double pipe heat exchangers with finned inner tube p m v subbarao professor mechanical engineering...

Double Pipe HEAT EXCHANGERS with Finned Inner Tube

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Ideas for Creation of Compact HX!!!

NTU Curves: Counter flow

NTU

How to decide the height of fin for a Double Pipe HX ?

nth order Longitudinal Fins

2/1

212

2

2

0

b

nnn

k

hm

bmdx

dnx

dx

dx

b

L

x=a=0b

x=b

bx

qb

L

b

qb

b

x=b x=a=0

xb

Effect of geometrical Order on Fin Effectiveness

Cost – Benefit Analysis of Fins

• The benefit of a fin is defined as effectiveness of a fin.• An ideal fin will have highest value of effectiveness.• An ideal fin is the one whose temperature is equal to temperature of

the surface.• This is possible only if the thermal conductivity of fin material is

infinitely high.• The effectiveness of an actual fin material is always lower than an

ideal fin.• The relative performance of a given fin is defined as efficiency of a

fin.• Provision of fins on a surface requires more material and hence more

capital cost.• A judicial decision is necessary to select correct factors of fin design.• Best fin design should have higher benefits with a lower amount of

material.

Performance of Least Material Strip Fin

Optimum shape for a given qb & b

mbk

hAhkq b

pb tanh

27918.02

3/122/1

And solve for Ap with [ tanh (1.4192) = 0.8894 ]

3

2

5043.0

b

bp

q

khA

627.0

Comparison of Longitudinal Strip Fin

profile area varies as the cube ofqb b/

To double the heat flow, you use two fins or make one fin eight times as large.

There is a virtue in using short stubby fins.

3

2

5043.0

b

bp

q

khA

Longitudinal Fin Of Triangular Profile

The differential equation for temperature excess :

b

L

x=a=0b

x=b

bx

qb

0)(

TThPdx

dxdT

kAd c

b

cs

bLxxLxLxA

tan2)(

Longitudinal Fin Of Triangular Profile

The differential equation for temperature excess is a form of Bessel’s equation:

xd

dx

d

dxm b

2

22 0

; m

h

k b

21 2

/

b

L

x=a=0b

x=b

bx

qb

Triangular Fin : Adiabatic Tip

The particular solution for ( )x is:

( )x

I m bx

I mbb 0

0

2

2

The fin heat dissipation is:

mbI

mbI

m

Lhq bb 2

22

0

1

The fin efficiency is:

I mb

mb I mb1

0

2

2

Optimum Shape (Minimum Material) for Triangular Fin

b

p

p

p

b

p

A h kA

h

k

bA A k

h

4 2

2 618813263

2

210560

2

1 2 2 3

2

1 3

1 3

/

..

.

/ / /

/

Comparison of Longitudinal Fins

Ah k

q

Ah k

q

pb

b

pb

b

05043

0 3471

2

3

2

3

.

.

Rectangular Profile:

Triangular Profile:

For the same material, surrounding conditions and qb b/which is basically the user’s design requirement.

Triangular profile requires only about 68.8% as much metal as rectangular profile.

Comparison of Longitudinal Fin

In both fins, profile area varies as the cube of qb b/

To double the heat flow, you use two fins or make one fin eight times as large.

There is a virtue in using short stubby fins.

Longitudinal Fin Of Concave Parabolic Profile

The differential equation for temperature excess is an Euler equation:

xd

dxx

d

dxm b

mh

k b

22

22 2

1 2

2 0

2

/

L

b

qb

b

x=b x=a=0

x

b

The heat dissipated is:

qk

bbb b

3

2

And the efficiency is:

2

3 or = 0.667

Optimum Shapes (Least Material) of Parabolic Profile

Double Pipe HX with finned inner Tube

Equivalent diameter of annulus heat transfer, De:

perimeter ledheated/coo

area freenet 4eD

244

Area Free2

12

rs WWHWN

DD

NWNHDDs 2Perimeter Cooled 1

NWNHDD

WWHWNH

DD

Ds

rs

e

2

2444

1

21

2

Longitudinally Welded fins

HSk

Ph

HSk

hP

Q

Q

fin

fin

f

ffin

tanh

max,

h, should be resulting heat transfer coefficient on annulus side.

Fins with surface area, Afin, communicate as much as heat as an area of tube surface equal to finAfin .

Therefore, the total annulus side effective area is Atube + finAfin.

The ratio of total surface area to effective surface area is called as overall finned tube efficiency factor.

Accounting of Heat Transfer due to strip Fins

total

fin

total

finfin

basefin

basefinfinfinnedtube A

A

A

A

AA

AA1

Effective annulus side overall heat transfer coefficient:

hh finnedtube

Overall Heat Transfer coefficient of finned Double tube HX:

insidetube

total

tubepipe

total

A

A

uLk

ADD

hU ,

1

1

2

ln11

More Ideas for Compact Double Pipe HXs

• The configuration should be similar to a straight double-pipe heat exchanger.

• But both the tubes are concentrically curved to take advantage of the space saving characteristics and through enhanced heat transfer coefficients.

• One such idea is double pipe Hx with the helical geometry.

• There are some distinct advantages from this type of design over hair pin DPHX.

• Firstly, the whole surface area of the coil will be exposed to moving fluid, eliminating the dead-zones that could be found in the outer tube of hair pin hx.

• Secondly, the flow in the outside tube will also experience secondary flows.

Helical Double-tube HX