selection of surface and design of plate-fin heat...

16
_ . . ) ( . (Max.allowable pressure drop) . . ) (VPI . VPI . VPI . VPI . . VPI . . Selection of Surface and Design of Plate-Fin Heat Exchangers Using Rapid Design Algorithm M.R. Jafari Nasr and A.Kalantari Petrochemical Research & Technology (NPC-RT), P.O.Box: 14358, Tehran-Iran ABSTRACT The objective of this paper is to present a design procedure for compact plate-fin heat exchangers based on full utilization of pressure drop. Since, design engineers need to indices for optimum selection of plates, an appropriate index is developed and then based on the rapid design algorithm, developed by previous investigators, the best enveloped has been modified. The developed index, volume performance index (VPI), considers the opposing resistances due to foling formation on both side of heat

Upload: dokien

Post on 20-Aug-2018

214 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_��� �� ������� �� ��!

"#� ��� $�#�%&'�

������ ��� � � � ����� �������

�������� ������ � ���!� "���

�����

������� ��� � ������ �� � ����� ���� ���� �

��� ������ !" ���#$ ��$ %&� ���'(� ��)�$ �(*���

*� ���" ���'�� �+ ,*�� �� ������ �$-� . !�/� ��� ��

01��� ���� ��� *�� !2��� � $ %&� ������ ���� ��3

4��56 ������ ��� � ����7 �� 8���� 9/��� :�2*

;*� 4�� !<��� � !=*�� . >���� �������� %&� ���

� 8?�@� !� !��� � �� �56 ;6� ���� ��� ������6 �����

���/� >&��� 8��A� �(�)�$ � ��(����($ �

) ������ ����/� >��� $ �-�6�C D�� '� ��� ;��/� �

4�(E � 4����� ( �?� �� ��� �� �?�6�G �+ '� @ H !" ��

�� �=H�� ��7 !� �� ��(��� ,���� ���' ���� � � !�6�C

;*� 4�(�I�C ��& .�� !=*�� %&� ��� J*��� !�/� ���

4��56 �(6 ;(�K ������ �$ 9� � ����7 ���� ���� �!�6�

'I� �56 ;6� L��M"� !� ��(�*� �+ �� !" ;*� 4�� !<���

J��*� >�H �(Max.allowable pressure drop) !�

����� ;*� 4�� !�6�C �?� �� ����7 N�$ . �� O�� ���

!=*�� J*� ;6� �(� !2��� !" ��(����($���� 9�� P�

�� ���" �� !<��� �� 9� � LI� � 8���� 9/��� Q��3 ��56

;*� 4�� 4�� . �� � R2* 01��� ���� M(� 4�* O�� P�

LI� ������ %&� D�S� J*�)(VPI ;*� 4�� !<��� .

���" �� �I�� �� ����T�" ��I� !" ���2*VPI

C�M� ;��� ��$��& ��� . J*��� :�2*VPI � !#�/�

4�� !(� ������ ����� � ���2* 01��� ���� ��$������

;*� . ;6� !� �*��*� ���� ��M�$ ����7 � R2* 01���

�$������ '� 4�S�*� � >�" �56VPI 9�� �

��� �� U/V� ��(����($���� . ���� ����7 ������-��

/�� ���� W���+ ��=�2� ���� � !#�/� � X��� � !<��� Y7

��� 4�� W��'+ !�/� �� 4�� �"Z . �$������ '� 4�S�*� �

VPI 4���V� �� �� ������� %&� ����5(� !" ���2*

!���� '� 4�S�*� � � 01��� ���� !���� ��(��� '������

� 9� � >" LI� [\* � ����7 �?� ���� 9� � �� !���� !

;*� 4��+ ;*� . !" ��� 4�� ����7 ���� � Q(��� ��� !�

��=�2� ����� LI� '� ���T�" ����� ����T � ���I�

��� !���� 4�� �"Z.

Selection of Surface and Design of Plate-Fin Heat Exchangers Using Rapid Design Algorithm

M.R. Jafari Nasr and A.Kalantari Petrochemical Research & Technology (NPC-RT),

P.O.Box: 14358, Tehran-Iran ABSTRACT The objective of this paper is to present a design procedure for compact plate-fin heat exchangers based on full utilization of pressure drop. Since, design engineers need to indices for optimum selection of plates, an appropriate index is developed and then

based on the rapid design algorithm, developed by previous investigators, the best enveloped has been modified. The developed index, volume performance index (VPI), considers the opposing resistances due to foling formation on both side of heat

Page 2: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_���...

��

transfer surfaces so that it presents the more relaible results than the others. Bsed on the developed index an algorithm is examined with a case study to show how much it could be applied effectively. Using this index, it is

revealed that the total volume of heat exchanger can be obtained many times smaller and more compact than the common indices.

�����

���� ��� � �� � ����� ����� ��� )PFHE( � ���

� ���� �� �� ��� �! �" �# ����� $�%&��� ���

�# �' *�� � ��+�� $�, ��� - ./0� 1�234

) *�'5 .( ���� ���, ��� 7#�� �" $�!�8� � ���9 �! �%����+

� �&���� � 1��� :�;;" �+ 1�234 ��! �� �'�;;" � .

��;9 �! <, - �����= 1��� ��>?� ./# ��;9 �! <, �%;��

��" �! �, ��@ ��! �� ��A� �� � �!�! �� B-�>� ������� *���

���' �� �?��C . �;�%! �"���� ��+- �, ��� � �3�?D� ���

���� $�%&��� $��#� :�;�E, ��F ���,�G� �/>� � � ���

����� ������ :��- ����# �� ��H� ���� �� � �� �� - .

���� ����� $�%&���� $�%&��� ��� ���# �! ��0� ���

��F�" �! ��� �� ��I+ �J � �" ���� ����E� �����

����� ������ - B�C - ��# ���# -� 1��� �+�� KL?A

<M� ��- $� �! ���� 1��� ��>?� ./# :@�!) N �9��

3

2

m

m5OOO( $�%����+ ��! ����� ����� ���� - ����� ��- :

����� ���� �� ���� ��" ��' � $�;��� P�?D�

��M� $�,�� � �� :����� ��! �?'� �! �;����� �� �

�'�! �� ���� Q�/# �#�;, - �, ����+ . ���� �� ������

:�#�;, $�, ��;+ � ��G;� ��� ���� R�- Q�/# ��� ��I,

��" �! ����+ �I# �, �� ���! �" �;'�! �� 1��� ��>?�

���' �?��C . :�, ���� ��� �� ���� �-�?� $�%'-� ��

$��� : ���� ���-�2� ��;9 �! �%����+ $�,�� � ��

�#�;, Q�/# :S����J �J �� �" ��' �� �?��C �G� ��

��� �������! ����� K�, �! P�?D� �� �-�2� ��- �G� �

���H� 1��4 T�?#� *!�U -��M� �� �.

<, $�V�� W-� �! ��� �� � �� � ����� ���� ����

�� B�M� . ��! - �%����+ �� � �� �X"�� �J�� �" �'-�

���' �� �?��C �G� �� ���� K�, ��;9 �! B�@ �����

]Y[ . �� ���� �� Z�� W-� :�&�>� �� �� ����� $�%&�

����� Q�/# ������� $�! ���%&�X�- �' ��! ��" �! ���

��-J: �;'�! [D � ���� $�?! �� 1��� ��>?�

�# �' . ���� ���� $�! �����= ./# $���� ��8�

���� ������ �� Q�/# �� �" ����� - ���� ��+- ���

8� ���! ���' [D � �0��! �� ���� $�?! E�� ���,���

�'�! �?'� ��+- ����� �� �� �%�J \�D?� $�!.

��� �� $��8?� $�%'-� �! � 1��� ��>?� Q�/# ����I9

��" *��2� - ��EM�:

:��� K�^� _0��! <M� K�^� _0��! ����+ ./#

�! `I� $-��� � �8!�� ��;9 �! 1��� ��>?� _��a :���

- 1��� ��>?� ./# ��- $���b .

:�, *��2�- ��EM� ��� �� T�#�! Q�/# ����I9 �0��>�

�c� ./# \�D?� �3�d- �%+ �� � $ ��3?# *!�U 1�9L�

�;;" �� . �! Q�/# ���� �� e���I9 �%���2� - ��EM� ��� ��

���' �� ��! ��" �! ��3;� *�' . :�8U- ������ ���&�� ��

��;9 �! ���! �" �2/# \�D?� ��' �?��C ��" �! �3+

�# �HC��=f� :���� ��" ����I9 $-��! . ����I9 ���!�;!

�# ��I, Ec�� <, ��;" ��- _�"�� �� Q�/# . ��� ��

-� �, �� � Q�/# \�D?� ���?! �" �&�4 W-� g�, �a��

W-� �&�>� �� �� - �0�� ��+�� :�,� ��U �G� ���� �I#

- ./# \�D?� $�! $ ��# ���� ����� ���� ����� ���

����I9 [A�' B�%3� �! ���� �! - ���EI, 1��4 �!

Page 3: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

����� ��� �� �� � ���� �� �������

��

��������� �� �� � ��� �� � ��� ���� ��� �� !"�#� $%&� ' (�)� *�+��

�# �' �c� <M� . ��I, �" �'� �+�� ���! ���� �

- �! ��@�! ������ �! ���%&��� �?'� �� ���+ ���4 �/#

�# ��! ��#�;%� �G� ���� :$�HC �����# �;�E, - $h�� . �!

�� �� � ����� $�%&��� ��!��" i�#- $�, �;��� �! �+��

\�D?� $�! _#�;� $�, [A�' � ��3?# B-E& :�8;4

��' �� T�0� :�%&��� ��� �� �;�%! ���� - ./# . ��;"��

� $�! �3�?D� $�, [A�' *��#- � ��3?# $��E� �!���

�! ����� Q�/# \�D?� ��;jI, - 1��� ��>?� �;�E�

�# �' �c� ��>>2� 7#�� @�! ����I9 . �?! �&�>� �� ��

�!���� $�! ��>>2� $�# � $��%; �� $�%'-� ���?I%�

\�D?� $�! $�?�#�;� [A�' kl# - �-�� �%&��� ����I9

���I9 �! Q�/# �� � ����� $�%&��� ���� $�! �" @�! �

�! .�24 ���� <?���V& - ��' �� �c� :�' �� �8#��

�' �,�A �� �� � �, [A�' �� .

�������� �� ��� � ��� �

��0� ���8� :��3� - ��# $�, [A�' � ���)(f

j �" �#

?���H� ��>>2� � $���0! 7#�� �# �' � . $�! ��0� ��

���� �J *4�� - ��#�2� �' �� - ��# $�, �&�& �! ���%&���

�# �?��C ��U �!���� - �0��>� . ��X� $�!Kumar ��

*��#- $�! - ��&�;�� ��9 � �3�?D� ����>� $�! � ��0�

�# ��" <#� P�?D� 1��� ��>?� �;�E�]5m[ . �j��;F

A ��� $�! ��0� :1��� ��>?� �;�E� *��#- � �4�

)(f

j ��U ��# $�, �&�& �! n�!�� $�, �;2;� � �� �����

��- �! 1��� ��>?� ��0� �E�� �G� �/>� � ���I� �� :���C

��# $�, �&�& �! ���%&��� �! ��0� �?�E� g�, �� � ��

�'� �,�D� . �� � *��2� �� ��>?� �� � Q�/# ����

��! ��" �! ��� �� <, 1���.

7#�� �%!� � [A�'Gough �8&�/� �� S����I, -

���� B�J ����+ �� ���� $�, �&�& �� 1��� ��>?� S�E�

���C ��U �8&�/�]5Y[. $�! �" �� �� �� � : ��>>2� ��

A�! ���VF :�����I9 ��&�;�� ��9 � ��8� ��>� �� � �

��� �! ��0� $�? �! ����" :1��� ��>?� �;�E� *��#-

�V��) ��# $�, �&�& �! ��0� �?� - ( �'� �;,�A . �?�� ��

*��9 ���" �0��>� :���, [A�' ��;F �#��! �� �#�#

�� 1��� ��>?� _��a - �&�& �� ���# ����+ o��/4

��# $�, �&�& $�! :��0�� ��&�;�� ��9 �# �' �� . ��

����+ �9�# S,�" �/#- �! *��#- �� � ��3?# ���&��

��# $�, �&�& �! ��0� $�?I" ��&�;�� ��9 �� eLI9 �, �&�& ��

�;" �� ��".

Smith ��0� S����I, - f

St �!���� [A�' ��;9 �! �

;�� ��9 1���p� �! � Z�� ��0� - ����" ���8� �� �� ��&�

�� ��I� <#� �I?���V& T��>�]r5[ . �M�?� E�� ��>>2� ��

Page 4: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_���...

��

�� o��/4 _��a S�E� ��0� ��F �" �� �?��C

1��� ��>?� _��a S�E� ��0� � ��@�! �' �� $�, �&�&

��>?� S�E� ���!�;! :�# ��# $�, �&�& �! �0��>� ��

B�I� �� � �� S�E� �I�U �! 1��� �� �� �" �' �,�A

�,�A *I9 �� $�-�;� �� $��C��" �! �!t�+ � 1��4

�#�".

7#�� $�V�� [A�'Webb �J �� �" �# �' �c�

Q�/# $�, ��0� ���8� *��' :�G� ���� *��9][As

A :

`I� 1��U][SP

P ����� ��! - ])()(

[SUA

UA �� �;'�! ]ru[ .

���# - �;;"�-�2� ��;9 �! *��9 � *��9 -� ���� �, ��

��' �� ��� K�, i!�� ��;9 �! . :[A�' �� � ��3?# ��E�

- �, �V?��C B�+ �! n�!�� ����� ��-�>� ���" v�2��

�'�! �� �&�& ���� ����� ��-�>�.

7#�� E�� $�V�� [A�'Walker S����I, - ]rr[ -

�I, ��� �Polley S����I, - ]rO[ �# �' ���8� . ��

��0� � �0����9 [A�'f

St3 �� $���� �� �C -

./# �E�� �! ��' iU- �� :��J �#� �! �J � ��0�� ��>�

� [D � �� � �� ��>� �� $� �! ��0�� �����

���.

&�;�� ��9 _0� �! [A�' �� �C $�! ���,���I� �� ��

�� � 1��� ��>?� Q�/# �� - �'�� $�, �&�& - ��# �&�&

�'� �,�A ��+- �UL� n�>� �, �;2;� �� ��! w��' <#� .

*��9 �� :��&�;�� ��9 ��>� �" ��' �� ��� ���!�;!

*��#- $��C��" �! ��E� ��I?� ���8� �� <%� $���"

�� 1��� ��>?� �;�E� $�, �&�& �! �0��>� �� ���� $�, �&�&

�'�! �� ��# . �! ���,���I� ��;F �8&�/� � �" $�V�� �M�?�

n�>� �X" �� Z�� [A�' �%;� �� �" �# �� ��J �� �#�

��@�! $��>� ��# $�, �&�& �! ��0� �' �� $�, �&�& $�!

S�E� ��&�;�� ��9 S,�" �! E�� �J �E�� ���! :�#

�!�� �� . *��#- � ��3?# B�V;, �! �" �# �;8� ��! ��

�! :�, �&�& �� �9�# S,�" ��M� <b���9 :��>?� �;�E�

$�?I" ���� ���� ����� ./#) ����� �3�d- �� $� �!

R�- �� � �� �� �� - ��8� (�'�! �� ����.

�� �" �# �' �c� �^� $�38+ 7#�� $�V�� [A�'

iU- 7#�� eL�U �" �# �^A�' QL4Polley -

��! �' �c� S����I, . ���# *A�� 1�= [A�' �� ��

�, �&�& �� 1��� ��>?� _��a $-� �! ����� $�, ��-�>�

�# �' �?��C �G� �� �!�A �! . �! �' QL4 [A�'

1��4f

St

Rthopp

3

5.1

.

.)1

1(

+��' �� P��8� ]5x:rx[.

������ ����

��&�� :�� � ����� ���� ���� �� �#�# K�,

���� ��8! �-�2� �� - <M� - ��- �G� � ��- ���?�F�"

<I�E"�� y�-�2� �� � �G� ���� ����� ��! �" �# �G�

�;" ��-J�! :��M� �� � �� . �! �! ���� �?�F�" $�%IM�

�;,� �� �c� � ��@�! ����I9 �" ���/# ���! ��"

�'�! �� ��H� ����.

��- ���?�F�" �" ���/# \�D?� :���� �, �-�' ��

�;'�! �� Q�/� :�;,� �c� <M� - ��- �G� � � . :�����9 �!

�� �j��;F - �# Q�� \�D?� ��&- @�! ����I9 �! Q�/#

*��� ���! :��' z>� �%?��-�2� � ��� ���� ��?0D�

P�?D� Q�/# \�D?� �� �&�?� ����I9 $�%�CR�- �!

���C ��U �G� �� :�� �����.

<M� ����I9 [A�' ���-J �#� �! W-� �M;� ��)VPI(

7#�� �" ./# \�D?� $�!Nunez - Polley ]u[ �c�

��' �� ���! :�# �' .

� ���� �I# �� �� 1��� ��>?� $�! $h�� �����

�I, $�! ���� �#�# �&��8� �! ��� �� 7���� ���� �I# �

��J �#� �! ��� {/!� �" $��� �! �0��:

)5 ( T

t

h

mCA P

∆∆=

1

|

Page 5: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

����� ��� �� �� � ���� �� �������

��

���! ��� 1��4 �! ���&-���, �/U �� � ./# �� $�! �"

��' ��.

)r ( A

V

A

LAd C

h 44 ==

�� ��>?� _��a 1�h �/!� }!�/� ��?��?# ��9 1���9 � �

��" ��� ��� �� ���:

)u ( CP

AmC

hSt .=

7!-� _�"�� �!5 �� u �! ��� *�' �! ���� <M� $�! �����9

��J �� �#�:

)x ( T

t

St

AdV Ch

∆∆=

4

��� �� �� � �� �&��8� � :����+ ��J ./# $�! �3��8�

���� �?0,]~[��' ��D?# ���� �� :��� 1��4 �! :

)� (3

1

22

⎥⎦

⎤⎢⎣

∆= f

Pd

VmA

hC δ

$�HV��+CA �&��8� � � �&��8� �� x�,� �� �M�?� :

)�( ⎥⎥⎦

⎢⎢⎣

⎡⎥⎦

⎤⎢⎣

∆⎥⎦

⎤⎢⎣

∆∆= 2

1

3

2

1

23

2

)(2

St

fd

P

m

T

tV hδ

{&��8� �#� �I# �� �- 1���9 -�� ����� ���� ��! �!

./# �� ����I9 �! �AJ 1���9 ���&�� �� ���' �� n�!��

��' �� 7���� [D � . ����I9 [A�' :1���9 �� k�9

<M�)VPI( �&��8� �� �" ��' �� ����� ~ �' �� �� �

�# . �" $��� �! ��>F �, :��' �� ��� VPI �?C�E!

k�9�! - �# �?�F�" ���� <M� �'�!.

)~ ( hdf

StVPI

2

13

)(=

- ��?��?# ��9f �M�?� �� - �;'�! �� ��&�;�� ��9 � �8!��

�# ��&�;�� ��9 � �8!�� E�� <M� ����I9 [A�' .

?2� ��>� ������� [A�' :�'�! [D � ��&�;�� ��9 *I

�! �2/# \�D?� $�! ���� $�?! �� ��� �� � ����I9

��! ��" �! ����I9 ���?%!.

��� �� P�?D� Q�/# $�!VPI _0��! � Re �� �� -

$�! ��� �� � �9�# _���� ���! - ��" <#� ���I�

��" \�D?� ./# ���?%! . $�, ���I� ��5 �� � [A�'

�' <#� 1-�3?� ��� � P�?D� Q�/# $�! <M� ����I9

�# . \�?" � Q�/# ��Keys & London �?��C�!

�� �' . :��&�;�� ��9 � $ ��! �, �� $���I� ��;F ��

�# [D � :��� � ����I9 ���?%! �" �2/# . ���?�F�"

��M� �� � �� ���? �! �! �#�?#� � ��;�I� �! ���� <M�

��J �� �#� �! ./# �����=�� \�D?� - ����+ . ����

�� � *��" ��3?# �" ���� W-� �8#�� �! ���� :�0D�

\�D?� �! B-� ���� - �?'� � :���# �� ��I� � �� �

�� �� �" ���/#Re :���� � ����I9 ���?%! [D �

��' �� ��I� . :@�! ������ �! ���/# �,��!��" � �A�! ��

����+ Q�/#)Frontal Area( ���" ����+ ��� - ��E!

�;;" �� ��M� . �;��� ���� $�%?��-�2� �" $���� ��

�?I" ������ �! ���/# :�� � ���f� <I�E"�� ����+ ./#

���C �;,�A ��U �#��! ���� . $�, �;2;� ���� �� ��

VPI ��" �! ���� $�! $�8! ./# \�D?� $�! �;��� ��

���' ��!.

Page 6: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_���...

��

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10

Re Number (Thousands)

VP

I

ppf 46.45T

ppf 30.33T

ppf 25.79T

ppf 19.86

ppf 16.96T

ppf 14.77

�������� VPI �� �� � ������� ��� ��� �Plain Fin

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10

Re Number (Thousands)

VP

I

lpf 3/8-6.06

lpf 1/2-6.06

lpf 3/8-8.7

lpf 1/4-11.1

lpf 3/8-11.1

lpf 3/16-11.1

�������� VPI �� �� � ������� ��� ��� �Louver Fin

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

Re Number (Thousands)

VP

I

osf 1/8-15.2

osf 1/9-25.01

osf 1/10-27.03

osf 3/32-12.22

osf 1/4-15.4(D)

osf 1/6-12.8(D)

�������� VPI �� �� � ������� ��� ��� �Offset Strip Fin

Page 7: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

����� ��� �� �� � ���� �� �������

��

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10

Re Number (Thousands)

VP

I

11.5-3/8W

11.44-3/8W

17.8-3/8W

�������� VPI �� �� � ������� ��� ��� �Wavy Fin

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10

Re Number (Thousands)

VP

I

ppf 46.45T

ppf 30.33T

ppf 19.86

lpf 1/2-6.06

lpf 1/4-11.1

lpf 3/16-11.1

��������VPI������� ��� ��� �� �� ����! "���� #��$%!

���� �� #��$%! Plain Fin & Louver Fin

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10

Re Number (Thousands)

VP

I

osf 1/10-27.03

osf 1/4-15.4(D)

osf 3/32-12.22

11.5-3/8W

11.44-3/8W

'� �� #��$%! Offset Strip Fin & Wavy Fin

Page 8: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_���...

��

���� ����VPI

������� ���� ��� ����)( To∆ ��� ���� �

����� ����)( T∆�� ���� �� ����� �� ! �"# $!�� ��:

)% ( Toh

UT ∆=∆ .

1

���� &�'��� ������� *"�+ ,-"� ! ��� �!U ���. !

/�� 0"�1� 2!�3 �"#:

)4 ( OPPRhU

+=1

11

�!��� #�% � 4������ /��� :

)56( )()1(1

OOPP T

tRh

T

t

∆∆+=

∆∆

7��1� ���89"�� �! ;��"�<�56 $!�� �� = $!�� >55 /�� !

��? �����:

)55 (

⎥⎥⎦

⎢⎢⎣

⎡+⎥

⎤⎢⎣

∆∆∆= 2

1

3

3

22

1

2

3

2

)()1(2

)(St

fdhR

P

m

T

tV hopp

O δ

��� �� 0"�1� �"# ���. ! @�� A�.� B���:

)5C (

2

13

3

2

)/

()1

1(

hopp d

fSt

hRVPI

+=

��� ���� �� �� �VPI

B��� ��VPI 2���� ���D� #� >��! @�� 0"�1� ��3 E

����� ��<����'�) #� ���� /���'� >����� /���'� 2���

@��F � @���"� >�� �9���G H�� ( ��! @�� �I-��. . K��-L

7��1� �� @�� M��� �"�� B���5C �� >��� ���G ��E !

N�O�� ��P ���D� ���. Q"�oppR��� �� @�"� �!�� ! .

���������= � R S$� T�� �� ���! �� ���D� Q"�

Plain fin11.11 � 06.68

3−Louvered ��U !

��� �� N�V� ��G��� . ��"�#� �! ��� �� @���V� E ��U N���

oppR B��� N�O�� #� VPI��� �� ���E .

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1000 10000 100000

Re Number

Mo

dif

ied

VP

I Ropp=0

Ropp=0.0001

Ropp=0.001

Ropp=0.01

�������� �� ���� �������� ����� ���� VPI ��� ���� Plain Fin 11.11

Page 9: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

����� ��� �� �� � ���� �� �������

��

��� ������ Q�-K��% �� 56 �� ���! �� B��� Q"� ��!��E

����� /���'� #� �� @W"� ���'� ���! >�E87� X�� S$� T��

�-�� �� N�V� . �9��9L E ��� �� BYV� �!�� ! �Z-"� ��

��� /���'� 2���� N�O�� ��D? $'� �� ����� �� �����

���! �D[� >0��Y� A�$� ��,��\ ��� �-]-� �����!.

N��� ��� �.�� �,"O�� ��-1� >�����! $'� Q"� ���! L�G

/�^3 �� ! �� #�7�-"� ��\ -��� $'� Q"� Q,�7 ��� M���

�-E �� ��^'� O"���� . *��-� ���� &�'��� S$� _�Y���

\ #�7�-"� @���]� ! �9�^!/��� ����� �����.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1000 10000 100000

Re Number

Mo

dif

ied

VP

I

Ropp=0

Ropp=0.0001

Ropp=0.001

Ropp=0.01

�������� �� ���� �������� ����� ���� VPI ��� ��� !"#� Louver Fin 3/8-6.06

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1000 10000 100000

Re Number

Mo

dif

ied

VP

I

Louver 3/8-6.06

Plain 11.11

������$� %&���� VPI ��� ���� Ropp=0.0001

Page 10: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_���...

��

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1000 10000 100000

Re Number

Mo

dif

ied

VP

I

Louver 3/8-6.06

Plain 11.11

������'� %&���� VPI ��� ���� Ropp=0.001

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1000 10000 100000

Re Number

Mo

dif

ied

VP

I

Louver 3/8-6.06

Plain 11.11

������()� %&���� VPI ��� ���� Ropp=0.01

����� ������ �

���� ����� �� � �� ���� ��� ���� ����

��� ���� ��� ��!�"�# $�%���&' (' )*"+���$

(��, ���&' -��.�/� -� 0�.����1����2 ( 3�' . 3"

��/� ��� )%� � � 5�&� 6�"�# 0" ��&' (' ���

�7� �� 8/��� ��/� (* 69 :��� ��;�! <"�=� . ��>�*?

�;�! 8�� �!�� �� ���&' @�A -��"$ ���� -� :��� �

��� �"� �"$ :��B � $�.�7"� ��?.

)D( baj −= Re

:��/?j F"��� �"$ :��B � 6��/.�� �����' 6�7? �

��� ��:

)H ( 3

2

Pr.Stj =

��� �� F"��� �"$ :��B � 6��!�� ��? � ��!�, ��?:

)IJ2 F. ( k

CPµ=Pr

)IJ2 K ( P

C

Cm

AhSt =

(��, ����� ��/� -� – �� �� :��B � $�.�7"� ��? L 3�'

��� �� F"��� �"$ :��B � � MA �>�.����1 �AN $:

)II ( C

h

A

md

µ=Re

:O���� <����D �� II :��� ��;�! <"�= -� 69 �� �

h�1� �� �%��! :

Page 11: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

����� ��� �� �� � ���� �� �������

��

)IP( b

Ch A

Kh −= 1)1

(

CA�$9 MA � ��� 6�"�# hK��� �� �"$ :��B � :

)IQ( 3

2

1

Prbh

Pbb

h

d

CamK

µ−=

�.����IP R�S $ �� �� :��B � � :��� ��;�! <"�=

6�� 6�"�# �$9 MA � 6�"�# ���# (?� L �>"+�'

�7� ��.

�A � ���� -� � �� �&� ��� � � ��&' (' �� -

6�� �� L�7� �� 8/��� �>"+�' R�S � 6�"�# �$9 MA

�� ��� � . ��/� ��T1 U�? �� � ��&' (' �� ����/?

��� �� �"$ :��B � �7� �� �V� �����:

)IW ( 2

2

..2 CC A

m

A

AfP

ρ=∆

X�>AB <"�= �"��;� �"�!�Y @�A <�Z -� f �� �

3� $�.�7"� ����[�\JJ � IJJJJ $�.�7"� ��? � 6�� ��L

��� ��T/*1 3� .( �"$ :��B � :��/?:

)I\ ( yxf −= Re

x � y �7�� �� �� �Y �"��;� . 0" ��� :��� ��;�! MA

�A � 8�� L ��/� ��� )%� $ �� �� 6�7? � ��/� (*

� �"� �"$��� �:

)I] ( TVA α=

α ��� MA ^�! 6�*1 �� ��� _�! MA ��71 �����,

��� �� ��/� ��� )%� � ��/� (* 0" . <����

:O����II LIW �. I]��� �� �"$ `A � � �%7� :

)Ia ( yTP Ac

VKP −=∆ 3)1

(

69 �� ��

)ID ( y

h

yy

P d

xmK

ραµ

2

2−=

��� ��. -�bc"�# � CA �.���� $ IP �.���� �� Ia �%��!

)"��d ��:

)IH ( zT

h

P hVK

KP

2=∆

69 �� ��

)PJ( b

yz

−−=

1

3

��� �� . �.����IH �� �7� �� �V� � �>�.����1���� ���

:��� ��;�! <"�= � ��� )%� � � 6�"�# ��&' ('

�7� �� 8/��� 6�"�#.

��� ����� ���

��� �� �"$ :��B � :��� ��;�! ���� �� �.����:

)PI ( LMTUAFQ ∆=

<���� ��� :��� ��;�! <"�= F"��� � � 69 6�� �� ��

��� �B�� �"$ �A � �� ���:

)PP(

⎥⎦

⎤⎢⎣

⎡+++

∆= )

1(

1)

1(

1

2

22

1

2

1

11

1R

hA

AR

hTF

QA

LM ηη

��1

A � 2

A (* �� � :��� ��;�! ��� MA <���� �

I �P�77� �� �V� .

�� ��;�! MA � ��/� ��� )%� e �A� (* 0" ��� :�

�.����I] �!�� �� f� �� )1 � . �7"+c"�# $ g,A -�

(*I � P �.���� $ I]��� �� �%��! :

)PQ (

⎥⎦

⎤⎢⎣

⎡+++

∆= )

1(

1)

1(

1

2

222

1

111

Rh

RhTF

QV

LMT αηαη

�.����PQ L����� ���h� $ �� �� 6�7? � � ��/� ��� )%�

�7� �� �V� :��� ��;�! <V�= � MA ��71.

��� 6���!� �"$ :��B � )1 ��/� (* �1 MA ��

��� �� F"���:

Page 12: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_���...

��

)PW (

⎪⎪⎭

⎪⎪⎬

⎪⎪⎩

⎪⎪⎨

−⎥⎦

⎤⎢⎣

+= 1

)2

()2

(

)2

()2

(tan1

2

1

2

1

δτ

δτη

k

hk

hh

fs

(��, ����� -��.�/�2 �� � ��!�"�# ���S� i�! �j! $ 3�'

`��Cross-Flow � Counter-Flow�!�� �� )�T;� .

��� ��Cross-Flow )1 $ �;�T� ��!�"�# -�1��T�

&' (' � ���� � �7�T1 6�"�# (* �� �1 �� ���� ��

( �"b, 6�>� . ��� L6�"�# �1 -� ��&' (' �.���� ��

�7� �� 5�&� � 6�"�# ��� U�? � ��/� . )%� 0" -�

���� ��/� i���� � U�? ���k� �" 5�&� �"��# MA �

�"b, 6�>� L��� <�7� ��� � ���.� � ��� ���� �

��� ��.

��/� ���� ��Counter-Flow �� �� 6�"�# -�1��T� L

8/��� )1 � 6�"�# �$9 @�A �%��! �� � �7�T1 �>" (*

�!�� �� . ��� (* �� ��.�!�� ���� � U�? (�/l� m[� �

� ��� �� (�/l� )1 �� (* -� 6�"�# MA L_�d

g>?� . ���� ��&' (' � ���� 8;' �� ( 3" �%��!

, 6�>� (* 0"�� $ n�7� ��� � �"� -�c"� � ( �"b

��� ���� (; �A� �.� . :��/? � (* �� ��71 3� f�/��

��� �� 6�7? �"$:

)P\ ( 1

11

22

1

2

2C

h

h

C AdB

dBA

δδ

=

��� ���� ���� ��� ���� ���� ������

I2 ���� �� (* � _�d (* L��� �>"+�' R�S

���T!�)ρ( ����� (�'�h L)PC( �"���d ("�1 L)k( L

��"$�>T"�)µ( �c�'�d K�� (���;� � L)R ( 6�7? �

�!�� �� ��'�d �j! �� -����.

P2 ���# 6�"�# ^�! ���� �����*? ���? )°m( ��&' (' L

)P∆( � _�d ��� �#��S � -���� -�1 :��� �#�� L

�!�� �� ��'�d �j! �� -���� 6�7? � ��.

Q2 $ ����� � �� � _�d L(* ��� -� �"�!�Y MA i�!

VPI ��77� �# �[�B (���=� ��� 5�&� )a ( ("�1 �

��77� �# �[�B �"���d)K ( �� -���� 6�7? � �j!

�!�� �� ��'�d.

W2 �"��;� hα � Cα����' $ �� � _�d 6�"�# -�

abb

b

Ch

hhh

2++=

βα �

abb

b

Ch

CCC

2++=

βα

�!�� �� �/�[� .b � β MA � f� �� ��71 -�1 ���?

�! � � ��� �!�� �� 5�&� MA i�! K�� .α MA (/T!

� ��� ��/� �� )%� � ��/� (* 0" �� :��� ��;�!

����' $)P2Qae ( o#��]W[( ��� ��'�d� .

\2 �"��;� hK � PK -��.���' e/� IQ � ID (* -�

�[� �� � _�d�!�� �� �/.

]2 �"��;� h -��.���' $ �� � _�d (* -� IH �

<T�� TV) ��/� �� )%� (�!�� �� �/�[�.

a2 �"��;� η) MA ����� 6���!� ( �� � _�d (* -�

����' $PW <T� � � h $ �� �� ��S �� TV � (

�"9 �� (�.

D2 �"��;� Hh � Ch � Hη � Cη � hα � Cα �.���� ��

PQ �!�� �� -�bc"�# . �AS ��Z �.���� 0" ��B�� �.����

<T� � TV �� 6�T'� 3���! ��� e"�� $ �� (

� ��� ��TV�"9 �� (� � ��/� �� )%� �7�" .

(��, ��/� ���� )�"��c.2 � �&� L�T*1�! 6�"�# � 3�'

6�"�# �$9 @�A �A � � �#�� � �.� ��� �� r�' (.��

� ���� L)1 � (* �� �� 0" �� 8;' ���� ��&' ('

�j! �� o#�� 6�7? � (* 69 �� ( �"b, 6�>� (*

��T � (* 3" � �c"� (* ��&' (' � ��� �� ��'�d

( . L��� ��'�d �j! �� o#�� 6�7? � �� (* �d

:��� ��;�! <"�=h �"$ :��B � �� (* � f� ��

�� �1�S:

Page 13: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

����� ��� �� �� � ���� �� �������

��

)P]( C

Z

TP

CC Kh

Vk

Ph C

C

1

)(∆

=

:O���� � �#�� � IH � P\L)"��

)Pa (

H

H

c

H

CH

ch

zy

y

TP

CyH

hHH

hCC

H KVk

P

db

dbh

1

3

3

3 ).

()(⎟⎟

⎜⎜

⎛ ∆= −

−−

ββ

�"��;� Ch � Hh �.���� �� L���9 (� � PQ (� � -�

6���9TV�!�� �� 3"+c"�# .

����� ����� � ��� ����� ���� ���� ��� �� �

����- ������ ����� � !�"

(��, ��/� ���� )�"��c. �� � 2 Lo��;�� 6�"�# � 3�'

��'�d� ����.�A� ���� �� -� �� �� ���� - �!�"� - ���!�

o#�� $ ���]Q[ o#�� � ]W[ ('�d ��N s"��$9 ���� . n"��!

��b. r�' o#�� $ ��B�� n"��! � ���!� �� �� �T"�;�

�7�� �� K��A� L���9 (� � �"��;�.

0" � f� �� LO� o#�� $ ��� ��'�d� ����.�A� ����

� ��� o��;�� 6�"�# i�! � -$�d 3� ��� ����!t -�

� ��uT� �>"+�' R�S � �����*? 8"�� � f� �� :�?v�

���# �� ��/��� ��'� ��� � @�A � f� �� :�?v� I

�! ��� �BvS.

o#�� �� ��#�� n"��! � ���!� $ �B�� n"��! �T"�;�]Q[ �

]W[ ���# �� P( ��� �BvS .

��������� �� �� ����� ����� ���� �� ��� ���� � ��� ��� !�"#�� $

��� �����) ��( �� �����) � (

������� ���

��/�� �/�� ���� ��� ���� �)/( skg

�� � ���� ���� ��� )Pa(

��� �! "�#�# $���% ���� )( C°

��� ��� ��#�& $���% ���� )( C°

������ � �� ���

!�/� �/! ��'���� )( 3mkg

��� �!� �*���% �'��+ )( Ckg

���/� ���/� �*���% ���,� )( CmW

2

���/� ���-/� ���.01��# )cP(

��� �� ����� ���

Plain Fin 11.1 Louvered 3/8-6.06 23 40�

��-�/� ���-/� $���% 5�6��� �7��8� 9��:

�� /� �/� $���% 5�6��� �7��8� "��

����/� ���/� �0�;�� �7��8� 9��:

<�13=�

����/� ���/� <�13=� �0�;�� �7��8� "��

�/�� �/�� >'� �*���% ���,� )(Cm

W

°

�/� �/� �'?@ ���A: )mm(

Page 14: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ���� �� � ��� � ��� ������_���...

��

��������� �� �� �� ������ ���� ����� ��� �� �� ��

�����B C���]�[ C���]�[

��-/� ��/� ��/� �� DE% ��)( 3m

���� �-� ��-� � .,70F�� �,G

��� ��! ��� � .,70F�� �,G �

�!� �!! ��� � D?'� 9��: )(2 Cm

W

°

-� - �! � D?'� 9��:� )(2 Cm

W

°

��-/� ���/� ���/� 23 ���,���

��/� ��/� ���/� �,��� 23 ���

���� �����

������� ��� � ���� ��� � ���� ��� ����� ��� ��

� ��� �� ���� ���� ��� ���� �!��" ��� #�$� �%&�'

�� ���( ��� �)�*+*, ��-� ���� � �.(/ �� ���*0� 1�2+��

� ��3� ��45 �5� ��64*� �657( 8( �� �� � ��� ���9!

:.� �;��' <� 1��2' ���=6�� ;��> 1��2? ;�' �� ��2��5

:� @���� �� �6����( ��� ����� A$� B*( ���) � �(� ���$(

�(� ��� . � ��� ��� ���� ����- ��� ���� ��� ��

��45 #�$� �"�D ���6�� �� ��45 E��� F�G6(� ���

�*&,H ��� �� 8( � A��2� �*5 . ��� ��� ���� 1�4( �*2+��

� ���� � ��� 8"I� 1��� �J�� <� �� ���=6�� ��B

� ����2�� ��' 1�B*� � ���$( �K, 1�%�� ��!��" ��� ����L�

������� ��� �� �� 8"I� ;��> *MN! O��" #�L6(� J�� @�(

���� �2���� . �� 1/ ��B�� ��� ���� ���! ��� �����

� ���� 1�4( ���45 ��� #�$� �"�D ���- :6���7�� ��

���.

���� � ���

A : O��" #�L6(� J��2m

CA : 1��- ���/ J��2m

PC :#�*� �!��" �*5QCkgJ

°

hd : �%*����*� �>m

f :� R�%�S� A����� �� #�*

th : #�*� O��" #�L6(� A��KmW ./ 2

J :1$&� �!��" ��6��5

K : �!��" ����� A��KmW ./

L : #�$� #�Dm

m : ��- 1��- O��kg/s

P : T�, 1��!W

P.I.: �%&�' ���)Performance Index(

Q : �!��" ���W

Re : ����2�� ��'

oppR : �!��" ��� ����L�mK/w

St :1�6(�6�� ��'

U : O��" #�L6(� ���!� A��KmW ./ 2

V : #�$� :3"3m

������ ����

tP∆ : ��45 �5�]/[ 2mN

t∆ : �.��2*�! W�L( �� #�*� O��" -�� O�**X!][ C°

oT∆ : ���!� ���� YI6��][ C°

T∆ : ��&*5 ���� YI6��][ C°

ρ : #�*� 6*0(��]/[ 3mkg

µ : #�*� ��(�)]./[ smkg

δ :Plate Spacing [mm]

Page 15: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

����� ��� �� �� � ���� �� �������

��

�����

[1] L.Wang, B. Sunden, "Optimal Design of Plate Heat Exchangers with and Without Pressure Drop Specifications", Applied Thermal Engineering 23 (2003) 295-311 [2] L.Wang, "Performance Analysis and Optimal Design of Heat Exchangers and Heat Excahnger Networks", Doctoral Thesis, Lund Institute of Technology, Sweden, 2001. [3] M. Nunez, G.T. Polley, E. Reyes, A. Munoz, "Surface Selection and Design of Plate Fin Heat Exchangers", Applied Thermal Engineering 19 (1999) 917-931 [4] W.M. Kays, A.L. London. Compact Heat Exchangers, 3

rd ed. McGraw-Hill, 1984. [5] M.A. Taylor, "Plate-Fin Heat Exchangers: Guide to Their Specification and Use", 1

st ed., HTFS, Harwell, 1987. [6] R.K. Shah, "Plate-Fin and Tube-Fin Heat Exchangers Design Procedures", in: R.K. Shah, E.C. Subbarao, R.A. Mashelkar (Eds.), "Heat Transfer Equipment Design, Publshing Corporation", Washington, DC, 1988, pp. 255-265. [7] R.K. Shah, "Compact Heat Exchanger Surface Selection, Optimization and Computer- Aided Thermal Design", in; S. Kakac, R.K. Shah, A.B. Bergles (Eds.), Lkow Number Flow Heat Exchangers, Hemisphere New York, (1983), pp. 845-874. [8] G.T. Polley, M.H. Panjeh-Shahi, M. Picon-Nunez, "Rapid Design Algorithms for Shell- and-Tube and Compact Heat Exchangers", Trans. IChem E 69, (Part) A (1991) 435-444. [9] R.K. Shah, "Compact Heat Exchanger Selection Methods, Advances in Compact Heat Exchanger Technology and Design Theory". 6

th Int. Heat Transfer Conf., Toronto, Canada . Hemisphere, New York, (1982), pp. 193-199. [10] T.A. Cowell, "A General Method for the Comparison of Heat Transfer Surfaces", J. Heat Transfer 112 (1990) 288-294. [11] G.T. Polley, C.M. Reyes-Athie, M. Gough, "Use of Hheat Transfer Enhancement in Process Integration", in Heat Recovery Systems and CHP 12 (3) (1992) 191-202. [12] J.F. Campbell, W.M. Roshnow, "Gas Turbine Regenerators: a Method for Selecting the Optimm Plate-Sinned Surface Pair for Minimum Core Volume", Int. J. Heat Mass Transfer 35 912 (1992) 3441-3450. [13] E.M. Smith, "Direct thermal Sizing of Plate-fin Heat Exchangers", in: Proceedings of the 10

th International Heat Transfer Conference, Brighton, UK, (1994), pp. 55-66.

[14] M.R. Jafari Nasr, A. T. Zoghi, H. R. Khakadaman, Performance Evaluation of Heat Transfer Enhancement in Heat Exchanger Design, Tahghigh, No 43. (2002) [15] M. R. Jafari Nasr and A. T. Zoghi, Tahghigh, Vol.11, No2. (2001). [16] A. Bejan A. "Entropy Generation Through Heat and Fluid Flow" John Wiley & Sons, New York, NY, (1982). [17]. A. P. Bejan, ad Letters in Heat and Mass Transfer, Vol. 7, (1980) 97. [18] M.J. Gough., J.V.Rogers. and C.M.B.Russel, HTFS RS417, 134 (1982) 123-134. [19] P.B.E.Kumar, “Heat Transfer in Vertical Tubes with Coiled Wire Turbulence Promoters”, M.Sc. Thesis, Dept. of Mech. Eng., McMaster Univesity, (1968). [20] G. T. Polley and Dominique, "Optimal Tube Bundle Geometries", Proceedings of 10

th Int. Heat Transfer Conf., Brighton, IChemE, (1994). [21] J.W.Smith, R.A.Geowen, and M.E. Charles, Chem.Eng. Sci., 23 (1968) 751-758-1968. [22] V. Walker and D. Wilkie, “The Wider Application of Roughened Surfaces as Developed for Advenced Gas Cooled Reactors”, Symp. On High Pressure Gas as a Heat Transport Medium, IMechE, London 10 March, paper 26, (1967).

Page 16: Selection of Surface and Design of Plate-Fin Heat ...pr.ripi.ir/article_253_66f17bc6170e14efc01e169582c88def.pdf · Selection of Surface and Design of Plate-Fin Heat Exchangers Using

���� ����! "�#� !��$ � %&� '�()�_*�+...

��

[23] R.L. Webb, Int. J. Heat and Mass Transfer, Vol. 24 (1981) 715-726. [24] M.R. Jafari Nasr, G. T. Polley, A. T. Zoghi, "Performance Evalution of Heat Transfer Enhancement". CHISA, Praque, (2002).