference at the two ends of the exchanger,

)()(

ln

)()(

12

21

1221

tTtTtTtT

TT LMTM

[13]


Also, regardless of the exchanger design, if a phase change occurs, such as condensation or boiling (and the liquid is not subcooled or superheated), then:

(Th)in = (Th)out or (Tc)in = (Tc)out

and TTM = TLM

Therefore, for concentric pipe heat exchangers and pure fluid condensers or evaporators,

TTM = TLM.

As we will find out later, this is NOT the case for shell-and-tube heat exchangers.


Film Coefficient Film Coefficient

Recall: Sieder-Tate equation for flow in pipes:

14.0333.08.0

023.0

w

p

k

CDG

k

hD

14.0333.0

Pr8.0

Re023.0 NNNNu


Tubing Dimensions (BWG)Tubing Dimensions (BWG)


Example Problem

Benzene is cooled from 141 F to 79 F in the inner pipe of a double-pipe exchanger. Cooling water flows counter-currently to the benzene, entering the jacket at 65 F and leaving at 75 F. The exchanger consists of an inner pipe of 7/8 inch BWG 16 copper tubing jacketed with a 1.5 inch Schedule 40 steel pipe. The linear velocity of the benzene is 5 ft/sec. Neglect the resistance of the wall and any scale on the pipe surfaces. Assume the L/D of both pipes is > 150.

Compute:

a) Both the inside and outside film coefficients.

b) The overall coefficient based on the outside area of the inner pipe.

c) The LMTD

cbe 150a – transport spring semester 2014 temperature driving force concentric pipe heat...

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