numerical simulation of dehumidifying fin-and-tube heat

9
Purdue University Purdue e-Pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2002 Numerical Simulation Of Dehumidifying Fin-And- Tube Heat Exchangers. Model Strategies And Experimental Comparisons C. Oliet University Politecnica de Catalunya C. D. Perez-Segarra University Politecnica de Catalunya S. Danov University Politecnica de Catalunya A. Oliva University Politecnica de Catalunya Follow this and additional works at: hp://docs.lib.purdue.edu/iracc is document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at hps://engineering.purdue.edu/ Herrick/Events/orderlit.html Oliet, C.; Perez-Segarra, C. D.; Danov, S.; and Oliva, A., "Numerical Simulation Of Dehumidifying Fin-And-Tube Heat Exchangers. Model Strategies And Experimental Comparisons" (2002). International Reigeration and Air Conditioning Conference. Paper 550. hp://docs.lib.purdue.edu/iracc/550

Upload: others

Post on 11-Apr-2022

4 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

Purdue UniversityPurdue e-PubsInternational Refrigeration and Air ConditioningConference School of Mechanical Engineering

2002

Numerical Simulation Of Dehumidifying Fin-And-Tube Heat Exchangers. Model Strategies AndExperimental ComparisonsC. OlietUniversity Politecnica de Catalunya

C. D. Perez-SegarraUniversity Politecnica de Catalunya

S. DanovUniversity Politecnica de Catalunya

A. OlivaUniversity Politecnica de Catalunya

Follow this and additional works at: http://docs.lib.purdue.edu/iracc

This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.html

Oliet, C.; Perez-Segarra, C. D.; Danov, S.; and Oliva, A., "Numerical Simulation Of Dehumidifying Fin-And-Tube Heat Exchangers.Model Strategies And Experimental Comparisons" (2002). International Refrigeration and Air Conditioning Conference. Paper 550.http://docs.lib.purdue.edu/iracc/550

Page 2: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

������������ �� ��������� ������� ��� ���������������! "��$#�!��"%& ����'%(���*)+� �,�� -� �/.����� ��0#"���*�213� ���*�����4���' �����#'��-�

���� �/."5����6������7�� �� ������5� ��68�9���$�

:<;>=@?BADCFEHGI:<;KJ3;ILNMFOPCRQPSUT�CRV(WXOYOPWZG[T>;\J]W&^8_R`\G\ab;c=4?BAd`XWegfihPjlkmfon�fipqhFrYsutwvYxupNyzf{n(k}|~hF���Kfqkm�ihFpqx�|�yHfoeI|wsurwk��BeIn\n>e\���X�(|w��rwk}|�jmrwkmx�yzf{n�f�km��rwjm�ipihzx�|�x���hFf�kmvY�qjmxupU|

� hzx��Yfqkm�lx�j}|~j[��rYsux�jm�ipihzx�pi|�yzfNeI|~j}|~su�FhP��|H�RegrYsurw���w�Y�R�Y� �w�Y�¡n�f�klk}|w�l�m|¢�d£I|�kmpifisurYhF| ���&¤�¥R|wxuhn�fis§¦g¨ª©w«~¬D­Y©~¬¯®~©Y­H¦ ���Y¦ ­ �P��°�±c²�³R¨ª©w«w¬D­w©~¬¯®w©w­H¦ �H�w¦ ���

��¬B��|~x�s§³�s�|w�Hjmx�fU´µs�|~�zjmxufY¦ ����jU¦ �z¥�pY¦ fi�i��¶Ifi�¢¥F|wvwfY³�·�jljm¥&³ ¸Y¸�¶\¶\¶{¦ �z¥�pY¦ fi�}¸~s�jmf

¹/º¼»{½3¾/¹/¿À½nI·Fxu�>¥F�z�FsuxupU|~jmxurwh¢¥zkmfqjmfqhRyz�Ijmr�pirYhPjlkmxu�F�Hjmfµjmr�|���f�jljmfqk>�FhFyzfqkm��j}|~hRyzxuhzv�rYhÁjm·Ffª��r�yHfisux��m|�jmxurYh¢r~��yzfi·��F��x�yHxu���Hx�hzvNÂFhz¬D|whFyH¬

jm�F��f�·zfU|~jNfqÃHp}·R|~hFvYf�km�i¦¢nI·zf¡¶IrwkmÄ]xu�N�F|w�lfUy]rYhÅjm·Ff�¥zkmfi�lfihPj}|�jmx�rwh2rw�c|�pqr�yzf4�Begƪ�8¤F¤z�µ�R|w�lfiy9rYh2|@yHfqj}|wxusufUy9��r�yHfis�jm·R|~j|whF|ws��H�lfi�gjm·zfc·zfU|~jgfqÃHp�·F|whzvYfqkI|w�\|{�lfqjgrw�&ÂRhz¬D|~hRyH¬djm�z��f\fisufi��fihPjm�i� ¶>·Ff�kmfcjm·zf[·zfU|~jgpirYh�� fip�jmx�rwhÇ|whRy¡��|~�l�8jlk}|~hF���Èf�k\rYhÇ|wx�km�lx�yzf�l�zkl�È|wpifq�¡|~kmf�jlkmfU|�jmfUy9surPpU|~s�s��2xuhb|~hÅxuhFhFr��w|~jmxu� f¡¶I|U�P¦¢±\pipirwk}yHxuhFv�jmr¢jm·zf¡jlkmfU|~jm��fihPjor~�\jm·Ff�·Ffi|~j�pirYhFyz�Fp�jmx�rwh9jm·zkmrw�Fvw·9jm·FfÂRhz�i��j¯¶grÁ� f�km�lx�rwhF�ª·F|U� f���fqfih9yHfi�lpqkmxu��fUyX³�ÉYÊwË~ÉwÌ�Í}ÎlÊ4��r�yzfisZrwh4jm·zf����Fs�jmx�yzxu��fihF�lxurwhR|ws(�lxu���Fs�|�jmx�rwh9|~hRybÏmÉwÐmÑdÍ���r�yHfis��R|~�lfUyrYh¢jm·zfo�F�lforw��ÂRh�fqÒ�pixufihzpixufi�i¦ªn(rYvYf�jm·Ffqkc¶>x�jm·4jm·F|~j[��r�yzfis§�R|¡�lx���¥zsufqkµ�z�zjc�§|~��jmfqkªpir�yHf��dÓ��zxup�Äzegƪ�8¤F¤z�I�R|w�lfiy¢rYh@fihPjm·R|~su¥��yzx�ÔXfqkmfqhFpif{��fqjm·zr�y�xu�[xuhPjlkmr�yz�zpifUyX�z¶>·zfqkmfox�hzhFr��w|~jmxurYhz�cxuh¢kmfis�|�jmx�rwh¢jmr�pis�|w�l�lxupU|~sZ��fqjm·Fr�yH�\·R|U� f{��fifih�x�hPjlkmr�yH�FpifUyX¦I±¼pqkmx�jmx�pi|wspirw��¥R|~kmxu�lrwh9rw�I¥�fqkl�Èr~km��|whFpqfY��pi|w¥R|~�Fxusux�jmx�fq��|~hRy<|wpipi�Hk}|wpq�]|~v |wxuhz��j��lrw��f¡fqÃH¥�fqkmxu��fihPj}|ws�kmfq�l�Fs�jm�{¥F�z�Fsuxu�l·FfUy4xuh]jm·FfNjmfip}·FhFxupU|~ssux�jmfqk}|~jm�Hkmfo|~kmfN|wsu�lr�¥zkmfq�lfihPjmfUy&¦

Õ×ÖÙØ0ÚÅÕ ¿ÀÛÁ¹b½ÝÜ�¾ Ú

Þ[ß ·FfU|�j>jlk}|whF���Kfqk[|~kmfU|���|~xukl¬B�lx�yzf¡à á¢â�ã ä�åUæ�ç�è � rws��z��fY�HpirYhFyzfihz�m|~jmfªÂFs��éà á�ê�ãë ��rYxu��j[|wx�kc�l¥�fipix�ÂRp{fqh�jm·F|wsu¥P�@à ìRíwîPïYðYã ä ÂRhzx�jmf{pirYhPjlkmrYs&� rws��z��fY�z|wx�kl¬B�lx�yzf¡à á¢êqãë å ¶\|�jmfqkc�m|~jU¦�sux�ÓP�zx�yÁ�l¥�fipY¦�fihPjm·R|~s�¥P�@à ìRíwîPïPãòñ |w�z�lrYsu�zjmfo·��F��x�yHxujD�¢à î�ïYówíwîPïYð~ãëRô ¶\|�jmfqkcs�x�ÓP�Fx�y��l¥�fqpY¦�fihPjm·R|wsu¥P�@à ìRíwîPïPã õ[kmfifiÄÇsufqjljmfqkm�öá�ð yHkl�Á|wx�kc��|w�l�\÷Fr�¶Ùk}|�jmf¡à îPïzíYøqã ù�úUû ·Ffi|~j>jlk}|whz���Èfqk[pirPfqÒ�pqx�fqh�joà ñ2í~á¢âiü�ãöá ó ¶\|�jmfqkc�Y|~¥�rwkc��|w�l�I÷Fr�¶Ùk}|�jmf¡à îPïzíYøqã ù è û ��|w�l�\jlk}|~hF���Èf�k[pqrPfqÒ�pixufihPjNà îPïzíYøiáÇãöá¢ç ÂRsu����|w�l�I÷FrU¶!k}|�jmf¡à î�ïzíwøiã ý Þ ÂRh¢egþÿ·Ffi|~j>jlk}|whz���Èfqkc�l�zkl�È|wpif�à á â ãöá�� � åUæ�ç�è pirYhFy&¦���|~�l�>÷FrU¶!k}|�jmfY�HÂRsu�éà î�ïzíwøiã � yzfqhF�lx�j¯�4à î�ïzí�á ê ãöá�� � ��� ß�� ç û pirYhFy&¦���|~�l�>÷FrU¶!k}|�jmfY�FyHkmrY¥zsufqjm�{à îPïzíYøqã ¤H�z�FxuhRyHfqÃH�� ¥zkmfi�l�l�Hkmf¡à �Z|~ã � yHkl�Á|~xuk ç surYhFvwx�jm�RyzxuhF|ws(jm�z��fª¥Fx�jmp}·]à áÁã � ¶\|�jmfqk[�Y|~¥�rwk û jlk}|whz�l� fqkm�m|ws&jm�F��fª¥zx�jmp�·<à áÇã � ¶\|�jmfqk[s�x�ÓP�Fx�yö� � ß�� ó pirYh�� fqpqjmxu� fª·Ffi|~joà ñ!ã � sux�Ó��zx�yÁÂRsu�ö��� ·FfU|�j>jmr¡sux�ÓP�zx�y�ÂRsu�éà ñ!ã � �m|~jm�Hk}|~jmfUyÁs�x�ÓP�Fx�yÁ¶I|~jmfqkö��� ·FfU|�j>jmr¡�lrYsux�y��l�zkl�È|wpif�à ñ!ã ï �m|~jm�Hk}|~jmfUyÁ�Y|~¥�rwk>¶\|�jmfqk� jmxu��f�à øiã � xuhFsufqj� jmfi��¥�fqk}|�jm�zkmf�à ß�� ã � rY�Hjmsufqj�� ÷R�zx�yÇ� fisurPpix�j¯�Á� fip�jmrwk{à á@íwøiã

"! Õ ½Ý¾ Ö$# Ü�¿À½ ! Ö!Õ%'&)(+*�,-(/.0*21�3+465�7/58,91:5<;+=>7/,-(+?-58@BAC7/,ED-5�4F585�(G5<;01�58(/A�&HD-58I)JKA�1�3/.+&)5L.KMN@BO-PQ,R(S3/P�58@�&T=�,-I6,-(/.U5�;WVF58@�&HPX5�(S1B,-IFV6O-&H(S1YO-M

D0&)58Z\[^]�O9ZY5�D_5�@L`+1B7+5�@B5a,b@B5aA�1�&HI)IcA�O-PX5a,-A�V658=d1>A�1B7/,91e&)(S1B@�OW.W3/=�5f&HP�V6O-@�1B,-(S1^3+(/=�5�@�1B,b&H(S1�&H58A^&)(g1�7+58&)@e,b(/,-I)JWA�&HA8hiZ:,91B5�@D9,bV6O-@j=<O_(/.W5�(FA�,b1�&HO-(k`FMN@�OSAl1�MNO-@BPK,91�&HO-(m`F(+58Zn&HP�V/@�O9D_58.o5�(/7/,b(/=�58.pA�3+@�Mq,-=�58A8`/r/(+*s1B3+4F5R1�7/5�@BPX,-It=<O-(S1>,-=d1�@�5LA�&TAl1>,b(/=�5-`5<1>=b[cu�Mv&)(F.W3/A�1�@B&H,-I/,bV+V/I)&T=�,-4+&)IH&)1lJa&TAC.W58A�&H@�5L.v`-5�w6O_@�1CPR3/Al1xMNO0=�3/AtO_(X1�7+5LA�5y3+(F=<5�@�1B,-&)(S1B&)5LA�[cz:7+5yO-4+{l58=d1B&)D_5yObM|1�7/&HAxV/,bV65�@&TA'1�OjV+@B58A�5�(S1C,e=�O-(S1�@B&H4+3W1�&HO-(R&)(KA�&)(/?-IH5<*�V+7/,-A�5i=�O0O-IT,b(S1C.W5�703+PX&T.W&}MNJ0&H(+?er/(W*~,b(/.W*s1B3+4F5:7+5L,91C5�;W=>7F,b(+?_5�@>AmPXOW.W5�IH&TA�,b1�&HO-(k`4658=�,-3/A�5eO-M�1B7+5�&H@y&HP�V6O-@�1B,-(/=<5j&H(�,b&H@�*~=<O_(/.W&)1�&HO-(+&H(+?X,b(/.�@�5�MN@�&H?-58@B,b1�&HO-(KrF5�IT.+A�[

PF Computing Services
R5-5
Page 3: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

� Ae1B7+5U7+&H?-7/58A�1jIH5�D_5�ItO-M:A�&)PR3+IT,91�&HO-(�V+@BO-V6O_A�58.v`k1�7+5KV/,-VF58@fV+@B58A�5�(S1BAj,�.W5�1B,-&)IH58.�PXOW.W5�I����Y]��i�+�/�\Zy&)1�7�,o.W&HA�*=<@B5<1B&HAB,91B&)O_(�ObMy1B7+5�7+5L,91�5<;+=>7/,b(/?-5�@a&)(�rF(W*�,-(/.0*21�3+465�58I)58PX5�(S1BA8`tZy7+5�@B5K1B7+5G,-V+V+@BO-V+&T,91B5U?-O9D_5�@B(+&H(+?o58�S3/,91B&)O_(/Aa,-@�5,bV/V+I)&H58.k[�z:7+5fPK,-&)(�MN5L,91B3+@�5LA�O-Mt1�7+5�=<OW.W5R,-@�5��2��IH&)5�1R� �E���<hy&T�^�^&TAB=<@B5<1�&H�8,b1�&HO-(�O-Mt1�7+5R7+58,b1�5<;+=>7/,-(+?-58@^.WO_PX,-&)(�&H(S1�O,�A�5�1YO-M�=<O_(_1B@�O_IFD_O-IH3+PX58AY,-Air/(W*~,b(F.0*s1B3+465�58I)58P�58(S1BA8`WZy7+5�@B5^46Ob1B7�IHOW=�,bI61B7+5�@BPXO-V+70JWA�&T=�,-I/V+@BO-V65�@�1�&H58A:,-(/.U58P�V/&)@B&H=8,bI=<O05��K=�&)58(S1BAy,b@B5j=<O-PXV+3+1�58.k�W&)&��:�S1�5L,-.WJUO_@:3+(/A�1�58,_.WJ�,-(/,bIHJWA�&TA��0&H&)&��:%'I)5�;W&)4+IH5j?-58O-PX5<1B@�JK,b(F.�=�&)@>=<3+&)1�@BJ|�W&)D+� � =�=�3+@>,91�55�D9,-I)3/,b1�&HO-(�ObMC1B7+5X7+58,b1j=�O-(/.W3F=d1�&HO-(�,b(/.gPK,-ABA^1B@B,-(/A�MN5�@�1�7+@BO-3+?_7p1B7+5K=<O-(S1B&)(03+O_3/A�rF(/Ae3/A�&H(+?o,�PR3+I)1�&T.W&)PX58(/A�&HO-(F,bIPXOW.W5�Im�s,-.WD9,-(/=<5L.aD_5�@>A�&HO-(F�<�bD+� � ;W&T,bI+7+5L,91C=<O_(/.W3/=<1�&HO-(R1�7+@BO-3/?-7R1�7+5:1B3+4F5LA��SD0&T�'u~(S1B5�@B(/,bI0�/O9Z�.W&TAl1B@�&H4+3W1B&)O_(R1B7+@BO-3+?_77+5L,-.W58@BA:,b(F.GA�5�@BV65�(S1�&H(+58A8[

��&)1�7�1�7+5gO-4W{l5L=d1�&HD-5oO-Mj.W58D-58I)O_V+&)(/?�,�=�O-PXV+3W1B5�@UPXOW.W5�I�,bV+V+IH&T=�,b4/I)5G1�O�1B7+5�&H(/.W3/A�1�@BJ$(+5L=<5LA�A�&}1B&)5LA�`Y(03+PX5�@B&H=8,bIA�1�3/.W&H58A^7/,ED-5a4F585�(oMNOW=<3/ABA�58.�O_(o1�7+5�,b(/,-I)JWA�&HAyO-MC.W&}w|5�@B5�(S1^IH5�D_5�ITA�O-MtA�&HPa3+IT,91B&)O_(k[�z:7+5aV/@�5L=<&TA�&HO-(oObMc1B7+5a@B58A�3+I)1BA^,-@�5,b(F,bIHJ0A�58.gMNO-@j1B7+@B5�5KIH5�D-58IHAjO-M:A�&HPa3+IT,91B&)O_(��NMN@�O_P�7+&H?-7+58@j1�O�IHO9Zi58@j?-5�(/5�@>,bIH&}1lJp,-(/.�=<O-PXV+3+1B,91B&)O_(/,bIc1B&)PX5�=�O-(/A�3+PXVW*1�&HO-(6�dht&��:,-.WD9,b(F=<58.G.W5�1B,b&HIH58.GPXO0.+5�IC�q,_.WD9,b(/=�58.F�Y]^�i�+�+�<hF.W5�1B,-&)IH58.�PXO0.+5�Ik3/A�&H(+?XPa3+I)1�&T.W&HP�58(/A�&)O_(/,bIvrF(G=�O-(/.W3F=d1�&HO-(,b(F,bIHJ0A�&TA��b&H&��c4/,-A�&T=y.W5<1>,b&HI)5L.RPXOW.W58Im�N4/,_A�&T=L�Y]^�i�+�+�<hS.+5<1B,-&)IH58.�PXOW.W5�I/3/A�&H(+?jr/(K5��U=<&H5�(/=�&)5LA��_&)&H&T�c�L*~�^zy��4F,-A�58.�PXO0.+5�I�q�S3+&T=> /�Y]��i�/�+�Y3/A�&)(+?U,�PXOW.W&)r/58.G5�(S1B7/,bIHV0J_*�PX5<1B7+OW.�,-(/,bIHJWA�&TAj�qz:7+@B5�IH -58IH.��)¡L¢E�N�d[

�t;WV65�@B&)PX5�(S1>,bIk@B58A�3+I)1BAYMN@BO-PQ1B58=>7+(/&H=8,bIkIH&}1B5�@>,91B3+@�5U�q�CIHPX,-7/.WJ�� £-���<`F,b@B5j3/A�58.�MNO-@^,K=�O-PXV+IH5<1B5f=<O-PXV/,-@�&TA�O-(�O-Mc1�7+5(03+PX5�@B&H=8,bIvPXOW.W5�ITAy.W58D-5�IHO-V658.�MNO-@:1B7+58A�5f.W587S3/P�&T.W&)MNJ0&)(+?UA�&)1�3/,b1�&HO-(/A8[

¤ Ø Ö$#/Ú Û ! »ª¹b½ ! Ö!Õ

¤:¥� #�¦k§0¨t©�ªl¦m«­¬|®y«�¦°¯�¨t«�±'¨t²^¬|¦�« ¿�³ Ú »N» ¨t²^«µ´�¨t¶S©�¬ ¿�³ Ú »�»^·%'&)(+*�,-(/.0*21�3+465f7+5L,91^5�;W=>7F,b(+?_5�@>Ay,b@B5f=<O-PXPXO-(/I)J�3/A�5L.o&)(p,-3W1�O_PXOb1�&HD-5\@>,-.+&H,b1�O-@>A8`+5�D9,bV6O-@>,91BO-@>A:,b(/.�=�O-(/.W58(/A�5�@>A�[

%+3/5�I0=<O-(FA�3+PXVW1B&)O_(f,b(/.a.W58A�&)?_(\@�5LAl1B@�&T=d1B&)O_(/Av&H(0D-O-IHD-5c1B7+5x(/58=<5LA�A�&)1lJ^1BO�@�5L.W3/=�5t1�7+5iZi58&)?_7S1�,b(/.\A�&H��5CO-MW1�7+&TAm5L�S3+&)V/P�58(S18[z�OaO-4+1B,b&H(K1B7+&HAi&HP�V/@�O9D_58.X5<�U=�&)58(/=<J�1�7/5�&H@x1B7+5�@BPK,bI|,b(/.X�F3+&H.W*�.WJ0(/,-PX&H=^4F587/,ED0&)O_3+@xPR3/Al1:465�A�1�3/.W&H58.�&)(�.W5<1>,b&HI6Zy&)1�7,b(¸,-V+V+@BO-V+@B&T,91�5�PXOW.W58Is[¹z:7/5g,b(/,-I)JS1B&H=8,bI^PX5�1�7+OW.+AUMNO-@�7/58,91G5<;+=>7/,-([email protected]�&)?_(n���E*~�^zy�f`:%�*~º�z:» ¼e[)[H[ �½,b@B5�(+Ob1=�,-V/,b4/I)5e1�O�A�,b1�&TAlMNJ�1�7+&TA�=>7/,-I)IH5�(+?_5-`/.+3+5j1�OX1B7+5aA�1�@BO-(+?XIH&)PX&)1B,91B&)O_(/AyO-M'1B7+5�&H@^,-(/,bIHJWA�&TA�[i��3+PX5�@B&T=�,bI�A�&HPa3+IT,91B&)O_(�?_&)D_58A1�7/5\VFOSA�A�&)4/&)IH&}1lJ�ObMt,b(/,-I)JWA�&)(+?R1�7/5j1�7+58@�PK,bIk,-(/.��/3+&T.0*�.+JS(F,bPX&H=j465�7F,EDS&HO-3/@YO-Mm1B7+&HA�58�S3+&HV+PX5�(S1�&)(o?_@�5L,91�[email protected]<1>,b&HIs[

z:7+5iV+7+5�(/O-PX5�(/,�&H(f1�7/&HA'58�S3+&HV+PX5�(S1c&HA�3+(/A�1�5L,-.WJ_`E1�7+@B5�5�*�.+&)PX5�(FA�&HO-(/,-IS,-(/.\3/A�3/,-I)IHJ\Zy&}1B7f1B3+@�4/3+I)58(S1��/O9Z�@B5�?_&)PX5LA�[z:7+5y?_5�O-PX5�1�@BJ\&HAcD_5�@BJf=<O-PXV+IH5<;RZy&}1B7X,e7+&H?-7K=>7/,-(+(+58I+.W5�(/A�&)1lJ-[cz:7+58A�5YMN58,91B3+@B58AcIH58,-.a1�O\,e@B58A�O-IH3W1�&HO-(XAl1B@B,b1�58?-J\4/,_A�5L.O-(p,�.W&HAB=<@B5<1B&HAB,91B&)O_(�,b@BO-3+(/.�1B7+5f1B3+4F5LA^,_A^A�PX,-I)I�7+58,b1^5<;+=>7/,-(+?-58@BA\�sA�585U� �9��`��¾L�',-(/.��À¿8�'MNO-@�[email protected]�1B,-&)I��\�q%'&H?/[\¡E�d[��D-58@j1�7+5LA�5�PX,_=<@BOb*~=<O_(_1B@�O_I�D_O-IH3+PX58A8`k1B7+5�=<O_(/A�5�@BDE,b1�&HO-(�58�S3/,b1�&HO-(/A\O-MYPK,_A�A8`�PXO_P�58(S1�3+PÁ,b(/.�58(+5�@B?-Jp7F,ED-5K465�5�(,bV/V+I)&H58.k[a��(/A�1�5L,-.WJ_`k3+(+&T.W&HPX5�(/A�&)O_(/,bIt,-(/,bIHJWA�&TA^&TAj,-ABA�3/P�5L.v`vZy&)1�7�(+5�?_I)&H?-&H4+IH5R@>,-.W&T,91B&)D_5a7+5L,91e1�@>,b(/A�MN5�@\,-(/.pD0&TA�=�O-3/A.W&TA�A�&HV/,91B&)O_(k[�z:7+5iPXO0.+5�IS3/A�5LAkD9,b@B&T,b4+IH5t1�7/5�@BP�O_V+70JWA�&T=�,-I-V+@BO-V65�@�1�&H58A�,b(/.\A�VF5L=<&)rF=CD9,-I)3+5LAmO-M+7+58,b1m1B@B,-(/AlMN58@�=�OS5��U=<&H5�(S1BA,b(F.UMN@B&H=<1�&HO-(GMq,-=<1�O_@BAYO9D-58@:58,-=>7GPK,-=�@�O-*�=�O-(S1�@BO-IFD-O-IH3+PX5-[

%'&)?_3+@B5�¡_h���3/P�58@�&T=�,-IcP�OW.W58I)&TAB,91�&HO-(�ObMi1�7+57+5L,91c5<;+=>7/,b(/?-5�@'=<O_@�5_�b.W5<1>,b&HISO-M+1�7/5irF(W*�,-(/.0*1�3/4F5\58I)58P�58(S1BA

 à ÄÅNÆ

Ç È ÉÊ ËÌ Í Î Ï Ð Ñ�Ò Ó ÔÕNÖ

× Ø ÙÚ Û

Ü

Ý�Þ ß à áâbãäåæ ç è é ê ë ì íî

ï

ð

ñ

ò

óô õ ö ÷øNùúû

üýþ ÿ

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

. / 012 3

%'&)?_3+@B554+hc��5�1^7+58,b1y5<;+=>7/,b(/?-5�@y,-(/,bIHJWA�&TAi*CPX,-&)(G1B5�@BPXAz:7+5jV+@B5�D0&HO-3/A:,b(F,bIHJ0A�&TAiIH58,_.+Ai1�OK,�(+O-(+*2IH&)(/58,b@y=�O-3+V+IH58.�58�S3/,b1�&HO-(GA�JWA�1�5�Po`WZy7+OSA�5j@B58A�O-IH3W1�&HO-(�?-&HD-5LAx1B7+5jD9,b@B&H,-4+I)5

.W&TAl1B@�&H4+3W1B&)O_(�&H(�1B7+5��/3+&T.+Aj�768 `WVk`Wz��Y,b(/.�&)(�1�7+5\A�O-IH&H.K58I)58PX5�(S1BAj�qz��xMNO_@i1B7+5eZy7+O-IH5�7/58,91:5<;+=>7/,-(+?-58@8['z:7+5\=<O_3+V+IH&)(+?ObMC,-I)Iv1B7+5f58I)58P�58(S1BAy&TA^.WO_(+5\&H(p,KA�58?-@B5�?_,b1�5L.UZ:,EJ�Zy&)1�7+&H(p,X?-IHO-4/,-IvMN3+IHI)JG&HP�V/I)&T=<&)1�1�@>,b(FA�&H5�(S1�@B58A�O-IH3W1�&HO-(o,bIH?-O_@�&)1�7+Po[z:7+5\.W58D-5�IHO-V658.�PK,91�7/5�PK,91B&H=8,bI|PXO0.+5�Iv(+5858.+AY1B7+5j5�D9,bIH3/,91B&)O_(�O-M�7+5L,91:1�@>,b(/A�MN5�@y=�OS5��U=<&H5�(S1BA:,b(F.UMN@B&H=<1�&HO-(�Mq,-=d1BO-@>A�[cu�1

Page 4: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

,bITA�Oa(+5858.+AY&H(WMNO-@BPK,91�&HO-(�ObMmV+@B58ABA�3+@�5e.W@BO-VU&H(�A�&)(/?-3+IT,b@B&}1B&)5LAi,-(/.K1B7+5�@BPK,bI|=<O_(_1>,-=<1Y@B58A�&HA�1B,-(/=<5LA�[t�i3+@B@�58(_1BI)J_`S1�7+5j=<OW.W53/A�58A:4/,_A�&T=e5<;WV65�@B&)PX5�(S1>,bIk=<O_@�@B5�IT,91B&)O_(/AiV+3+4+IH&HA�7+5L.�40J�Ob1�7/5�@y,b3W1B7+O-@>A:&H(�1B7+5\O-V65�(GIH&}1B5�@>,91�3/@�5K�l�H¡<��`k��4L��`k� 9b���<[

z:7+5�=�O0.+5^.W58,-IHACZy&}1B7U4FO-1�7K5�;0VF,b(/.W5L.�r/(W*~,b(/.W*s1B3+4F5�,b(/.�4+@>,b�858.Rr/(W*~,b(/.W*s1B3+4F5^?-5�O_PX5<1�@B&H58A8`bZy7+&T=>7U,b@B5:1�7+5�PXOSAl1&HP�V6O-@�1B,-(S1�&H(�=<O_PXV/,-=<1e7+5L,91e5<;+=>7/,b(/?-5�@>AyrF5�IT.v[fz:7+5�5�(+7/,-(/=<5L.�7+5L,91e1�@>,b(/A�MN5�@e?-58O-PX5<1B@�&H58A�Al1B3/.W&H58.g,-@�5a1�7+5�V+IT,b&H(k`Z:,EDSJU,-(/.GI)O_3+D-58@�5L.Kr/(FA�[4W[H¡-[H¡ � &H@��/O9Z ,b(/,-I)JWA�&HA

z:7+5:=<OW.W5:=�,-IH=�3+IH,b1�5LAm1B7+5Y7+58,b1'1B@B,-(/A�MN5�@c,b(/.aV+@�5LA�A�[email protected]@BO-V�,91c58,_=>7aPK,-=�@�O-*�=�O-(S1�@BO-IbD_O-IH3+PX5Y,_A�A�3+PX&H(+?�,�3+(+&)MNO-@BPD-58I)OW=�&}1lJU.W&TA�1�@B&)4+3+1�&HO-(�,_=<@BO_ABAC1B7+5��/O9Z =<O_(S1�@BO-I6D-O-IH3+PX5jA�5L=d1�&HO-(��N3+(/&H.W&HPX5�(/A�&HO-(/,-I|1�@B58,91BPX5�(S1>�<`W4SJX1B7+5j@�5LA�O_I)3+1�&HO-(UO-M1�7/5�,-.W5L�S3/,91B5�58(+5�@B?-J_`kPK,-ABAf,b(F.�PXO_P�58(S1�3+P 4/,bIT,b(/=�58A8[�z:7+5K?_I)O_4/,bIC,-&)@��/O9Zn&TAf.W&HD0&H.W5L.�.W5�V65�(F.W&)(/?�O-(�1�7+5U�/O9Z@B58A�&HA�1B,-(/=<5eObMc58,_=>7��8O-(+5jObM�1�7+5\7/58,91�5�;+=>7/,b(+?_5�@L`-1BOK?-5�1y,�3+(/&}MNO_@�P O-3W1BI)5�1:V/@�5LA�A�3+@B5eD9,-I)3+5_[:y5�MN5�@B@�&H(+?�1�OU7/58,91y1B@B,-(/A�MN5�@L`/,XI)OW=8,bIm=8,bIT=<3+IT,91B&)O_(GO-Mc1�7+5fVFA�JW=>7+@BO-PX5<1B@�&T=eV/,b@>,bPX5�1�5�@>A\�q.+5�Z:*�VFO_&)(S1y1�58PXVF58@B,b1�3+@B5L�V65�@BP�&)1BAi,\.W5<1B5�@BPX&)(/,b1�&HO-(XObM|1B7+5^.W@BJ<;EZY5<1t��O_(+58AtO_(�1�7+5^,-&)@>A�&H.W5�A�3+@�Mq,-=�58A8`-,b(/.K=�O-(/A�58�S3+58(S1�IHJfObM|1�7/5^A�58(/A�&)4+IH5=;9IH,b1�58(_17+5L,91i@>,91B&)OSAC,b(F.XDE,-VFO_@i=�O-(/.W58(/AB,91�&HO-(K@>,91B58Ai,91x5L,-=>7KPK,-=�@�O-*�=�O-(S1�@BO-IWD_O-IH3+PX5a�q%'&H?/[>4-�<['z:7+&TAi&HAiObMv?-@B58,b1x&HP�V6O-@�1B,-(/=<5&H(�=�O-PXV/,-=<1\5�D9,bV6O-@>,91BO-@>A�,-(/.�,-&)@>=<O0O_I)58@BA8[fu�MiZY5<1f=�O-(/.W&)1�&HO-(FA\,b@B5RV+@B58A�5�(S1\Zy&)1�7�A�3+@�Mq,-=�5�1�5�PXV65�@>,91B3+@�5LAe4F58I)O9Z¹1�7+5MN@B5�5��8&)(/?\VFO_&)(S18`_MN@BO_A�1CMNO-@BPK,91�&HO-(X&TAx,-(/,bIHJWA�5L.v`_=8,bIT=<3+IT,91B&)(+?j1B7+5�=>7F,b(+?_58At&H(XMN@�OSAl1x1�7+&T=> 0(+58ABAC,b(F.�MN@�OSAl1i.+5�(/A�&}1lJ_['z:703/A8`,X.W@BJU7+58,b1�5<;+=>7/,-(+?-58@i4658=�O-PX58Ay,XV/,-@�1B&H=�3+IT,b@y=�,_A�5eObM'1�7+&TA�,-(/,bIHJWA�&TA�[

z:7+5\PXO-&TA�1�,b&H@��FO9Z PK,91B7+5�PK,91B&H=8,bIvMNO_@�PR3+IT,91�&HO-(o&TAyV+@B58A�5�(S1�5L.G&)(p.W5�1B,-&)I�&)(o(+5�;S1�58�S3/,91B&)O_(/A8[i��@�O_V+I)5�1�MNO-@BPK,91B&)O_(&H(�A�3+V65�@�*�AB,91B3+@B,b1�5L.f,b&H@c&HA�1B,- -58(a&H(_1BOe,_=�=�O-3+(S18['z:7+5yA�58(/A�&)4+IH5:,b(/.RIH,b1�58(_1c5�(/5�@B?-&H58Ac,b@B5C1>,b -58(a&H(S1�O\=<O_(/A�&T.W58@B,b1�&HO-(f&H(R,?-IHO-4F,bIF,-&)@i5�(+58@�?_JR5L�S3/,91B&)O_(k[c�C(S1�7/,-I)V0J�MNO-@BPa3+IT,91B&)O_(K7/,-Ax4F585�(GA�7+O9Zy(U,_Ax465�&H(+?a1�7+5e4F5LAl1iMNO-@i1�7+&TAY,b(/,-I)JWA�&HA8[ � Pa3+I)*1�&T.W&HPX5�(/A�&)O_(/,bIvA�&)PR3+IT,91�&HO-(�ObM�1�7+5jZY5<1�1B58.�=<O-(S1B&)(03+O_3/Air/(/A:7/,_Ai&[email protected]�7+5j7+5L,91y,b(/.�PK,-ABAC1B@B,-(/AlMN58@y=�,bIT=<3/IH,b1�&HO-(k[z:7+5j1B@B,-(/A�D_5�@>A�,-I6,-(/.�I)O_(+?-&)1�3/.+&)(/,-Iv7+58,b1y1�@>,b(/A�MN5�@:5�w65L=d1BA�7/,ED-5�1�7+58(o4F585�(o&)(F=<IH3/.W58.k[

��@�J�,-&)@L`WZ:,91�58@:DE,-VFO_@8`WIH&T�_3/&H.�r/IHP PK,-ABA:4/,-IH,-(/=<5_h??A@CBEDFHGJILKNMPOQRGES TVUWOQXG=S Y[Z]\ ��¡L�??A@ BEDF_^JI`KaMPOQX^ S T UWOQb^ S Y ZcUdOQXe S fEYhg-i UWOQXe S jlklTnm7gporq �s4-�??A@ BEDF_tuI f&Yhg-i KNMvOQ gS T UwOQ g�S Y ZxOQXe S fEYhg-i �y9_��C(+58@�?_JU4/,-IH,-(/=<5eO9D-58@i1B7+5f,b&H@�=<O_(S1�@BO-I|D-O_I)3+PX5_`W&)(/=�I)3F.W&)(/?KI)&T�S3+&H.�r/IHP &H(S1�5�@�Mq,-=�5-h??A@ z Fb{<|}U�~ F[� I���MPOQRGES T�|�TVUWOQXGES Ys|<Y�MPOQ e S fEY-g-i�| f�� ���h� � MvOQ e S jlklTrm�ghonqr| t � � �h�n� � ZdU O�L� �q£S�

�C(+58@�?_JU4/,-IH,-(/=<5eO9D-58@i1B7+5\IH&H�S3+&T.�r/I)Poh??�@ z F�{<|}U�~ F�� I5� t MPOQbg�S T&| t � �h� � UWOQ�g�S Yr| t � �h� � U�OQ e S fEYhg-i�| f_� ���p� � Z O�L� U O�5� �2¾-�

]�5L,91�,b(F.�PK,_A�Ai1�@>,b(FAlMN58@�=�,bIT=<3/IH,b1�&HO-(kh�:,-A�&H=�PX5<1B7+OW.z:7+5e=�,bIT=<3/IH,b1�&HO-(UO-Mk1�7+5e7+5L,91y,b(/.�PX,_A�Ax1�@>,b(FAlMN58@x1BO9ZY,-@B.+At1�7+5j7+5L,91i5�;+=>7/,b(+?_5�@YA�3+@�Mq,-=�5^&TA:=�,bIT=<3/IH,b1�58.U4SJKPX5L,b(/A

ObM6,b(a5LAl1B&)PK,b1�&HO-(aO-M+1�7/5YPX5L,b(aA�3+@�Mq,-=<5i1�58PXVF58@B,b1�3+@B5��q3/A�&H(+?\,b(F,bIHJ_1B&H=8,bI0,-.W&T,b4F,91�&T=trF(a5<�U=�&)58(/=<J+�',b(/.k`b=<O-(FA�5L�_3/5�(S1�IHJ-`1�7/5RPX58,-(�A�3+@�Mq,-=<5�,b4/A�O-IH3W1B5R703+PX&T.W&}1lJ_[fz:7+&TA�PX5L,b(p1B5�PXV65�@>,91�3/@�5R&HAj=�,-IH=�3+IT,91�5L.p3/A�&H(+?U1B7+5�1�Ob1>,bIc7+5L,91e1�@>,b(/A�MN5�@B@�5L.1�O�1B7+5\@�5�MN@�&H?-58@B,-(S1:,-(/.�46Ob1B7G1�7+5jr/(�,-(/.�=�O-(/.+5�(/AB,91B5�rFI)P 1�7+58@�PK,bIv@B58A�&TAl1>,b(/=�58A8[O� e T�� ^������ Yhi�m�g-Y fEYpo�j Z�¡�¢ q B D£ U D£ f&Yhg-i K�¤ TOQRe S f&Yhg-i¦¥ � Yhi�m�g-Y fEYpo�j Z�¡ iVq B D§ U D§ � GlqrS fEY-g-i K�¤ T �y¨_�

� .WD9,b(F=<58.�PX5<1B7+OW.]�O9ZY5�D_5�@L`9,�PXO_@�5y,-=8=<3+@>,91B5Y,-(/.�=<O-(FA�&TAl1B5�(S1tPX5<1�7/O0.�O-M6.W5�1�5�@BPX&)(/&)(+?e1B7+5y7+58,b1C,b(/.�PK,-ABA�1�@>,b(/A�MN5�@t&TA'1�O\A�&)PR3+IH,b1�5

1�7/5�7+5L,91:,b(/.KPK,_A�Ax1�@>,b(/A�MN5�@x1�Oa1�7+5�r/(+(+5L.�A�3+@�Mq,-=<5LAt1>,b -58(U&H(_1BOR,_=�=<O_3+(S1xPXO-@B5^IHOW=�,bIF&)(+MNO-@BPX,b1�&HO-(k`_1�@>,b(FA�D_5�@>A�,-I/,b(/.

Page 5: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

IHO-(+?_&}1B3/.W&H(/,bIc7+5L,91e1�@>,b(/A�MN5�@L`v5<1>=b[Rz:7/&HAe7/,_A�465�58(�.+O-(+5X3/A�&)(/?G,�1lZiO-*�.+&)PX5�(FA�&HO-(/,-I'A�&HPa3+IT,91B&)O_(pObMYO-(+5Rr/(�MNO-@j58,_=>7=<O_(S1�@BO-I|D-O_I)3+PX5\IH5�D_5�Iv&H(�1B3+465<*~,9;W&HAy.+&)@B58=<1�&HO-(��q.W5�1B,-&)IH58.G5<;WV+IT,b(F,91�&HO-(G&H(G(/5<;01^A�5L=d1B&)O_(F�d[ � M�1�5�@�1�7+&TA�A�&)PR3+IH,b1�&HO-(k`+1�7+5IHO0=8,bI'D9,bIH3+58Ae,b@B5a?_@�O_3+VF5L.oMNO-@�1�7/5�=�O-@B@�5LA�V6O-(/.+&)(+?���O-(/5f1�O�58,_=>7pPK,-=<@BOb*~=<O_(S1�@BO-IkD_O-IH3+PX5-`v,b(/.�1�7+58(g&H(_1B@�OW.W3F=<58.g&)(1�7/5\?-IHO-4/,-I67/58,91^,-(/.�PX,_A�A:4F,bIT,b(/=�58AYV+@B58A�5�(S1�5L.�,-4FO9D_5-[

O� e T�� ^ S fEYp� ��� G�j ^ G�� e o�j Z ©fEYh�Jª¬« ¡¬¢ q B £ ghT e Glg U £ fEY-ghi­S gpT e Glg K º ¤OQRe S fEY-g-i®S fEYp�a¥ G�j ^ G�� e o�j Z ©fEYh�Jª¬« ¡ iVq B § ghT e G7g U § � GlqrS fEY-ghi­S gpT e Glg K º ¤ ��¿b�

:y5�MN5�@B@�&H(+?�1BOe1�7+5y,b&H@'�/3+&T.0*~.WJ0(/,bPX&T=i465�7F,EDS&HO-3/@8`9&)1tPa3/A�1t4F5:3+(/.+5�@BI)&H(+58.a1�7F,91c1�7+5�=�OW.W5iV/@�5L.W&H=<1BA'1B7+5:&)(+IH5<1�;EO_3W1�IH5<1V+@B58ABA�3/@�5:.W@BO-V�5<w|58=d1>A�`-1�7+5y=>7/,-(+?-5LA'&)(X 0&)(/5<1�&T=:5�(/5�@B?-JU�q,-(/.X=<O_(/A�5L�S3+5�(S1�IHJf,b(X,-=8=<58I)58@B,b1�&HO-(f1B5�@BPn&H(R1B7+5yPXO-PX5�(S1B3+P58�S3/,b1�&HO-(/A>�d`W&H(�Al1B58,_.WJUO-@y3/(/Al1B58,_.WJ�,b(F,bIHJ0A�&TA�[

z:7+5�D-O_I)3+PX5�40J�D-O-IH3+PX5X,b(/,-I)JWA�&HA�&HA�r/(F,bIHI)J�V6O_A�1�*�V+@BO0=�58ABA�5L.o1�OGO-4+1B,b&H(p1B7+5K,b&H@j?-IHO-4/,-Im1B&)PX5<*~.W58VF58(/.W5�(S1\&H(/=<@B5<*PX5�(S1BA�&)(G5�(S1�7F,bIHVSJ_`W 0&)(+5�1�&T=j5�(+58@�?_J�,b(F.�D9,bV6O-@yPK,_A�Ay=�O-(/.W58(/AB,91�&HO-(��NO_@:MN@�OSAl1:MNO-@BPK,91B&)O_(F�d[4W[H¡-[�4R%�&H(�,b(/,-I)JWA�&HA

z:7+5X=<O_(_1B&)(03+O_3/AyrF(�?_5�O-PX5�1�@BJ�&TAe3/A�5L.p&H(g5�;0VF,b(/.W5L.�r/(+*�,-(/.0*21�3+465R7/58,91j5<;+=>7/,-(+?-58@BA8`/O-MxZy&T.W5R3FA�5�&)(�@�5�MN@�&H?-58@�*,91B&)O_(g,b(F.g,b&H@�*�=�O-(/.W&)1�&HO-(/&)(+?F`/4+3+1\,-IHA�OU&H(�A�O-PX5aIHO9Z:*�VFO9ZY5�@e,b3W1BO-PXOb1B&)D_5f@B,_.W&T,91�O_@BA8[­¯x@�O9D0&T.W58.o1B7/,91e1�7/5a1B3+4F5X4/,_A�51�58PXVF58@B,b1�3+@B58Ai,b@B5�(+Ob1:,bIHZY,EJWAtA�&)PX&HIH,-@x465<1lZY5�58(�=<O_(_1B&)?_3+O-3FAt1�3/4F5LA�`S1�@>,b(FA�D_5�@>A�,-I+,b(/.XIHO-(+?_&}1B3/.W&H(/,bI67+5L,91i=�O-(/.W3F=d1�&HO-(,bIHO-(/?a1B7+5er/(/Ay=�,-(�465jObM�?_@�5L,91Y&)PXV6O-@�1B,b(F=<5-[tz:7+58@�5�MNO-@B5-`S1�7/5e3FA�3/,-Iv70JSV6Ob1B7+58A�&TAiO-M',_.W&H,-4/,91B&H=^4FO_3+(/.+,-@�JXMNO_@:1�7+5er/(5<�U=�&)58(/=<Ja=8,bIT=<3+IT,91B&)O_(a&TAc(+OjI)O_(+?-58@',_.W58�S3/,b1�5:&)M/1�3/4F5yZ:,bIHI01�58P�V65�@>,[email protected]&)w658@t4F5�1lZi585�(X,-.E{�,_=<5�(S1c1�3/4F5LA�[cz:7+5y=<OW.W5&H(_1B5�?_@B,b1�58AY,RPa3+I)1�&T.W&HP�58(/A�&)O_(/,bIkA�&)PR3+IT,91�&HO-(�ObM�1�7+5\=<O_(S1�&H(S3/O-3/Axr/(/A8`WZy7+5�@B5�1�7+5e1�3/4F5�*sr/(�,-(/.Kr/(+*�,-&)@:7+5L,91BA:,-@�5j=�,-I}*=<3/IH,b1�58.�MNO_@t1�7/5yr/(X��O_(+5^=<O_@�@B58A�V6O-(/.W&H(+?�1�O\1B7+5�PK,-=�@�O-*�=�O-(S1�@BO-ISD-O_I)3/P�5LA�`S,b(/.R1B7+5�(K@B58,-IWr/(K5<�U=�&)58(/=<&H58AC.+5<1�58@�PX&H(+58.MNO-@'58,_=>7fO-(/5iO-M+1�7+58Po[t�Y,-@�1B58A�&H,-(f.W&HAB=<@B5<1B&HAB,91B&)O_(f3/A�&)(/?�4+IHOW=> S*2&H(W*�ObwRPX5�1�7+OW.R&)(a1�7+5i1�3+465y,b@B58,_Ax�q%'&H?/[¬9_�k&HAc=<3/@�@B5�(S1�IHJ3/A�58.v`|,bI)1�7/O-3+?_7�ZiO_@� �&HA^4F58&)(+?G.WO-(/5\MNO-@^1�7+5R&)(S1�@BOW.W3/=<1�&HO-(�ObMt46OW.WJS*sr+1�1�5L.p,b(/.o3/(/Al1B@�3F=d1�3/@�5L.p.W&TA�=�@�5�1�&TA�,b1�&HO-(��q%'&H?/[£S�<[t�CD-58(�1B7+O-3/?-7k`+&)1�&TA:(+Ob1^=�I)5L,b@Y1�7/,b1^=<O_P�V/3W1B,b1�&HO-(/,-Iv5<w|O-@�1y=�O-3+IT.�4F5\@B58.W3F=<58.k[

%'&)?_3+@B5�9/hCzmZYOb*~.W&HPX5�(/A�&)O_(/,bIv.W&TAB=<@B5<1�&TAB,9*1�&HO-(\O-MW1�7+5Y=<O_(_1B&)(03+O_3/A|r/(FAk40J\=�,b@�1�5LA�&T,b(PX58A�7o3/A�&H(+?X4+IHOW=> _*�&H(W*2O-w

%'&H?-3+@B5f£FhYz�ZiO-*�.+&)PX5�(FA�&HO-(/,-Im.W&TA�=�@�5�1�&TA�,b1�&HO-(oObMt1B7+5R=�O-(S1�&H(03+O-3FA:r/(/A�40J3/(/Al1B@�3F=d1�3/@�5L.�PX58A�7

¤:¥s¤±°³² Õ ½ÀÜ ¬|®:«^¦µ´>®>¶�«­¶³·�¸N¹�¦k§»ºe²�²�¦m«µ¶H¼½¶<´B¨t¬|¦m¶ ¯E¾¿¼^©�¬<À ¿�³ Ú »�»^·� (o&H(/.W3/A�1�@B&T,bIv7+5L,91�5<;+=>7/,-(+?-58@i@>,91B&)(/?b*~.W58A�&)?_(�=�O0.+5\7/,-A:465�58(o.+5�D-58I)O_VF5L.�O_(�1B7+5\4/,_A�&TA:ObM'1�7+5j�E*~�^zy� PX5<1B7+OW.v`

3/A�&)(/?�1B7+5K5�(S1B7/,bIHV0J�VFO-1�5�(S1B&H,-ItP�5�1�7+OW.WO_I)O_?-J$�sz:7+@B5�IH -5�IT. �H¡8¢9����[email protected]�703+PX&T.W&}MNJ0&H(+?�7+5L,91\5<;+=>7/,-(+?-58@BA8[Rz:7+&TAe1�@B58,b1�*PX5�(S1^7/,_Ay465�5�(�3/V6.+,b1�5L.�,b(/.G&HP�V/@�O9D_58.�&)(pA�O-PX5f,-A�V658=d1>A�`/4/,-A�&H=8,bIHI)J�O-(o1�7/5f@�5L.W3/=<1�&HO-(oObMtA�O_PX5\ObM'1�7+5f@B58A�1�@B&T=d1�&HD-570J0VFO-1�7+5LA�&TAl;E1�@B58,b1�PX5�(S1BA��ÂÁk5ÄÃZ ¡-[ ¢+`c(+O-1RO-PX&)1�1B58.�1B5�@BPXAa&)($1�7+5�@�58IH,b1�&HO-(�465<1lZY5�58(�5�(S1�7/,-I)V0J�V6Ob1�58(S1�&T,bIi,-(/.�7+5L,911�@>,b(FAlMN58@8`W3+(/&H�S3+5erF=<1�&)1�&HO-3/Ay58(S1�7/,-I)V0J�=�O-(/=�5�VW1L`k[)[H[�d[C]�5L,91�5�;W=>7F,b(+?_5�@>AxZy&)1�7�.W@BJ<;EZY5<1�A�3/@�Mq,_=<58A:,-@�5\=�,-IH=�3+IT,91�5L.�Zy&)1�71�7/5RAB,bPX5fPK,91B7+5�PK,91B&H=8,bImMNO-@BPa3+IT,91B&)O_(k`F=>7/,-(+?-&H(+?KO_(+I)Jo,XMN58Z VF,b@>,bPX5<1B5�@>A:MNO-@^1�7+5�=�,bIT=<3/IH,b1�&HO-(oObMC46Ob1B7gA�&)1�3F,91�&HO-(FA�[Å�O_@�58O9D-5�@L`-VF,b@�1�&T,bIHI)JKZY5<1�1�58.GA�3+@�Mq,_=<5e7+58,b1y5<;+=>7/,b(/?-5�@>Ax,-@�5j,bITA�Oa1>,b -58(�&H(S1�OX,-=�=�O-3+(S1L`0.+&)D0&T.W&)(/?R1B7+5j7+58,b1y5<;+=>7/,b(/?-5�@&H(o1�7+5f.W@BJ�,-(/.GZi5�1�V/,b@�1BA8[i�0V658=�&H,-Im,91�1�58(_1B&)O_(o7/,-Ay465�58(oMNOW=<3/ABA�5L.GO-(�.W58A�&H?-(oV+@BO0=�58.W3/@�5LA�hc&��:7+58,b1y1�@>,b(/A�MN5�@�=8,bV/,_=d*&)1lJgO-@jO_3W1�IH5<1a,-&)@j1B5�PXVF58@B,b1�[email protected]�&H?-(�@�5LAl1B@�&T=d1B&)O_(/A���&)&��eIH&)PX&)1�58.�=�OSO_IH,-(S1jD_5�IHOW=<&)1lJ6��&)&H&��j=<O-(S1B@�O_ItObMY=�O-@B@�5L=d1\=<&H@B=�3+&)1BA?-58(+5�@>,91B&)O_(k[

Page 6: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

z:7+&TA�=<OW.W5_`/�S3+&T=> +�Y]^�i�+�|`F7/,-A:465�58(pA�7/O9Zy(o,_Ay,XD-58@�JU3FA�5�MN3+Ik1BOSO_IvMNO-@�,K�_3/&H=> �,-(/.G@�58I)&T,b4/I)5\7+5L,91y1B@B,-(/AlMN58@�,b(/.V+@B58ABA�3/@�5U.W@BO-V =8,bIT=<3+IT,91B&)O_(�ObMyr/(+*�,-(/.0*21�3+465�7+5L,91�5<;+=>7/,b(/?-5�@>A8[Gu�1�7/,-Aa4F585�($=�O-(/=�5�&HD-5L.�,-Aa,pMN@�&H5�(F.WI)JS*�3/A�5�@a=�O0.+5-`Zy&)1�7�@B5�PXOb1B5f,-=�=�58ABA:D0&H,XZY5�4k[Yz:7+5\IT,91�1B5�@yMN5L,91B3+@�5\IH58,_.+A:1BOK4F5�1�1�58@^PK,b&H(S1�58(/,b(/=�5-`/A�58=�3+@B&}1lJ�,-(/.oV65�@�MNO-@BPX,-(/=<5_`+,b(/.,bIHIHO9Z�Ay=<O-PXV/,-(0J�=<3/A�1�O_PX5�@yO-@�=�O-PXPX5�@>=<&T,bI)*s1B58=>7+(/&H=8,bIvAl1>,9w�,-(o58,-A�J�,_=�=<5LA�A:Zy7/5�@B5�D-58@:1�7+58J�,-@�5jZYO-@B S&H(+?F[Cz:7+5f,b&HPObMm1�7+&TAYV/,bV65�@Y&HAi1BO�A�7+O9Z¸,fV65�@�MNO-@BPK,b(/=�5^D9,bIH&T.+,91B&)O_(UObMk1B7+5jA�&HPXV+I)&)r/5L.�,bV/V+@�OS,-=>7K&H(�=�O-PXV/,b@B&TA�O_(KZy&}1B7�1B7+5e.+5<1B,-&)IH58.=<OW.W5jV+@B58A�5�(S1B58.�4F5�MNO-@B5-[C%+O_@yPXO-@B5�&H(WMNO-@BPK,91B&)O_(GA�5�5X� Æ9��[Ç ÚXÈ]ÉÝÚ ¾ ! Ø Ú2Õ ½¢¹/Û�¿ Ö!ØÊÉ ¹ÿ¾ ! » ÖÙÕ

�0O_P�5a(S3/P�58@�&T=�,-I}*�5<;WV65�@B&)PX58(_1>,bIk=�O-PXV/,b@B&TA�O_(/A:7/,ED-5a4F585�(pV65�@�[email protected]�1B7+5a,-3W1�7+O_@BA^&)(�O_@B.+5�@y1BO�D9,bIH&H./,91�5f1�7+5(03+PX5�@B&H=8,bIt=<OW.W5LAj.W5�D_5�IHO-V658.�MNO_@e1�7+5X46O-3+(/./,b@BJp=<O-(F.W&}1B&)O_(/Aj,b(/.g?-58O-PX5<1B@�&H58Ae&H(SD_O-IHD-5L.�&)(�1�7/58A�5�,-V+V+IH&H=8,91�&HO-(FA�[���(1�7/5y(+5<;01tV/,b?_58A8`91�7/5Y5�;WVF58@�&HPX5�(S1B,-I01�58A�1BAcV65�@�[email protected]�CIHPX,-7/.WJ�� £9�6,b@B5Y=�O-PXV/,[email protected],b?S,b&H(/Al1'1�7/5y(S3/P�58@�&T=�,-IW@�5LA�3/I}1>A�[%+O_@:MN3+@�1�7+58@y&)(WMNO_@�PK,b1�&HO-(oA�585�� ¨9��[Ç:¥� ¹ ©�¶ ² ¬|®:®xª�¦a¶ ¥ ¿ ¼�¸ ¿ ¼ ¥ ³ ¦k¨'§ ²=Ë ¨t¶0¶�§³¶+¨t²^¶_´>¦a¶

�t;WV65�@B&)PX5�(S1>,bIW.+,91>,�MNO-@'1�7+5yD9,-I)&T.+,91B&)O_(aO-M/1�7/5Y(03+PX58@�&T=�,-I0=�OW.W58A'MNO_@c.+5�703+PX&H.+&}MNJ0&H(+?j7+58,b1c5�;+=>7/,b(+?_5�@>A�A�&HPa3+IT,91B&)O_(7/,_A:4F585�(�O-4+1B,b&H(+5L.UMN@BO-PQ�xI)PK,b7F.WJ�� £9��[xz:7+5\?_5�O-PX5�1�@BJU,b(/.G46O-3+(/./,b@BJ�=<O_(/.W&)1�&HO-(/Ay,-@�5jV+@B58A�5�(S1�5L.�&H(G1B,-4+I)5LA\¡\,b(/.4W`W@B58A�V658=d1B&)D_5�IHJ-[

£b*�@BO9Z �9*�@BO9Z%/,_=<5f,b@B58,/`0P}Ì ¢+[ 9S¿A4 ¢+[ 9S¿A4Å�&H(+&)PR3+P �/O9Z ,b@B58,Í;fMN@BO-(S1B,-I|,-@�5L, ¢+[¾9£ ¢+[¾9£��3+PR4F58@�ObMcZ:,91�58@y=<&H@B=�3+&}1>A ¡&¨ ¡&¨�iO-&HIm.W58VW1�7k`/P ¢+[H¡�£ ¢+[�4JƯC@B&)PK,b@BJ�A�3+@�Mq,-=<5\,-@�5L,+`0P¦Ì ¡-[ � 9+[¾�058=�O-(/./,b@BJ�A�3/@�Mq,_=<5j,b@B58,+`0P¦Ì 9-�/[ £ ¿Î¨/[ Æzm3/4F5a,-@�@>,b(/?-5�PX58(_1 �S1B,-?-?-58@�5L.v`W=<&H@B=�3+&)1BAy=<@BO_ABA�*�=�O-3+(S1�58@x�FO9Zzm3/4F5aA�V/,_=<&H(+? ¯CI�Ï�9_4W[ ��P�PЯt17Ï�9_��P�P�iO-V+V65�@:1B3+465aA�V658=�&}r6=�,91B&)O_(/A �R[ �R[�Ï ¡E¾W[ ÆaPXPo`+ud[ �a[ÑÏ ¡8£/[ ¨aPXP�iO-V+V65�@:rF(oA�V658=<&)rF=8,91�&HO-(FA ¢+[H¡&¨_¾aPXPQ1B7+&H=> |`W£_¨_¾ar/(/A7;EP

z',b4/I)5X¡-h�Òe58O-PX5<1B@�J�.W5<r/(/&}1B&)O_(�O-M�1B7+5R�i3�;-�i3o,b&H@>=<O0O-IH5�@:3+(/.+5�@�A�1�3/.WJzm5LAl1��OF[

:yO9Z�A � &H@£ Y � T �:� � &)@ § Y�q 0?-Z®;E 0?S,-A>� � &H@ OQ

�N 0?³;9A>� ��,91B5�@£ Y � T �:� ��,91�58@ OQ�N 0?³;9A>�

¡<* � £ 9b£F[ Æ ¢/[ ¢_¢S¿J9 ¢+[ 9-�_� �/[ £ ¡-[�49£H44E* � £ 4JÆ/[ Æ ¢/[ ¢_¢S¿JÆ ¡-[�49£S� �/[ £ 4W[�4-¾-¢99* � £ 49£F[¿ ¢/[ ¢_¢A¨�Æ ¢+[ 9AÆ_4 �/[ £ ¡-[�49£0¾£b* � £ 9�4+[¿ ¢/[ ¢/¡&¨_4 ¡-[ £_�-£ �/[ ¾ ¡-[�4J9/¡¾E* � £ 4b�/[ £ ¢/[ ¢/¡�£S� ¡-[ �S¿W¡ �/[ ¾ ¡-[�4JÆ-£¨9* � £ 49£F[ � ¢/[ ¢/¡&9�¨ ¡-[ £_4_¾ �/[ £ ¡-[�4J9S¾¡<*n� � 9b£F[ 4 ¢/[ ¢_¢S¿-¾ ¢+[ �AÆS¾ �/[ 4 ¡-[ ÆAÆ/¡4E*n� � 4_¿W[ ¢ ¢/[ ¢_¢A¨S¾ ¡-[ ¨�4-� �/[ 4 ¡-[ Æ-��Æ99*n� � ¡E¿W[¿ ¢/[ ¢_¢A¨/¡ ¡-[ ¨A¨�9 �/[ 4 ¡-[ �AÆ/¡£b*n� � 9A9/[ Æ ¢/[ ¢/¡&¨_� ¢+[ ¨_¾-� �/[ 4 ¡-[ ÆA9/¡¾E*n� � 4J¨/[ � ¢/[ ¢_¢AÆ�9 ¡-[ ¢+¡L¢ �/[ 9 ¡-[ ÆA¨-£¨9*n� � 4W¡_[ 9 ¢/[ ¢/¡E4_¾ ¡-[ 9-�/¡ �/[ 4 ¡-[ ÆA¨S¾

z',b4+IH5�4Wh>�YO-3+(F.+,b@BJU=<O_(/.W&)1�&HO-(/A

Page 7: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

Ó WX_� T �x� �t;WVk[ ,-.WD9,-(/=<5L.

�Y]��i�/�4/,-A�&H=�Y]��i�+�

�S3+&T=> �Y]^�i�+�

¡<* � ¡-¡_` 4 ¡E4+[ ¨_� ¡E4W[ ¨b£ ¡E9+[H¡&Æ4E* � ¡L¾+` � ¡L¾+[ £S� ¡L¾W[¾W¡ ¡E¾W[ ÆAÆ99* � ¡8¢/` 9 ¡-¡_[ ¢_� ¡-¡-[ ¢_¾ ¡_¡-[ 9AÆ£b* � 4W¡_` 9 4W¡_[ £S¢ 4W¡-[ £�Æ 4+¡-[�4b�¾E* � ¡&Æ/` Æ 4b¢/[ ¢_� 4b¢+[H¡�£ ¡EÆ+[ Æ-¢¨9* � ¡E¿W` £ ¡E¿W[ £_£ ¡E¿0[ £�Æ ¡9¿0[¾b¢¡<*n� ¡8¢/[ £ ¡8¢/[ 4�4 ¡8¢+[H¡8� ¡L¢+[ £�¨4E*n� ¡-¡_[ Æ ¡-¡_[ £_Æ ¡-¡-[ £/¡ ¡_¡-[ �A¨99*n� ¡8¢/[ 4 Æ+[ Æ-� Æ+[ Æb£ ¡L¢+[H¡8�£b*n� ¡-¡_[)¡ ¡8¢/[ Æ_� ¡8¢+[ Æ-¢ ¡_¡-[ 9_¾¾E*n� ¡8¢/[ � ¡8¢/[ ¨�Æ ¡8¢+[ ¨S¿ ¡L¢+[ ��4¨9*n� ¡E4+[ 9 ¡-¡_[ �0¿ ¡-¡-[ �b£ ¡=4W[ 9A9

z�,-4+IH5�9+hx��3W1�IH5<1^,-&)@:1B5�PXV65�@>,91�3/@�5

Ô WX_�  0?_ZÕ; 0?_,-A��

�t;WVk[ ,-.+DE,-(/=<5L.�Y]��Y�+�

4/,-A�&H=�Y]��i�+�

�S3+&T=> �Y]^�i�+�

¡<* � ¢/` ¢_¢S¿Î9 ¢+[ ¢-¢0¿Î9 ¢+[ ¢-¢S¿J9 ¢/[ ¢_¢S¿J94E* � ¢/` ¢_¢S¿ÎÆ ¢+[ ¢-¢0¿ÎÆ ¢+[ ¢-¢S¿JÆ ¢/[ ¢_¢S¿JÆ99* � ¢/` ¢_¢A¨AÆ ¢+[ ¢-¢�¨AÆ ¢+[ ¢-¢A¨�Æ ¢/[ ¢_¢A¨�Æ£b* � ¢/` ¢/¡�£_¢ ¢+[ ¢+¡8£�9 ¢+[ ¢+¡�£_9 ¢/[ ¢/¡�£H4¾E* � ¢/` ¢/¡&9-¢ ¢+[ ¢+¡E9A9 ¢+[ ¢+¡&9-£ ¢/[ ¢/¡&9-£¨9* � ¢/` ¢/¡-¡&9 ¢+[ ¢+¡_¡E¿ ¢+[ ¢+¡-¡9¿ ¢/[ ¢/¡-¡9¿¡<*n� ¢/[ ¢_¢S¿b¾ ¢+[ ¢-¢0¿E£ ¢+[ ¢-¢S¿9£ ¢/[ ¢_¢S¿-¾4E*n� ¢/[ ¢_¢A¨_¾ ¢+[ ¢-¢�¨_¾ ¢+[ ¢-¢A¨S¾ ¢/[ ¢_¢A¨S¾99*n� ¢/[ ¢_¢A¨+¡ ¢+[ ¢-¢�¨+¡ ¢+[ ¢-¢A¨/¡ ¢/[ ¢_¢A¨/¡£b*n� ¢/[ ¢_¢-�+¡ ¢+[ ¢-¢_�+¡ ¢+[ ¢-¢-�/¡ ¢/[ ¢_¢-�/¡¾E*n� ¢/[ ¢_¢S¿-¿ ¢+[ ¢-¢0¿ÎÆ ¢+[ ¢-¢S¿JÆ ¢/[ ¢_¢-�_¢¨9*n� ¢/[ ¢_¢-�A¨ ¢+[ ¢-¢_�S¿ ¢+[ ¢-¢-��¨ ¢/[ ¢_¢-�0¿

z',b4+IH5j£/hx��3W1BI)5�1^,b&H@�,b4/A�O-IH3W1�5j703+PX&T.W&}1lJ

Ó×Ö _� T �x� �t;WVk[ ,-.WD9,-(/=<5L.

�Y]��i�/�4/,-A�&H=�Y]��i�+�

�S3+&T=> �Y]^�i�+�

¡<* � ¡8¢/` 4 ¡8¢/[ ¢_� ¡8¢+[ ¢-� ¡L¢+[ ¢_¾4E* � ¡8¢/` 9 ¡8¢/[ 9�9 ¡8¢+[ 9A9 ¡L¢+[�4b�99* � Æ+`¾ Æ+[ £-£ Æ+[ £-£ Æ/[ £H4£b* � ¡&9/` ¾ ¡&9/[)¡9¿ ¡&9+[H¡�£ ¡E9+[ 9A¨¾E* � ¡&9/`)¡ ¡E4+[ ¨-£ ¡E4W[ ¨+¡ ¡=4W[À¿b¾¨9* � ¡E4+`)¡ ¡-¡_[¿W¡ ¡-¡-[À¿9¢ ¡_¡-[À¿ÎÆ¡<*n� ¡8¢/[ � ¡8¢/[ �_4 ¡8¢+[ �+¡ ¡L¢+[ �+¡4E*n� ¡-¡_[ 4 ¡-¡_[ 4A¨ ¡-¡-[�4b� ¡_¡-[�4b¢99*n� Æ+[ � Æ+[ �A9 Æ+[ �b£ Æ/[ �_¢£b*n� ¡-¡_[ Æ ¡-¡_[ �_¢ ¡-¡-[ ��4 ¡_¡-[ �-�¾E*n� ¡8¢/[ � ¡8¢/[¿W¡ ¡8¢+[À¿Î9 ¡L¢+[À¿0¡¨9*n� ¡-¡_[ £ ¡-¡_[ 9_� ¡-¡-[ 9AÆ ¡_¡-[ 9_¾

z',b4+IH5a¾Whx��3W1BI)5�1^=<O0O-IT,b(S1:1�58PXVF58@B,b1�3+@B5

Ø�  ����

�t;WVk[ ,-.WD9,b(F=<58.�Y]��i�+�

4F,-A�&H=�Y]^�i�+�

�S3+&T=> �Y]��Y�+�

¡<* � Æ+` 9S¿J¨ �+[À¿Î9b£ �/[¿-¾W¡ �+[¾JÆ�94E* � ¡E¿W` Æ�9+¡ ¡8�+[�4b¢�Æ ¡L�+[H¡&¨�¨ ¡E¿W[ ¨�Æb£99* � ¾W`À¿E£H4 ¾W[ £_¢�4 ¾+[ £F¡E4 ¾W[ 9-¢_�£b* � 4-¾+` �/¡&9 49£/[ ¢AÆ_� 4A9+[ Æb£_9 4-¾+[ ¢�ÆS¿¾E* � 49£F` Æ�¨A9 4A4W[ £S¾b£ 4�4W[�4-¾_¾ 4J9/[ ¢�¨S¿¨9* � ¡&Æ/`)¡E¨�4 ¡E¿0[H¡�£F¡ ¡9¿0[ ¢-�/¡ ¡E¿W[ ¾S¿J4¡<*n� 4W¡_[¿W¡-¡ 4W¡-[ �S¿W¡ 4+¡-[ Æb£_¨ 4W¡_[¿J¨b£4E*n� 4-¾+[ ¢_4A4 4-¾W[¾9£_Æ 4_¾W[ ¨b£_Æ 4-¾+[ ¢�¨_¾99*n� ¡E4+[ ¨_�S¿ ¡E4W[ ÆS¿b� ¡E9+[ ¢�4-¢ ¡E4+[¿W¡�££b*n� 4JÆ/[ Æ0¿E£ 4JÆ+[�4b¢�9 4AÆ+[ 9_¾-� 4JÆ/[ �_¢A¨¾E*n� 4b¢/[ ¾AÆ-� ¡&Æ+[ Æ+¡9¿ 4-¢+[ ¢-¢�Æ ¡&Æ/[ ��Æ-¢¨9*n� 4J¨/[ 90¿9¢ 4J¨+[H¡&Æ_¢ 4A¨+[ 9A9-£ 4-¾+[ Æ_�_¾

z�,-4+IH5�¨+hx�Y,bV/,_=<&)1lJ�CIHPK,b7/.WJp1�58A�1�5L.�,GA�5<1fO-Mx1lZY5�IHD-5X£b*�@BO9Zn,b(/.��9*�@�O9Z¹7+58,b1j5�;+=>7/,b(+?_5�@>A�`v46Ob1B7�&H(�.W@BJg,b(/.�ZY5<1a,b&H@�*�A�&H.+5�A�3+@�Mq,-=<5

=<O_(/.W&)1�&HO-(/A8[Gu~(+I)5�1�*�O-3W1BI)5�1RD9,bIH3+5LA\ObM:1�58PXVF58@B,b1�3+@B5-`'703+PX&H.W&)1lJ�Zi58@�5K?_&)D_5�(k`�1�O_?-5<1B7+5�@aZy&}1B7�1�7+5��/O9Z =�O-(/.+&}1B&)O_(/A\O-(46Ob1�7G�/3/&H.+A8[C%+O_@:1�7+5\Zy7/O-IH5fA�5�1:O-M'46O-3/(/.+,b@BJ�=�O-(/.W&)1�&HO-(FA:3+(/.W58@�Al1B3/.WJ-`+1�7+5\@B58A�3+I)1BA:O-4+1B,b&H(+5L.�Zy&)1�7o1B7+@�585\.W&}w|5�@B5�(S1(03+PX5�@B&H=8,bIe,bV+V+@BO_,_=>7+58A����Y]��i�/��Zy&)1�7 4F,-A�&H=p,-(/.�,-.+DE,-(/=<5L.�r/(�1B@�5L,91�PX58(_1L`^,b(F.¸�S3+&H=> /�Y]^�i�+�+��,b@B5pV+@B58A�5�(S1�5L.,b?S,b&H(/A�1C5<;WVF58@�&HPX5�(S1B,-IF.+,b1B,\&H(K1>,b4+IH58A×9j1�OÙ¨+[¬�i5L=�,-3/A�5^ObM|1�7+5eA�PK,-I)I6.W&}w|5�@B5�(F=<58AiObM|1B5�PXVF58@B,b1�3+@B5�465<1lZY5�58(�,-.E{�,_=<58(_11�3/4F5LA�`c1B7+58A�5K1�5LAl1>AaZY5�@B5U,b(�O_V+V6O-@�1�3+(+&)1lJ�1�OpV65�@�MNO-@BP ,pDE,-I)&T.+,b1�&HO-(�ObMy1B7+5�.W58D-58I)O_VF5L.�(S3/P�58@�&T=�,-IC1BOSO_IHA8`c4F5L=�,-3/A�57+58@�5\,-.+&H,-4/,91B&H=�r/(o46O-3+(/./,b@BJ�=<O_(/.W&)1�&HO-(G&HAy,X@B58,_A�O_(/,b4+IH5�A�&HP�V/I)&)rF=�,b1�&HO-(o70J0VFO-1�7+5LA�&TA�[tz:7+58@�5�MNO-@B5^1B7+5f,b(F,bIHJ_1B&H=8,bI|r/((03+PX5�@B&H=8,bI|1B@�5L,91�PX58(_1>A�=�,-(o4F5\3/A�58.GV+@BO-V65�@BIHJ-[ � IHA�O/`/,-(/.�MNO-@:1B7+5aAB,bPX5j@�5L,-A�O-(/A8`01�7+&TA�=8,-A�5e&TAy(+O-1y1�7+5a4F5LAl1�O_(+5j1�OA�7+O9Z¸1B7+5f=�,-V/,b4+&HIH&}1B&)5LA:ObMm1B7+5f,-.+DE,-(/=<5L.�=�OW.W58A8[

%+@BO-P 1B7+5XV+@B58A�5�(S1�5L.g.+,b1B,+`v&)1\&HAj=�I)5L,b@BI)JpA�7+O9Zy(�1B7/,91j1�7/5X=�O-PXV/,-@�&TA�O_(p465<1lZY5�5�(�(03+PX5�@B&H=8,bIc,b(/.�5<;WV65�@B&)PX58(_1>,bI@B58A�3+I}1>A'&HAt,_=�=<3/@B,b1�5x&H(X,bIHP�OSAl1t,bIHI01�7/5:,-(/,bIHJWA�5L.j1�5LAl1>A�`bMNO-@t46Ob1�7�7+5L,91t,b(/.RPK,-ABAm1B@B,-(/A�MN5�@c@B,b1�5LA�[mz:7/5:.+@�JS*�Zi5�1cA�3+@�Mq,-=<5=<O_(/.W&)1�&HO-(G7/,-A:,-IHA�OR465�58(�ZY5�[email protected]&T=d1B58.�&)(o,bIHI61�7+5fA�&)1�3/,b1�&HO-(/A8[tz:7+5j@�5LA�3+I)[email protected]&)w|5�@B5�(S1y(S3/P�58@�&T=�,-Iv,bV+V+@BO_,_=>7+58A,b@B5o�_3/&}1B5o=�I)OSA�5�58,_=>7$Ob1B7+5�@X4658=8,b3/A�5G1�7+5oIHO9Z°1�58P�V65�@>,[email protected]&)w|5�@B5�(/=�58A�4F5�1lZi585�(�,-.E{�,_=<58(_1�1�3/4F5LA�`Y,-A�5<;WV+IT,b&H(+58.,b46O9D-5_[�z:7+5�.+,91>,jV+@�5LA�58(S1�58.X&H(X1�7/&HAxV/,bV65�@C&TAv{l3FAl1i,\r/@BA�1xA�5<1xO-M|(03+PX58@�&T=�,-I}*�5<;WV65�@B&)PX5�(S1>,bI+=<O_PXV/,b@B&HA�O-(�ZYO-@B \MNO-@x1�7+5=<O_PXV+I)5�1�5�DE,-I)&T.+,b1�&HO-(UO-Mk1�7+5e.W&)w658@�58(_1:IH5�D-58IHAiObMk(03+PX58@�&T=�,-IFA�&)PR3+IH,b1�&HO-(UO-Mkr/(W*~,b(F.0*s1B3+465^7+5L,91i5�;+=>7/,b(+?_5�@>Ax.W58D-58I)O_VF5L.40J�1�7+5�,-3W1�7+O_@BA8[$]^O9Zi58D-5�@L`cMN@BO-P 1B7+5o?-O0OW. 58A�1�&HPK,91B&)O_($&H(�,-I)IY1�7/5GV65�@�MNO-@BPK,b(/=�5�VF,b@>,bPX5<1B5�@>A�`c1B7+&HAK=�O-PXV/,-@�&TA�O_(&TA\,�D_5�@BJp&HP�V6O-@�1B,-(S1\=�O-(WrF@�PK,91B&)O_(p1B7/,91\1B7+5XP�OW.W58I)&TAB,91�&HO-(�7/,_Aj4F585�(�.W5�D_5�IHO-V658.�=<O_@�@B58=<1�IHJ-[X%+@BO-Pµ1B7+&HAa,b(/.�(+5<;01D9,bIH&H./,91�&HO-(FAe1�7+5U=�O0.+58A\.W58D-5�IHO-V658.�=�,-(�465U,-.+58�S3/,91B5�IHJp3/A�58.�MNO-@j1B7+5K@>,91�&H(+?�,b(F.�.W5LA�&H?-(�ObMY1�7/&HA\5L�S3+&)V/P�58(S18[Uz:7+5

Page 8: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

7+&H?-7+58@k1B7+5Y.+58A�&)@B58.\.W5�1B,-&)ISObM+&H(WMNO-@BPK,91B&)O_(a,b(/.e1B7+5Y7+&)?_7+5�@m1�7+5i1�58PXVF58@B,b1�[email protected]&)w658@�58(/=<5i4F5�1lZi585�(a,_.E{�,-=�5�(S1m1B3+4658A8`E1�7+5�Y]��Y�+��=<OW.W5\Zy&)1�7�,-.WD9,b(F=<58.�r/(�(03+PX58@�&T=�,-Iv1�@B58,b1�PX5�(S1�3/A�5f&TA�PXO-@B5j(+58=�58ABA�,-@�J_[i%+O_@y1�5LAl1>A�Zy&)1�7�IHO9Z 1�5�PXV65�@>,91B3+@�5.W&)w658@�58(/=<5X&H(�=�O0O-IT,b(S1jA�&T.W5-`m�S3+&T=> /�Y]��i�/�p&TA\,b(�5<;01�@B5�PX5�IHJp3/A�5<MN3/Ic1�O0O-IcMNO_@�1B7+5X&)(F.W3/A�1�@B&H,-It5�(+?_&)(+585�@e1�7F,91f.W58A�&H?-(/Ar/(W*~,b(F.0*s1B3+465\7+58,b1:5�;+=>7/,b(+?_5�@>A�[

� AY,b(�&)IHIH3/Al1B@B,b1�&HD-5�@�5LA�3+I)18`S1B7+5�&H(WMNO_@�PK,91B&)O_(U?-&HD-58(U40JU,aA�&)PR3+IT,91�&HO-(�3/A�&H(+?U�Y]��i�/�S*�,_.WD9,b(/=�58.U=�OW.W5�&TAYV+@B58A�5�(S1�5L.&H(�1�7+5KMNO_I)IHO9Zy&H(+?�V+&T=d1�3/@�5LA�[o%+O_@\1�5LAl1a£-* � �NZy&)1�7 .W587S3/P�&T.W&)rF=�,b1�&HO-(F�<`'1�7+5�.+5<1B,-&)IH58.�PK,-V/A\ObM:r/(�1B5�PXV65�@>,91�3/@�5_`',-&)@1�58PXVF58@B,b1�3+@B5-`+,-&)@y703+PX&T.W&}1lJG,b(/.�D9,bV6O-@�=�O-(/.W58(/AB,91�&HO-(�@B,b1�5LAy,b@B5�V+@B58A�5�(S1B58.�MNO-@�,K=<58(S1�@>,bIv,9;W&T,bI|r/(o&H(�r/?_3+@B5\¾+[

%'&)?_3+@B5X¾+h�%+@BO-PµIH5<M�1\1BO�@B&H?-7S18h^r/(g1B5�PXV65�@>,91�3/@�5_`k,b&H@�1B5�PXV65�@>,91�3/@�5_`k,b&H@j,-4/A�O-IH3W1�5�703+PX&H.W&)1lJg,-(/.g=�O-(/.W58(/AB,91�5�@>,91�5PK,bV/AYMNO_@�,X=<5�(S1B@B,-I|r/(oObM�£-* � 1B58A�18`+O_4W1B,-&)(+5L.G3/A�&H(+?K,-.+DE,-(/=<5L.F�Y]��Y�+�G=<OW.W5

%'&)?_3+@B5V¨/hmzm58PXVF58@B,b1�3+@B5iV/@�O-r/I)5LAc,bIHO-(+?e,�=�5�(S1�@>,bIWA�5�@BVF58(_1B&)(/5e�s,b?_,-&)(FAl1t,b&H@'�/O9Z^�d[t��4W1B,-&)(+5L.a3FA�&H(+?j,-.WD9,b(F=<58.6�Y]��i�+�=<OW.W5

%'&)?_3+@B5:¿0h�]�58,b1�1B@B,-(/A�MN5�@'V+@�O-r/IH58A',bIHO-(+?e,�=�5�(S1�@>,bI0A�58@�V65�(S1B&)(+5e�q,-?_,b&H(/A�1',-&)@��/O9Z^�d[C��4W1>,b&H(+58.\3FA�&H(+?j,-.WD9,b(F=<58.6�Y]��i�+�=<OW.W5

Page 9: Numerical Simulation Of Dehumidifying Fin-And-Tube Heat

ÁkOW=8,bIYDE,-I)3/58A�ObMj=<O0O-IT,b(S18`c1B3+465p,b(/. ,b&H@a1B5�PXVF58@B,b1�3+@B58AX,-@�5GV+@B58A�5�(S1�5L.�MNO-@K,�=<5�(S1B@B,-I:A�5�@BV65�(S1�&H(+5G&)( r/?-3/@�5b¨+`MNO-IHIHO9Zy&)(+?�=<O0O-IT,b(S1Y�/O9Z\`S1�7/,b1y&HA8`+,b?S,b&H(/Al1:,b&H@�*2�/O9Z\['u�1y&HA:=<IH58,-@�IHJKA�7/O9Zy(U1�7F,91:1�7+5e1B5�PXVF58@B,b1�[email protected]&}w|5�@B5�(F=<58AY&H(/=<@B58,_A�51�OR1�7/5j,-&)@Y&H(+I)5�1YV6O_A�&)1�&HO-(k[tu~(�r/?-3+@B5j¿\1�7/5j=>7F,b@>,-=d1B5�@B&HA�1�&T=yD9,bIH3+5LAxO-Mm7+58,b1i1B@B,-(/A�MN5�@:@B,b1�5e,b@B5^V+@B58A�5�(S1�5L.KMNO_@x1B7+5\A�,-P�5A�5�@BVF58(_1B&)(/5-[�ÚC,bIH3+58A�ObMxA�5�(/A�&H4+I)5G� ��Û f=Ü�G �<`6IT,91B5�(S1�� �5Ý f=Ü�G ��,b(/.o1BOb1>,bI'7+58,b1^1�@>,b(FAlMN58@R� � fEÜLG �:MN@BO-P­r/(g1�O�,-&)@e,b(/.1�7/5�7/58,91e1�@>,b(FAlMN58@^MN@BO-P r/(�1�O�1�3/4F5K,91e1�7/5RrF(g4/,_A�5o� � f=Ü�q �e,b@B5R.+&HA�V+IT,EJ-58.k[\u�1j&TAeD-58@�Jo&H(_1B5�@B58A�1�&H(+?U1BOoVFO_&)(S1jO-3W11�7/5^&H(W�/3+58(/=<5�ObMk7+5L,91i=�O-(/.W3F=d1�&HO-(X1B7+@BO-3+?_7X1�7+5^r/(U&H(�,b&H@��FO9Z�.W&H@B58=d1B&)O_(k`_1�7/,b1i&TACD0&HA�3/,-I)&H��5L.�1�7+@BO-3+?_7X1�7+5e.W&)w658@�58(/=<5465<1lZY5�5�( � f=Ü�G ,b(/. � fEÜ5q [�z:7+5UV+@>,-=<1�&T=�,bIY.W&TA�,-V+VF5L,b@B&)(/?�ObM�IT,91�58(S1a7+58,b1a1B@B,-(/AlMN58@a&H(�1�7+5o,b&H@f&H(+IH5<1R�8O-(+5�&HAR,bITA�O@B5�IH5�D9,b(S18[ Þ

¿ Ö!Õ ¿ÀÛÇÜ-» ! Ö!Õ »z:7+&TA�V/,bV65�@XV+@B58A�5�(S1BA�,b( O9D-58@�D0&H5�Z 1�7+@BO-3/?-7 .+&}w|5�@B5�(S1X(S3/P�58@�&T=�,-IYA�&HPa3+IT,91B&)O_($PXOW.W5�ITAX.W5�D_5�IHO-V658. 40J�1B7+5�,b3W*

1�7/O-@>AK��MN@BO-P�7/&)?_7+5�@j1BO�I)O9ZY5�@\?_5�(+58@B,-I)&)1lJp,b(/.�=�O-PXV+3W1>,91�&HO-(F,bIc1�&HPX5U=<O_(/A�3/P�V+1�&HO-(F�<hf&T�f,-.WD9,b(F=<58.�.W5�1B,b&HIH58.�PXO0.+5�I�q,_.WD9,b(/=�58.F�Y]^�i�+�+�<hv.W5<1>,b&HI)5L.�PXO0.+5�Ic3/A�&)(+?�Pa3+I)1�&T.W&HPX5�(/A�&)O_(/,bI�r/(g=�O-(/.+3/=d1B&)O_(g,b(/,-I)JWA�&HA8�6&)&���4F,-A�&H=R.W5<1>,b&HI)5L.�PXO0.+5�I�N4F,-A�&H=E�Y]��i�+�/�dh0.W5<1>,b&HI)5L.RPXOW.W58I/3/A�&)(/?jr/(K5<�U=<&H5�(F=<&H58A8�_&H&)&��tA�&)PXV+IH&)r/58.XPXOW.W5�I'�q�S3+&T=> /�Y]��i�+�/�dhb�E*~�^zy��4F,-A�58.�PXO0.+5�I3/A�&)(/?X,XPXOW.W&)r/58.G58(_1B7/,bIHV0JS*2PX5<1B7+OW.�,-(/,bIHJWA�&TA8[Cz:7+5f,-.WD9,-(/=<5L.F�Y]��i�/��&TAy5�;0V/IH,-&)(+5L.�&H(oPXO-@B5j.+5<1B,-&)I2`WMNOW=<3FA�A�&)(/?X1�7+5,91�1�58(_1B&)O_(�&H(�1�7+5K,-&)@�*�A�&T.W5�,-(/.gr/(�,b(/,-I)JWA�&HA8`kA�V658=�&H,-I)IHJ�&H(�.+5�703+PX&H.+&}MNJ0&H(+?�=<O-(F.W&}1B&)O_(/A8[��C;0V65�@B&HP�58(S1B,bIC=�O-PXV/,-@�&TA�O_(ObM'1�7/5f.W&}w|5�@B5�(S1yPXOW.W5�ITAy7/,_AyA�7+O9Zy(o,�@�58PK,b@B E,-4+IH5e,-?-@B5�5�PX58(_1:465<1lZY5�5�(o(03+PX5�@B&T=�,bIk,-(/.�5<;WVF58@�&HPX5�(S1B,-Ik.+,91>,RMNO-@�,bIHI1�7/5�(03+PX5�@B&H=8,bI+,bV/V+@�OS,-=>7+5LA�`94658=8,b3/A�5:1�7/5�5<;WV65�@B&)PX5�(S1>,bIW1B58A�1xZY,_AcVF58@�MNO_@�PX5L.RZy&)1�7KIHO9Z�=<O0O-IT,b(S1c1�58P�V65�@>,91B3+@B5�.W&}w|5�@�*5�(F=<58A8[tz:7+5eVFO-1�5�(S1B&H,-IF&H(�1B7+5j,b(/,-I)JWA�&HAxObM�,R.W5�703+PX&T.W&}MNJ0&H(+?Rr/(W*~,b(/.0*21�3/4F5e7+58,b1Y5�;+=>7/,b(+?_5�@x1�58A�1:7/,-Ai4F585�(oA�7/O9Zy(KMNO-@1�7/5f7+&H?-7+5LAl1^IH5�D_5�IkO-MCA�&HPa3+IT,91B&)O_(k[ � ?-@B58,b1:IH5�D_5�I�ObMt.W5<1>,b&HIm&TA�V+@B58A�5�(S1�5L.�MNO-@yr/(p,-(/.�A�5�@BVF58(_1B&)(/5j1�5�PXV65�@>,91B3+@�5_`/7+5L,911�@>,b(FAlMN58@�,b(/.�=�O-(/.W58(/AB,91�5j@>,91B5\PX,-V/A8[��Y5�7/,ED0&HO-3+@:1B@�58(/.+A�,-@�5\=<IH58,-@�IHJ�A�7+O9Zy(k`W&H(/=�I)3/.+&)(+?�7+58,b1y1�@>,b(/A�MN5�@�=�O-(/.W3F=d1�&HO-(1�7/@�O_3+?-7�1�7+5fA�O-IH&T.�58I)58P�58(S1BA8[ ß

¹ÿ¿áà Õ�Öãâ Û Ú�#åä/Ú2Ø Ú2Õ ½Ù»z:7+&TA�A�1�3/.+J�7F,-AU465�58( A�3+V+V6O-@�1�58.¸4SJ 1�7/5g�C3+@BO-V658,-("�iO-PXPX&HABA�&)O_(�&)(�1B7+5pMN@>,bPX58ZiO_@�  O-M\1�7+5���O_( ��3/=�I)5L,b@

�C(+58@�?_J�¯x@�O_?-@>,bPXPX5�æ0�e�®Ák��u�u�ua�q=�O-(S1�@>,-=<1�(03+Pa465�@�æ0����9b*l�YzCÆ_�9*�¿9¢/¡E4U�s��Òµ¡E4E*�Òeu�Òf�j����,b(/.o40J�1�7+5�çB�iO_P�&TA�&hè_(u~(S1�58@�PX&H(+&HA�1�58@�&T,bIk.+5f�i&H5�(F=<&T,RJGzm5L=<(+O_I)O_?AéT,=êR�q@�5�Ml[Cz:u��ëÆ�Æ9*~¢S¿-¿b¢_�<[

ì ¾ ÚRí¢Ú ¾ ÚÅÕ ¿ Ú »àu��ã�±N¦�±>p}·R|~xup�·zx�|@|~hRybnµ¦�±o¦�egrU¶Ifisus§�uîNÎlÉ&ï�ð_ñ�ÉwÌFÐhòUÎ�ñ�ÉwÌRʦó�ñmÎ�ÐmÐ�ôAñlÎLõCñnö�÷ùø�úzÉ&ñ�É ÍûïDÎ�ñ}ÑÈÐ�ï§ÑdÍqЦörò®ü�ýuÉ&ï5ð�ôFÏ}΢ÉwÌRÊ}þ�ö�ôHËwÎ�ñlÎlÊóuýuÉ�ïDÎVü8ÑÈ̦ÿ�ôAñpòiÉ Í}Î�Ðm���ZÃH¥�fqkmxu��fihPj}|ws&nI·Ff�km��|ws&|whFy¢°�su�Fx�y¢¤�pixufihFpif����i­Y�w� ���Rhzrz¦&�Y�(�i«P®��R� � ®�¦à �Uã���¦(eg·F|whFv¢|whRy]e[¦��2|whzvz���PÎ�ÌXÎ�ñ�ÉEý Ñ���ÎlÊ}úzÎmÉ�ï×ï�ñ�ÉwÌFÐhòUÎ�ñÁÍ�ö&ñ�ñmÎûýuÉ&ï§Ñö~ÌÙòûö&ñ�ý ö&ô�ËwÎ�ñ� �Ì�PÎnö���Î�ï�ñ��w���¯hPjU¦ �YrY�HkmhR|ws�Æ[fU|~jN|~hRy

� |w�l�[n(k}|whz���Èfqk����Å���i­Y­Y®Y���Rhzrz¦F©H� � ©Y©�� � «Y«z¦à ©�ãÇe[¦��z¦��ª|��YfihF¥�r~kljU�5øNö&ñ�ñlÎûýuÉ&ï§ÑöwÌzЮòlö&ñÙîoÎmÉ�ï¦ð_ñlÉ~ÌFÐhòUÎ�ñ]ÉwÌ�Êbü�ý ö���ü<ñ}ÑdÍûï§Ñö~̵ø�úzÉ�ñlÉ ÍûïDÎ�ñ}ÑÈÐ�ï§ÑdÍqÐböròLþ�ö&ô�Ë7ñmÎlÊRü8ÑÈÌz�[± �leg·F�¤��H��¥�rY�lxu�z��¤Hf�kmx�fq�i�F� rws§¦�®~­H���i­Y�w©H�R¥z¥(¦&�U­��H�Y®P¦

à «~ã�±N¦(Æ�¦���su��|w·FyH�]|whFy"!o¦�e[¦Z£8x�vwvY�i�¬ó>Î�ñ òlö�ñ#�¡ÉwÌ�Í}ÎLÿzÑ$��ôAýuÉ&ï§Ñö~Ìáösò�%ÍôAý ï§Ñ'&$(uö�� õCñ��*)DÉwÌ�Ê�+ ö&ñ-,�Î�ï/.`îNÎlÉ&ï 021 Í�úzÉwÌ3PÎ�ñ�Ðm���kmrPpqfifUyzxuhzvY� 4�5'6�¦7�Dh�jU¦HÆ[fU|~jcn(k}|~hF���Kfqk{egrwhz�KfqkmfihFpqfÇ�$�Å|w�l·zx�hzvwjmrwh����z� rYs§¦z«z�z¥F¥(¦z©Y�Y®��P©Y©Y��¦

à � ã�°g¦����lpU|whzfi�i��e[¦8��¦U��9qkmf�:q¬¯¤Hfqv |~klk}|��P|~hRyo±N¦<;µsuxu�w|H�<ð úFÎ�ñ���ÉEýHÉwÌRÊ>ü�ý ôHѧÊ=&¯Ê<�wÌRÉ���ÑdÍ?>µÎ�úHÉwËUÑö&ôJñ>öròNõ½ö&ôzÏlý�Î@&-÷FÑ ÷zÎCøNö~Ì�ÊPÎ�ÌzÐiÎ�ñ}ÐÉwÌ�ÊA0IË~É�÷Aö�ñlÉ&ïÂö&ñ}Ð@BC�EDVôF��Î�ñ�ѧÍ}É&ýaÿ�ï�ôzÊ��w�G�¯hPjmfqkmhF|~jmxurYhF|ws2�Yrw�zkmhF|wsZrw�CHµ�z��fqkmxupU|ws � f�jm·Fr�yz�[�ÈrwkoÆ[fU|~j{|whRy4°�su�Fx�y<°�sur�¶I���U­w­ � ���FhFrH¦R­���®~�H�#��®w­ � ¦

à 4�ãÇe[¦2��¦���9qkmf@:q¬¯¤HfivY|~klk}|4fqj�|~sd¦u��ð úFÎ�ñ#�¡ÉEý\ÉwÌRÊ�J�ô�ÑdÊ=&DÊ��~Ì�É���Ñdͦö�÷Hï§Ñ$��ÑÈÐ�É&ï§ÑöwÌ öròK �ÌL&DÉwÌ�Ê�&Âï�ôzÏ}Î}úFÎlÉ&ï�ÎM1 Í�úHÉwÌNPÎ�ñ}ÐO��Ñ ïpú ïpúzÎ÷HôJñy÷Aö~Ðiήörò½ö ÏûïBÉwÑÈÌzÑÈÌNÇÐmÑ�wÌzÑ gÍmÉwÌ�ï�ñlÎmÊ�ôFÍûï§Ñ�öwÌFЮöròoÏ�ö&ïpú@Ë�ö&ý ôF��Î�ÉwÌRÊP�gÎ�Ñ��úÎï§��°�xuhR|~sG!cfi¥�rwkljU¦7�Yrw�Fsufo¥zkmr8Q�fipqj �3;ª��©~¬¯eIn\­w�~¬®w�����Á�d°�±�nIƪ�2!µ�8���FÆ[fU|~jc|~hRy � |w�l�[n(k}|whz���Èfqk[n�fip}·FhzrYsurYvwxupU|ws�egfihPjmfqkN�BeIn\n>e\������rYs���jmfip}·Fhzx�p � hFxu� f�km�lxujD�Çrw��eI|�j}|wsurYhzx�|� � �8e\���Rn(fqklk}|w�l�m|���±[¥Hkmxus��~�Y�H�w¦

à ®UãR;�¦~õª|~kmp@S�|�¬Bþg|~s�s�|wyF|~kmfq�i�He[¦<��¦���9qkmf�:�¬�¤�fiv |�klk}|H�T�z¦<![xuvYrws�|H�P|~hRyo±N¦�;µsuxu�w|H�=õ�Î�ïBÉwÑ ý�ÎmÊ DVôN��Î�ñ}ÑdÍmÉEýÎÿFÑ$�®ô�ýuÉ�ï§ÑöwÌ�öròVøNö~Ì�ÊPÎ�ÌzÐiÎ�ñ}ÐÉwÌ�Ê�0IË~É�÷Aö�ñlÉ&ïÂö&ñ}ÐVU&ÐmÑÈÌN>ó�ôJñmÎ\ÉwÌRÊ�%4Ñ�1PÎlÊ�(>Πò�ñ}Ñ�PÎ�ñlÉwÌ�ï§�<�¯hPjmfqkmhR|�jmxurYhR|~s�egrY��¥Hkmfi�l�lrwk���hFvYxuhzfifqkmxuhFvµegrYhH�Èfqkmfihzpif8|~j����Hk}yz�Ffw�� rYs§¦R���&�U­w­Y�H�F¥F¥&¦R�w©Y­8�P�w«w«z¦

à ��ãÇe[¦7;µs�xufqjU�Fe[¦F��¦H��9qkmf@:q¬¯¤HfivY|~klk}|H�L;�¦Fõª|~kmp�S�|�¬Dþ8|wsus�|Yyz|~kmfi�i�7!N¦W;[k}yHr=Xzf�:Y�H|whFyY�H¦R¤��Ry�kmx[Z��Hõ{ÑÈÐqÎ#\³ö�ïDÎ�ñ��5ö�& J�ôN]dÊwѧÍ�öÇÊPΪÑÈÌ_ïDÎ�ñ#&ÍmÉ���ÏqÑdÉYÊ=ö&ñmÎ�ЪÍ�ö��V÷HÉ ÍûïÂö~Ð� ÉwÐ�&yý ]'^ûôHѧÊ=ö3B_��÷³ý ÑdÍmÉ ÍqÑa`wÌ¢É�ñlÉ Ê~ÑdÉ Ê=ö&ñlÎ�ÐoÊPÎ{É&ôJïÂö���öUÍqÑa`wÌb��Î�Ë~É�÷Aö&ñlÉ ÊEö&ñmÎ�Ðm�X±chR|wsufi�Iyzf��¯hFvwfihFxufqkcS�|� fip�d~hFxupU|H¦F²K�M�M�IegrYhFv~kU¦7Hµ|wpY¦Fyzfe�DhFvH¦ � fip�dwhFxupU|��R� rws§¦F«H�(�i­Y­Y����¥F¥&¦ � �H��� � � ®�¦

à ­�ãÇe[¦K;µs�xufqjU��e[¦ ��¦[��9qkmf@:q¬¯¤HfivY|~klk}|H��|~hRy ±o¦ ;µsux��w|H�®ü(ÉwÐ�ï�Í�öUÊPÎ�òlö&ñV �Ì7&¯É~Ì�Ê=&ï�ôzÏ�ÎXúFÎlÉ&ï�ÎM1 Í�úzÉwÌNPÎ�ñ}ÐXñ�É&ï§ÑÈÌNÙÉwÌRÊ ÊPÎ�ÐmÑ�wÌ_f^ûô�ÑdÍ�gAø�î 0�ÿ_ÿz���¯hPjmfqkmhF|ws?![fi¥�r~kljV�h!c¬¯eIn\n>eI���q¬D�H�9�dn�fqklk}|w�l�m|Y����ƵfU|�j�n(k}|~hF���Èf�k�n�fip}·FhzrYsurYvwxupU|ws[egfihPjmfqk��BeIn\n>e\��¦���rYs���¬jmfip}·FhFxup � hFxu� fqkm�lx�jD�Ár~��eI|~j}|~surYhFx�|@� � �8e\���W�ªfipifi����fqkc�~�Y�H�w¦

àu�U��ãP�z¦ ��¦FnI·zkmfisuÄ fqs�yX�Rnµ¦ ÆN¦Li{�Ffq·FhÁ|whRyY�z¦ �ÿ¦L![|w���lf��P�að úFÎ�ñ#�¡ÉEýZÎ�ÌzË�B8Î�Ì3wÑÈÌXÎmÎ�ñ}ÑÈÌNw�R©~k}yÇfUy&¦u�F��kmfihPjmxupif{Ƶ|wsus§���U­w­Y��¦