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Analysis and Optimization of Diffusion-Driven, Multiple-Effect Solar Still

Permanent Link: http://ufdc.ufl.edu/UFE0041158/00001

Material Information

Title: Analysis and Optimization of Diffusion-Driven, Multiple-Effect Solar Still
Physical Description: 1 online resource (229 p.)
Language: english
Creator: Mitten, Nathan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: brine, desalination, diffusion, distillation, effect, multiple, renewable, saline, solar, water, wick
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: ANALYSIS AND OPTIMIZATION OF DIFFUSION-DRIVEN, MULTIPLE-EFFECT SOLAR STILL Forty-percent of the world s population does not have access to clean, potable water. This need can be met in many cases by family-sized, solar-thermal desalination systems that turn saltwater and brackish water into fresh water. These systems can provide truly sustainable solutions for a community when they are affordable, reliable, and powered by a renewable energy source. The cost per liter of production from these systems can often be reduced by increasing the thermal performance. This study focuses on developing a detailed computer model in the Matlab environment based on first principles for analyzing the heat and mass transfer phenomenon within these systems in order to fully understand their operation and thereby improve their performance. The model includes two-dimensional resolution of temperatures, mass flow rates, salinities, and property data throughout the system both in the vertical direction along the evaporator surface and in the horizontal direction at each component boundary. This two-dimensional model is more accurate than the one-dimensional counterpart, especially in the later effects, due to the nonlinearities of the heat and mass transfer equations. The model also calculates the temperature drop through each component of the system including the partitions, wicks, vapor spaces, and condensation films. The analysis has elucidated the key design parameters with the highest impact on performance as defined by the Performance Ratio. All system parameters were logically categorized and parametrically modeled for different numbers of effects. The primary determinates of performance were found to be the sensible load on the system for heating the supply brine and the evaporative Heat Rate Ratio (HRR). Essentially, a lower sensible load allowed more thermal energy remaining at each effect to be passed through to the next effect, and a higher evaporative HRR meant that at each effect more heat was being transferred via evaporation than through other mechanisms. Based on these results, design guidelines were set forth to optimize the key parameters. It was found that novel heat recuperation systems proposed in this work were perfectly suited to both decrease the sensible load and increase the evaporative HRR. According to the model, a fifteen-effect system with multiple-stage heat recuperation is able to achieve a performance ratio over eight representing a production of nearly 70 kg/m2day at a solar insolation of 20 MJ/m2day. This is significantly greater than any other small-scale solar thermal distillation system in the literature.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nathan Mitten.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Ingley, Herbert A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041158:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041158/00001

Material Information

Title: Analysis and Optimization of Diffusion-Driven, Multiple-Effect Solar Still
Physical Description: 1 online resource (229 p.)
Language: english
Creator: Mitten, Nathan
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: brine, desalination, diffusion, distillation, effect, multiple, renewable, saline, solar, water, wick
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: ANALYSIS AND OPTIMIZATION OF DIFFUSION-DRIVEN, MULTIPLE-EFFECT SOLAR STILL Forty-percent of the world s population does not have access to clean, potable water. This need can be met in many cases by family-sized, solar-thermal desalination systems that turn saltwater and brackish water into fresh water. These systems can provide truly sustainable solutions for a community when they are affordable, reliable, and powered by a renewable energy source. The cost per liter of production from these systems can often be reduced by increasing the thermal performance. This study focuses on developing a detailed computer model in the Matlab environment based on first principles for analyzing the heat and mass transfer phenomenon within these systems in order to fully understand their operation and thereby improve their performance. The model includes two-dimensional resolution of temperatures, mass flow rates, salinities, and property data throughout the system both in the vertical direction along the evaporator surface and in the horizontal direction at each component boundary. This two-dimensional model is more accurate than the one-dimensional counterpart, especially in the later effects, due to the nonlinearities of the heat and mass transfer equations. The model also calculates the temperature drop through each component of the system including the partitions, wicks, vapor spaces, and condensation films. The analysis has elucidated the key design parameters with the highest impact on performance as defined by the Performance Ratio. All system parameters were logically categorized and parametrically modeled for different numbers of effects. The primary determinates of performance were found to be the sensible load on the system for heating the supply brine and the evaporative Heat Rate Ratio (HRR). Essentially, a lower sensible load allowed more thermal energy remaining at each effect to be passed through to the next effect, and a higher evaporative HRR meant that at each effect more heat was being transferred via evaporation than through other mechanisms. Based on these results, design guidelines were set forth to optimize the key parameters. It was found that novel heat recuperation systems proposed in this work were perfectly suited to both decrease the sensible load and increase the evaporative HRR. According to the model, a fifteen-effect system with multiple-stage heat recuperation is able to achieve a performance ratio over eight representing a production of nearly 70 kg/m2day at a solar insolation of 20 MJ/m2day. This is significantly greater than any other small-scale solar thermal distillation system in the literature.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Nathan Mitten.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Ingley, Herbert A.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041158:00001


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9M +&% $!&%,#,%&+" $$' *.&%#$((!6*#'& *!&%,#*%$#*)*!&% "#%(&!*++!6)%!0#%6#(%#$*&#(+#%& %#*4 "# %#$*!&%"#%(&!$(+#*&%#%(&!!6$"*# .&*#'"# +#%& ,#(+#%&%#%#, (#4"#6%(&!!6+**#*** (#(#"') %#$ ,A$$#%& ,"#%&' & &&.*%. +!�" $"&.*%.*"# %&' & &'%&*+%*"#$3#%#'"#%(&!##%,6 "#+ )*#3 &&)! 0" $" *)#0&#%4,!&,&'A%*#!#$ 3#$& ,*&%#*#'%#'$#%#B%&' & !**#*)%("#&.*%.#%&' *!& **#'%#'$# $'$ 3#!**#*4"# $ %$!& )"#)! ')%("#$!!#$%"#' !!& $&.#&$ 3#%+&** 3#4 &$ 3#*6*#(*"#$ %$!& *'% 3#.6&#!#$% $ +(+0" $"(&6 $%#&*#"# #)) $ #$6)"#"#%(&!*++!6. $%#&*#*"#& !##%,6$*(+ &'%#; %#* #!#$% $ 60" $" *&!0&6*$*B#))#$ 3#!6&3& !&.!#4 &** 3#*6*#(**#"# '#* 6' ))#%# &!%.6&$6)"#"#&#')! ''% 3#"#$ %$!& 0" $" $&!!#'&"#%(B* +"4"#&+ +# *&"#%0&6) +&** 3#!6%&*)#%% ,"#"#%(&! ##%,6)%(&$!!#$%"##3&+%& +%$#**)% %#!& 3#!6*"%' *&$#*4 "# %#$$!!#$ **#')%+&** 3#*!&%' !!& *"#6&%# %(&!!6)!&+!&#%#3&$&#'.#$!!#$%** $#" #6&%#* (+!#&''%#; %# &6%&$2 ,*6*#(&'"&3#!0(& #&$#%#; %#(# *4"#"#%"&' (&6*(&!!B*$&!#' !!& *6*#(**#' %#$*!&%$!!#$ 0" $" #,%&#' "# '#* ,%&"#%"&* ,*&'&!#$(+#*4 *'#$ )#*##(* .#(&'#.&*#'* ) $&!6"#*$&!#)+%'$ 4 %&' &!.&* 6+#*!&% !!*%(&!!6"&3#& #,%&#''#* ,! 2#" *0"#% #"#*!&%%&' & *%&*( #' "%,"& $! #',!&,&'&.*%.#'.6&*"&!!0 .&* )*++!60&#%0" $"

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MK *!&%* !!*H ,%#B7&' ,%#BI4"#6$& %(&!!6.#$&#,% -#'.6"#6+# )0&#%*++!6.6"#% #& &'.6"#(. #%)#))#$*4 %&* ,!##))#$*6*#("#"#%# $&!! ( )"# #%)%(&$#n& HnI 64"#n *"#%& )"#!&#"#&%&* )#%%#'"%,""#*6*#(3#%"# "#%(&!##%,6*++! #'"#*6*#(&*'#) # ; & BF4 nn nrn r = BF "#"#%# $&!! ( )%&* ,!##))#$*!&%* !! 60" !#"#&$&!3&!#) (*%&' &!.&* !!* *%(&!!6$!*#%4F9 >8F?4(# (#*"#n *%#)#%%#' &*#)) $ #$6 ,!#*&,# *.$!#&%!6" *# %( !,6 &'#;&# '#*$% .#(! +!#B#))#$ *0 "n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7 #* ,$(+! $& $!'#"*#)%&* ,!##))#$. &!* $!'#&'' &! $(+! $& **$"&*"#"#%(&!%&*+%.#0##$*#$ 3##))#$*"#*++!6 &'$!!#$ )(&**)!0*&'"#*%$%&!$* '#%& *)"#*&$246 +%'$ ,(%#' !!�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7 *6*#(0"#%# *!*"##3 %(#4!*"#*# .!###%,6+**#**#'.6"# )!0%&#)&6%#1#$$$#%&#%+%'$' !!& #0 "&#(+#%&%#&.3# &(. #%#+%#*#**#* .!###%,6!*)%("#*6*#(4 #&%#$+#%& )% +%#"#& ,"# !#0&#%*++!6$&.#*#'%#'$# *!**4 &!!6*#* .!###%,6%&*)#%*"!'.#%#'$#'"% ,""#3&+%*+&$#0 #&$"' !!& $#!!40#% ,"#%&' & "#& %&*)#%.#0##"##3&+%&%&' $'#*#%%#+%#*#*&+** .!#&%#&) (+%3#(# )" ##3&+%&%#( ** 3 6&' $'#*#%&.*%+ 3 6$&.#%#'$#'0 "$(+%( "# %(&**%&*)#% +#%)%(&$#4$/ 3#%6"#%(&!' !!& *6*#(%#; %#*"#&%#1#$ %'#%)%$'#*& &2#+!&$#.6%#(3 ,"#!&#"#&)$'#*& )%("#0&#%3&+%4"# "#%(&!* 2 *(*)## "#%"#&(. #& %"# 0&#%*++!6*%$#% *(# $&*#*"#,%'4%"#$(($&*#)* ,&(. # & %&*"#"#%(&!* 2 $3#$ $%%#*&%#$% $&!&'$&.#&$$(+! *"#'.6 ,)%$#'$3#$ +%( ,&%&!$3#$ %(&: ( ,"##))#$ )0 '$%%#*4*6*#( $%+%& ,"#%(&!*"%&,#$&(&: ( -#+%'$ & ,".6 ,"*26 %&' & )% (+%3#'"#&%#1#$ 4#*'6) '"&&%#'$ &(. # #(+#%&%#)%(FT9T+%'$#'G(%#' !!&#>9K?4"#%*'6 *"0*"&&#!#3&#'0 '*+##' $%#&*#*"#&%#1#$ &'"#%#)%#* !! +#%)%(&$#+&$% $&!+ 0"#%#"# $%#&*# !**#*"#"#%(&!*++!6 '#$&$#!"#.##) >M?4 @* '*% &!*6*#(*&'*(#*(&!!+&** 3#*6*#(**# "#0&#%*++!6 *%$#&!*)%"#&%#1#$ 4" *&$$(+! *"#*! 6 $%#&*#'"#&%#1#$

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7 $&&!*+%#"#&"# $( ,*%$#0&#%0" $" *$&!!#' "#&%#$+#%& 4(&6 $&*#*"#0&#%*++!6*%$#(&6.#&!0#%#(+#%&%# "&"#&(. #& %&' &!*"&*&($",%#&#%"#&$&+&$ 64" *$&.#&$$(+ *"#'.6%#1#$ ,"#& "# $( ,0&#%*++!6&!#%.6* ,&&'' &!*%+!*)!0%�" $" "#*#.&$2"#0&#%*%$#40 6"#%(&!##%,6$& #' "#(&**)!0*).% # $$#%& %+%'$ !!&#!#&3 ,"#' !!& %#+%#*#*! *"#%(&!##%,64"#&() ##%,6 *+%+% &!"#)!0%&#*+#$ ) $"#& &'"#'#,%##0" $""# #(+#%&%# *#!#3&#'&.3#&(. #4 $#"#)! 0%&#*&'#(+#%&%#*3&%6 .#0##$#!!*)(! +!#B#))#$ *"###%,6!**0 !!"#%#)%#.#' ))#%#)%#&$" #))#$4 $#"##(+#%&%#' ))#%#$#*&%#%#!& 3# !6!0"#*#* .!###%,6 &**$ &#'0 ""#*#)!0*(&6.#*(&!!$(+&%#'"# !&#"#&%&*)#%%#'.6 3&+%%&*+%"%,""##))#$4#*+ #" *"# *#* .!###%,6 "#(&**)!0* %#+%#*#*##%,6!*"##3 %(#&'$&&'' +3#%#&$"#))#$0" !#"# !&###%,6$&.#%#$6$!#' "##:' !!& #))#$4 %#:&(+!#&&++%: (&#$&!$!& )%&' !!& $#!!+#%& ,&&) %* *&,##3&+%&%#(+#%&%#)MT&'$'#*#%# (+#%&%#)J8T&' +**#** ,&)##'%&#%& nL*"0*"#*#* .!#"# %(&!!&')%#3#%6! #%) *&! #*++!6"#&#'4() # "$ # % & n r = = = BJ !#"#!&#"#%(&!!&' *($",%#&#%4

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7F # # % & nn nn = = =BM "#%#1#$#'.% #"#%(&!!&' *, 3# ;& B74() # "$ # % & n = = = B7 '"#%#1#$#'' !!&#"#%(&!!&'&*, 3# ;& B4() # "$ # % & n n n nn = = = B *## *#:&(+!#"#*#* .!#!&'"##3&+ %&% *G)"#!&# !&'4%" *%#&** ,*#* .!###%,6%#$6$! %%#$+#%& %#$6$!#"# "#%(&!##%,6 "#%#1#$#'.% #&'' !!&#* %#&(*+%#"#&"# $( ,0&#% *++!6*%#&(* *&'3&&,#*4*#&')%#1#$ ," #*#* .!###%,6' %#$!6"# #3 %(# $&.#*#'%#'$#"#"#%(&!!&' ##'#')%.% ,"#0&#% *++!6+"##3&+%&%#(+#%&%#)"&$#!!4 6* ,"#&#:$"&,#%*)%." "#%#1#$.% #&'+%'$' !!� "MG#))# $ 3##**H e I"#%#$3#%&.!# *#* .!#!&'$&.#* ) $&4 # # # & & & nn = + = + =eB *$&%#'$#"#%#; %#'!&')%"#& ,"#*&! #*++!60" $"0!6 %#+%#*#*&++%: (&#!69G)"#!&#!&'4 4 # # # & & & = = = B #&%#$+#%& *&$$(+! *"#'0 "&"#&#:$"&,#%0 $"2##+*"#)!0 *%#&(* *!&#'.#:$"&,#*"#"#%(&!##%,64$ #%)!0"#&#:$"&,#% #&.!#*"# $( ,0&#%*++!6&++%&$""##(+ #%&%#)"#%#1#$*%#&(

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78 &!!0 ,&!(*)!!%#$3#%6)"#*#* .!###%,64 +&%&!!#!)!0"#&#:$"&,#% .% ,*.")!0**(# #%(#' &##(+#%&%#&!! 0 ,&++%: (&#!6"&!) %#$3#%6)"#*#* .!###%,6>J?4 %(! +!#B#))#$*6*#(**#* .!###%,6%#$+#%& $&.#'# & ,!#B*&,#+%$#**% &+&%&!!#!(! +!#B*&,#+%$# **)%#&$" 3 '&!#))#$4 &$"*&,#"&* *00&#%*++!6)!0%�" $"#;&! *"#*()"#.% #)!0 %&#&'' !!&#)!0%&$"*&,#&!*"&* 0+#%& ,#(+#%&%#,%&' # 0 ""##3&+%&%#(+#%&%#.# ,&++%: (&#!6 #;&!"#$'#*#% #(+#%&%#)"#+%#3 **&,#4 ,!#B*&,#%#$+#%& 0!'"&3##;&!&!(&** )!0%&#*.#0##"# &!.% #A' !!&#*%#&(&'"#*++!6*%#&(0" !#(! B*&,#%#$+#%& 0!' "&3##;&! 3 '&!(&**)!0%&#*.#0##"#%#1# $A+%'$*%#&(&'"#*++!6 *%#&()%#&$"' !!& #))#$4"#+% (&%6' ))# %#$#&% *#* "##(+#%&%#4 "* ,!#B*&,# )&!!"#.% #%' !!&#)! 0%&#*)%(#&$"#))#$&%# "#%(&!$(( $& "#6%#&$"*(# #%(#' &##(+ #%&%#4"#%#)%#&)#%"# "#&#:$"&,#%"#*++!60&#%0 !!%#&$"*(# # %(#' &##(+#%&%#4" #%(#' &##(+#%&%#0 !!.#!0#%"&"##&% !6#))#$*E#(+#%&%#*0" $" "#%#)%#%#; %#&'' &!"#%(&! +&' 0 !!.#" ,"#%"&"#!&#%#))#$*E #(+#%&%#*0" $"0!' &'3#%#!6%& *#"##(+# %&%#)"##:$'#*#% &''#$%#&*#+#%)%(&$#4 (! B*&,#"#&%#$+#%& "##(+#%&%#) #&$".% #A' !!&#)!0%&# 0!'%#+%#*#"##(+#%&%#)"&' !!& #))#$4$#%B)!0"#& #:$"&,#%)%#&$"#))#$0!'&!!0"# 3 '&! *++!60&#%#(+#%&%#

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79 &++%&$""#+#%& ,#(+#%&%#)"&#))#$4 *(#"'0!'%#$6$!#"# *#* .!#"#&)%(#&$"#))#$0 "' *%+ ,"#' % 3 ,#(+#%&%#+# &!)% !!& 2#"#* ,!#B*&,#%#$+#%& 4)% &#!6'#*+ # *" ,"#)) $ #$6& %#$+#%& ,"#&#:$"&,#%)%#&$" 3 '&!#))#$ 0!'.##:+#* 3#&' $(+!#:4/ )#%"#0&#%*++!6+&**#*"%,""##3&+%&%0" #%#&+% ) *(&** *#3&+%&#'))"#*&! 6%( #%&!$$#%& $%#&*#'.6&* ( !&% +%+% 4"#%(&!##%,6(&6.#%#$+#%&#')%( *"#&#'.% #.&)#%0&%' (*.#%#1#$#')%("#*6*#(4(! +!#B#))#$*6* #(*#&$"#))#$(*%#1#$ 0.% #0"#%#.6 *#3#&!!6$!!#$#'&'$(. #'4$((#%$ &!*6*#(* .% #%#1#$ *%(&!!6&$ &!+%$#**'% 3#. 6#!#$% $+(+*4%*(&!!B*$&!# &++! $& *.% #%#1#$ $&.#.6&.&$"+%$#** %$ &!&' $&.#'% 3# .6#!#$% $&!+(+*%(#%#!6,%&3 & &!)!04 :&$(#"'*)' *+*&!&%#%(&!!6 $!'#' "#*!&%' !!& #%&%#(*! 2#!6'#"#)&$"&"#(&1 % 6)'$(##'*6*#(*&%#)% '#(*%& %#:+#% (#&!+%+*#*!6&'&%#( %#)$*#'"# "#%('6&( $+#%)%(&$#"&"#+%&$ $&! **#*4* (#"'*)' *% .#' %##0&.!###%,6'% 3#'#*&! & HnI.#$(#(% #+%#'( &.% # '#+*&!0 !!$#%& !6.#& (+%&$(+#)" #'#* ,&'0 !!! 2#!6)!!0# "##*&.! *"#'+%&$ $#*)"#$%%#$((#%$ &!'#*&! & '*%6&**"0 ,%#B $!' ,%#%*%$##3&+%& %'##+0#!! 1#$ 4"#%#(&6 .#*(#'#3 & *'#"##$( $*&'+%&$ $&! # *)*(&!!B*$&!#*6*#(*. (*(#"'**"!'$&%%63#%' %#$!64

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7K 3&+%& +'*&'%#%*%$#(#"'*))#% "#(*+%.&.!#*! )%*(&!!(#' (*$&!#*!&%' !!& *6*#(** $#' ##+0#!! 1#$ $&.# $*!6&'$(+!#: +%+#%#3&!& &''#* ,4 %#3&+%& +'*"#(* (+%&%#; %#(# *& (+#%(#&.!#!&6#%*"& ,%'0&#%*%$#*&%# $&( &#'43&+%& +'*.##) )%(" ,"*! &% *!& 0" $"0!'.#& &++%+% &#(&$"0 "*!&%'#*&! & (#"'*4n# %*%$#' *+*&!(&6))#% "#* (+!#*' *+*&!(#"'. %(#&! (+&$ *'6*"!'.#$'$#' )%&6* ) $&&(** $#. !, $&!&'(&% # )#$&.#'&(&,#'.6 #:$#** 3#*&! 6$$#%& *4 &!!60 "%#% *%$#(#"'*$&%#(*.# &2#' %#$!6$&( &#"#*++!60&#% &2#4 !#.% #' *+*&!+%#*#*#)"#(*%.!#* (#&*+#$*)'#*&! & (*$&*#*"#%#&%#+** .!#*6#%, #**$"&**&!+% '$ "#*#+&%& &' $!!#$ )"#%3&!&.!#( #%&!*&'"#)&%( )*&!B!3 ,. (&***$"&* $#%& *%& *)&!,@ $2!#6+%#*#*&"%,"% #&(#).% #%#1#$ + *)%*!&%' !!& +!&*>M?4rn "#(* (+%&+%$#** &6' !!& *6*#( *" #&$&!' !!&# +%'$ 0" $" *$!!#$#')%("#$'#*#%H*I4"# "#%(&!##%,6)%(" (&***%#&((&6&!*.#%#$+#%&#'* ( !&%!6"#%#1 #$#'.% #4%(! +!#B#))#$ *6*#(*"#)!0*&%##3#&!!6$(. #'&'(&6"## #%&+*%#&(# +#%& 4$((#%$ &!*6*#(+*%#&(#' !#'0&#% *&#%&#'&'+&% &!!6 %#( #% &! -#'0" $" (+%3#*&*#&'"#&!".##) *0" !#!0#% ,"#$%%* 3# +%+#% #*)+%#' !!#'0&#%4#%& *&$$(+ *"#'0 "&#'$%$&*$&'#% *+%&6#%&'"#* (+!#*(#"')%#( #% &! -& *'#.6&'' ,&*(&!!+%

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"#%# $&!'#3#!+(#)"#,3#% ,#;& &!,0 "&++%+% &# (+! ) $& *&'* '##*&%#$3#%#'$(+#.6$ (+#4%#&$" $(+#&*$&!#&&!6* *)&' ))#%# &!$%!3 !(#0&* -#'.&*#'& *&'&%'*&(+!#$&*#'##%( #"# (+%&$#)+&% $!&%#%(*4$#"# '( &##%(*&%# '# ) #'"#&++%+% &##;& *&%#' *$%# -#'&'& #%& 3# (#% $&!*! (#"' **#'*!3#"#*6*#(4" #('#! *.&*#'*#&'6B *&#+#%& &''#* $!'#&. !B ('#! )% (#B'#+#'#*!&% *!& 4"#)$* *"#$"&%&$#% -& &'+ ( -& )"#' !!& &' .& ,"#+#%)%(&$#(#% $*%#!&#'"#&&' (&**%&*)#%* (!& ) %#&!0%!'+%'$ 4!","'& !6 *!& $% 3#*%"#%"#&*%$#$%3#*$& .#' 3 '#' *$%## (#*#,(#*)%(&&!#% 6 "#('#!&'+%'$ %#*!*$&.#*((#', 3#&'& !6+%'$ 3&!#4 "#('#! *)'#'+&. !B *!3#%)! #&%*6*#(*)#;& $&!!#'*!3#45## ,%#FBF)%&*((&% -#')!0 &,%&()"#('#!4"# *6*#( *' *$% -#'&* ,%#FB8 "#3#% $&!' % #$ &' **!3#'.6*#++ )%("#+"% -&!#!#(#H1LI'0"#. (#!#(#H1L(I4 *&**(#' "&"#%# *,%&' # "#-B' %#$ 4"#*6* #()! #&%##%,6#;& )%#&$""% -&!#!#(# **!3#'.&*#'"#( .#%)#))#$*HI&++%+% &# .'&%6$' +(&**%&#*&'*&! #*)%( "#1B#!#(#&' #%& 3#!6 $3#%,#'#(+#%&%#'#+#'#+%+#% #*4"#*!3# '#(+#%&%#) #!' *"# *#'.&$2B$&!$!&#"#$% )"#3&% *"# &%&*)#%(#$"& *(*0 #&$"$#!!)%"&1"#!#(#4"##3&+%&#'(&**% &# *$&!$!&#')%#&$"#))#$ &' *"#*#'$&!$!&#"##0&!(&**%&#& '*&! 6)%"#1O#!#(#4

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F "#+%+#% #*#(+#%&%#*&')!:#*&%#*&3#')% #&$"#!#(#.#)%#(3 "##:#!#(#4" *+%$#** *%#+#&#' !"## %#*6*#( **!3#'4"#&! !!& +%'$ )%(#&$"' !!& $#!! *" #$(+&%#'"#*++!6(&** %&#$&!$!&#"#)##'%&#%& HnI4"#% &!*++!6%&# *"#&'1*#'&' "## %#*6*#( **!3#'&,& D" *%#+#&#' $3#%,#$#"#'#* %#'n *.& #'4* ( !&% #%& *"#+#%)%(#'0" #&6"#&%#$+#%& #$" ;# *&++! #'* $# $"&,#*"##(+#%&%#)"#*++! 6(&**#&$"#))#$0" $" %$"&,#*"#+#(+#%&%#*)%(#&$"#))#$4 *%#+#&#' $3#%,#$# *&$" #3#'&*#)$*& !##(+#% &%#*4)#%) &! $3#%,#$#"#*! &6+%+#% #*#(+#%&% #*%)!:#*"%,""# *6*#($&.#%#$&!!#'+&% &!!6% "# %# %#6. 6"# %&,,%#,&#'*%&,#(&% $#*4 #!#$#'"#&%(&**)!:#* $!' ,"##3&+%& % &#*$&.#*((#')%#&$" $#!!%)%"## %#*6*#(4"#+#%)%(&$#%& *.& #'.6"#&%&# +"# &!' !!&#+%'$ 4 %'#%&&!6-#"#+#%)%(&$#)"#*6*#(&* '#+#'*&+&% $!&% '#* ,+&%&(##%%#3 %(#&!$*%& "## %#*6*#( *+&%&(#% $&!!6*!3#' &*'#*$% .#'&.3#&$%**&'(& )"# '#+#'#3& % &.!#&')%&3&% #6) #))#$$*4"#%#*!*&%#,%&+"#'*"0 (+%& %#'*4"#*#%#'*$& "#.#*#', '#'#* ,#))%*.&*#'"#(*$% $&!+&%&(##%*4

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8 "#%# $&!#;& *"&'#*$% .#"#+#%& ) "#*6*#(&%#+%#*##')% #&$"$(+#4@&**%&*)#%##%,6%&*)#%&'$ $#%& #;& *&%#) +% (&%6 #%#*4$&!#&&!6* *.&*#'&*&'&%'*&( +!#$&*#0 !!"#!+'##%( # 2#6#%(*4"#+"6* $&!* ) $&$#)&!!#%(*0 !!.# '#*$% .#'4!!##%,6.&!&$# #;& *"&!6 $!'#"#&%&*)#%%&#*0 !! .#0% # "#)!!0 ,)%(C = rn FB %$%!3!(#&&!6*#*"#"#&%&# H; I *'#) #'&*"&$( "# $%!3!(#0"#%#"#"#&%&#H; I *"###%,6!#&3 ,"#$%!3!(#4 %$%!*%)&$#"#"#&%&# H; I *"&0" $"$%**#*"#!#)B"&'* '#)"# $%!*%)&$#0"#%#"#"#&%&#H; I *"&0" $"$%**#*"#% ,"B"&'* '#) "#$%!*%)&$#4" *$"*#&%. %&% !6'# "#)&$"& "#*6*#( &,%&(*"#"#&)!0*)%("#!#)"#% ,"4#%,6.&!&$##;& *"& 3!3##"&!+6)!0* 0 !!.#0% # "#)%() ;& FB4 + = + rn rn rn FB 0%2 *'#"#*6*#(%.6"#*6*#(&'"#%# &%#2 # $%+# &! ##%,6#%(*.#$* '#%#'4 $#"#*6*#()#;& *0 !!.#*!3#')% #(+#%&%#*&'"# '#&!,&*!&0&++! #*"#& % A3&+%( :%#&!!#"&!+ #*&%# %#0% #.6"# %$*&B+%#**%#*+#$ ) $"#&H + I&++%: (& *"0 ;& FBF4 ( ) @ FBF

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9 "#%#)#%#$##"&!+6 "#%#0"#%+%+#% 6$%%#!& **#'&' "#%#)%#&* (+! ) $& $&.#(&'#&'#;&#!6& ++%: (&#&6#"&!+6#%( 0"#%#"#*+#$ ) $"#&(&6.#&)$ )"#%#(+ #%&%#%"#%+%+#% #**$" &**&! 6HI4 @ FB8 *+ "#,!&,0" $" *%(&!!6,!&** **#'%#$# 3#" # $ '#%&' & "#& )!:0" !#'%&(& $&!!6%#'$ ,"#"#%(&!!**#*)%( "#&.*%.#%H ,%#FB9I4 &.*%.*&+% )"# $( ,%&' & 3#"#&)!: &'%#%&' & )"#&.*%.#% 0" !# %#1#$*"#&.6$3#$ &'%&' & #&(. #4 "#*++! #'*!&% %%&' & )!:H;5 *++!6 I *& '#+#'#+&%&(##%*#.6 "# 3#* ,&%0" $"&$*&*&"#&)!:.'&%6$' "#*6*#() #;& *4%'#%&$$)%' (#* &!#"&!+ 6)!0* "#*6*#("#*++!6 )!: *(! +! #'.6"#*6*#(E*$%***#$ &!&%#&&' "#%#)%#(*#;& *&%# 3# ##%,6%&#)%(4%" *+%#*#('#!% #)!#$ )%("#,!&, #:$!'#')%("#$&!$!& 4(###%,6 *&.*%.#' .6"#,!&,.&*#'"# &.*%+ 3 6HY I&'"#)!!0 ,##%,6.&!&$# *)%(!&#')% "#,!&,4 #%,6.&!&$#,!&,C> $ '#%&' & &.*%.#'.6,!&,?O>%&' & &'$'$ )%( &.*%.#%,!&,?L>%&' & &'$3#$ )%( ,!&,& %? ( ) ( ) + = + + r a FB9 "#%##&$"#%( *'#) #'* ,#(+#%&%#*0" $"&%# !&.#!#' ,%#FB84

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K ( ) D = r r FBK ( ) ( ) ( ( ( + D = -e e s FBJ ( ) ()( ( ( n D = FBM ( ) ( ) D = ( ( se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J #%&%#('#!"##))#$ 3#%&' & &.*%.#' .6"#&.*%.#%H88I4"#&$&! &( *.&*#'& ) #*#% #**((& '# "#+"#(#&)%#%&' & )%("#&.*%.#%&'%#)!#$ ))"#.&$2)"# ,!&,4"#3#%&!!&.*%+ $#)) $ # *&&++%: (& )" **((& &'& $$%� &++%: (&#!6G4 #%,6.&!&$#&.*%.#%C>#%&' & &.*%.#'?L>%&' & &'$'$ )%(&.*%.#%,!&,?O >$'$ "%,"+&% ? ( ) ( ) r + + = a t FB "#$'$ #%( *'#) #'4 ( ) ()( ( ( n D =FB %"#&&!6* *"#&.*%.#%.&$2*%)&$#+!#&*#%#) #%"##:*#$ '# "#)&$"& *"#*&(#&*"#,##% $+&% .&$2*%)&$#&&!6* *4 r "#)%)"#) %*+&% &$*&*&&.*%.#%0" !#&!*&$ ,&*"# $'#*& *%)&$#)%"##))#$*"#%#&)#%4"#.& $2*%)&$#&$*&*"# #%)&$# +0" $""#0 $2 ,(&#% &! *&'"#%#'4#%,6%& *+%"%,""#+&% *!#!6.6$'$ "%,""#*! '&' (+%& $* '#%"# (+%&$#) "#' %#$ &!*$&!#&&!6* *4" *'##%( #*0"#"#%$ '$ "#3#% $&! %#$ *#,! .!#$(+&%#'"& "#"% &!' %#$ 4*$&!#&&!6* $'$#'* ,"#.&*#$&*#*+#$ ) $& *, 3# "&+# %8H ,%#FBJI4

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M %+%#*#&'6B*&#$'$ 0 )%("#%(&!$ '$ 3 6"###%,6 .&!&$# *&*)!!0*C = + FBF 6+!,, "#.&*#$&*#3&!#*&'&**( ,&! # &%#(+#%&%#,%&' # &!,"#3#% $&!!#,")"#*6*#()%("#)! #%6&(. ##(+#%&%#"# ) &!&3#%&,##3&+%&%#(+#%&%# **"0"& "##(+#%&%#'%+&$%**"# 0 $2$&.#&++%: (&#'&*)!!0*C n = = = D FB8 $"!#&'*"#)!!0*$&!#&&!6* *C ) ) + + = +FB9 *$&*#'#"#3#%6" ,"&*+#$%& $'$ "#3#% $&!' %#$ )%%'#%*)(&, '#!0#%"&"& "#"% -&!' %#$ 0" $"$&"#%#)%# .##,!#$#'4"#"#B! #&%"#& ,&!,"# 3#% $&!' %#$ *$* '#%#' #3# )"#&3#%&,##3&+%&%#(+#%&%# *%#&$"#' !6#B;&%#%)"#0&6 '0"#+&% &49("#"% -&!$'$ %#(& *"%##%'#%*) (&, '#,%#&#%4#%,6.&!&$#+&% )%H+IC>$3#$ "%,"$'#*& ) !(?L>$'$ %,"+&% ?( ( = FBK @%#'#+" **"0 "#$'#*& ) !(&&!6* *) % ( 4

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7 #%,6.&!&$#+&% .&$2H+IC >$'$ "%,"+&% ?L>$3#$ 0 $2?( ( = FBJ "#"#%(&!%&*+%"%,""#0 $2 *, 3#&*C ( ) ()( ( ( n D = FBM "##))#$ 3#"#%(&!$'$ 3 62 #)) &$$*)%.""#*! '0 $2(&% :&'"# 0# ,)! '4* (+!#+&%&!!#!"#&%&*)#%('# *&'+#'0" $" *0# ,"#'.6"# +%* 6HM8I4 ( ) j j + = FB7 (%#'#& !#''#*$% + )"#"#%(&!%&*+%+ "#(#& "#0 $2*%$%# 0 !!.#, 3#4& "#0 $20&*' *$**#' "&+#% %#,&%' *$% $&!)$ *0 "# *6*#(.")%(&(&**%&*)#%&'"#&%&*)#%+#%*+ #$ 3#4"#)!!0 '#3#!+(#0 !!.% ,(%#% ,%"#+#%& & !+"#(#&&'+#%)%(&$# %#!&#'(&**)!0*&! 6&'##%,64@&**)!0&'3#!$ 6$* '#%& *C %&' &!!6"#(&**)!0%&##&$"0 $2 *'#) # '.6"#)##'%&#%& HnI '#) #'&*"#(&**%&#)*++!6' 3 '#'.6"#& !#3&+%& (&**%"# .&*#$&*#*6*#(*+#$ ) $& )nL(#&*"&"#*++! 6#&$"0 $2 *0 $#"# &!&(#3&+%&#'4* ,"#.&*#$&*#n&3# !$ 6&&!6* *+#%)%(#'

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)%(0" $" (+%& )%(& $&.#,!#&#''# #%( #"#)!0*%$%#0 "#0 $2.&*#'$!&** $+%*(#' (*$ #$#H ,%#FBMI4 *)!0*%$%#0 !! %"&3#&!&%,##))#$"#"#&%&*)#%(#$" & *(0 "#0 $24 #!$ 6*$&!#&&!6* *C"#"#n *, 3#&*)!!0*C r = FB '&3#%&!!(&**.&!&$# *, 3#4 (n + = r FB "#"#&3#%&,#(&**)!0* "#0 $2&%#&++%: (&# '&*)!!0*C (n FB "#(&**)!0%&#*$&0.#0% # #%(*)"# % %#$ &!3#!$ #*'#* 6 &'$%**B*#$ &!&%#&4 ( ) ( ) (n+ + n j r j r FBF n 4FB8 (n r r $$%' ,"#$"&%&$#% $' (#* *"#)!!0 $&.#*"0C '+ + 4FB9 !","&"% -&!$(+#)3#!$ 6(*#: *&"#0 $2*%)&$# %#!&#'"##3&+%& %&# *'##%( #'" &" *3#!$ 6'#*+!&6&!&%,#

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%!# "#3#!$ 6+%) !#"%,""#0 $24"#% $* '#%& '##%( ,"# 3#!$ 6+%) !#(* $!'#&$!*#%!2&&%$6)!0 "%,"&+%*(#' (4 @(#(.&!&$#C *#&'6B*&#((#(.&!&$#)%)!0"%,""#0 $2 *, 3#0" $" $!'#*&$&+ !!&%6+%#**%##%(&,%&3 6#%(&! #&%&%$6'%&,#%(&'B #&%)%('%&,#%(.&*#'%$""# (#%&'+ &')%"#%'#3#!+#'.6&%' >M8?4"#%# *&++! #'+%#**%#+# &!&* #$&*#0 "(&6$) #'+%* (#' ()!0+%.!#(*4 n $ + + $ r m r+ = + D FBK "#$&+ !!&%6'% 3 ,+%#**%# *!6%#!#3&)%+&% &!!6*&%&#'+%* (#' (0"#%#*%)&$##* *.#0##"#0 $2(&% :&' 0# ,)! '$(# +!&6H ,%#FB7I4" *$&+ !!&%6'% 3 ,+%#**%#.# 0##"#0##'&%#&H0&I&' 0##'&%#&H&I *"#%# $&!!6.&*#'"#*%)& $##* H[I$&$&,!#*H\I &'$"&%&$#% $%&' *H%I)"#(&% :HM9I = D q q s FBJ 0"#%#"#)!!0 ,'#) "!'*C s = D 4FBM "#,%&3 6#%( ;& FBK *&++%+% &#)% )!0 "#3#% $&!' %#$ &'$&.#(' ) #'&$$)%& $! #&,!#4 "#) %*#%("#% ,"B"&' '# *"#$!&** $&%$6)!0#%(4%#+%#*#*"#%# *&$#))!0'#"#

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)% $ '%&,0 "#*! '(&% :4 *! #&%!6 +%+% &!"#3#!$ 6&'%#!&#' .6"#+#%(#&. 6HrI4 "#*#$'#%("#% ,""&'* '#);& F BK$&.#$&!!#'"# %$""# (#%#%(&' *&;&'%& $#%("&%#+%# *#*"#)%('%&,$&*#'.6 $!! )"#)! '0 ""#*! '.*&$!#*4 *%# !&#'.6"#%)"#+#%(#&. 6 &'&$#)) $ #$ ) "&3&% #*.&*#'"#&%#)"#+%*(#' ( 4" ;&'%& $#%(!6$(#* +!&6&*"#)!0E*n#6! 'E*(.#%*%+&**#* 6 .&*#'r&*"#!#,"*$&!#4%"#.&*#$&*#"#n #6!'E*(.#% *$&!$!&#' &*)!!0*0"#%#"#3#!$ 6 *$&!$!&#'.&*#'"#( &**)!0%&#&'0 $2E*$%** *#$ &!&%#&C () n n =" $ +m rFB7 $#"#n#6!'E*(.#% *($"!#**"&#"#) %('%&,#%($&.# #,!#$#'&'"#3#!$ 6"%,""#0 $2$&.#%#+%# *##'.6"#)!!0 ,.&!&$# ),%&3 6&'$&+ !!&%6)%$#*C D + = $ +r m FBF $#"#&%$6)!0#;& *)) %*%'#% "# *+& &!'#% 3& 3#*"# "6'%'6&( $.'&%6$' *$&"&3#&%. %&%63&! #*4" *(#&*"&"#B *! +E$' *!,#%3&! '&'"#%#)%#"#3 #!$ 6+%) !# *!0)!0 +%* (#' ($&.#%#&*&.!6('#!#'&* )%(4" "#%0 *#20&**!,)!0

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F >M8?4" *&!!0*& (+%&* (+! ) $& )"# "#%(&!##%,6.&!&$#0" $"0 !!.# +%#*##'*"%!64 "#(&**)!0$&+&$ 6)"#0 $2 *%#!&#'"#3#!$ 6&.3#&'"#%#)%# '#+#'#"#! ; '+%+#% #*0 $2+%+#% #*& ')!0%#, (#C D + = = $ + r m j r j r FBF !0%#, (#*C &*#'"#'#3#!+(#*&.3# *+*!&#'"& &6!$& )"# #3&+%&%0 $2$&+# &!!6.#+#%& #) "%##' ))#%#%#, (#*C3#%)!0 *&%&#')!0&'*&%&#')!04%&3#% $&! 0 $2.# ,&$#'+.6,%&3 6 .# ,)##')%(&.3#&'0 "#3&+%& &!, "## %#*%)&$#"#%#(&6.#& %&* )%(3#%)!0*&%&#')!0*& %&#')!043#%)!0$$%*0"# "#+)"#0 $2 *)!!6*&%&#'H$&+ !!&%6)%$#*& %# #))#$I&'6#&.!# )!0"## %#6)"#*++! #'(&**)!0% r > FBF ;& FBF *+!,,#' ;& FBF4 $" m j r r > 4FBFF *+ &)&!! ,) !()%(*"#* '#*%) &$#)"#0 $2'#,%&3 6 !&+ *%#&$"#'&!,"#0 $20"#%#"#) !( "&*#3&+%&#'4#% ,"# *&%&#')!0%#, (#"#0 $2 *&'#;&#!6%&*+% ,"## %#6)"#(&**)!0 *"#%# *)&!! ,) !(.$&+ !!&%6)%$#*&%# 6#&$ ,"#)!04

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n *(& & #'#*%# "&'%6B'#*$$%4) %#&! 6&*(&!!&()3#%)!0%*&%&# ')!0 *+%#*#"#"#"#%(&! %#* *&$# *%#!& 3#!6$"&,#'* $#)%(*0 $2(&#% &!*"#%#* *&$# +% (&% !6'#"#0 $2(&#% &! *#!)&'"# ; '4 ;& FBFF$&.#(& +!&#'&'*#'*+#$ )62# 6$"&%&$#% $*)"# 0 $2 )3#%)!0 *'#* %#', 3#"#(&: (('#* ,( &**)!046&**( ,"# $&+ !!&%6+%#**%# *-#%&'*# ,"#'#* %#'(&**)! 0&"#+)"#0 $2& #%($&.#'#) #'"&&$$*)%"#3#%&!!)! 0$&+&$ 6)"#0 $2.&*#'"# $2#**H 0 I+%* 6H]I&'+#%(#&. 6HrI4

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9 $ n r m j = FBF8 $&!0 $23#!$ 6C !"," **#' "#('#!"#!$&!)!0 3#% $&!3#!$ 6&!,"#0 $2 (&6.#) #%#*H ,%#FBI4"#$&!$!& *, %#&!6* (+! ) #'.6"#&%$6)!0 &**(+ 0" $"&!!0*& )%(3#!$ 6+%) !#&' "#%#)%#"#3#!$ #*' %#; %# #,%& &$%**"#0 $24n&"#%"#3#!$ #*$&.#' %#$!6%#!&#'"# (&**)!0*.6"#$%***#$ &!&%#&&'"#+%* 6* $# "#(&**$&!6%&3#! "%,""#+#*+&$#)"#$%***#$ &!&%#&4" *.&*#'"#&**(+ "&"#%& )"#+#*+&$# "#$%**B*#$ "#&!$%**B*#$ &!&%#& "#*&(#&*"#+#*+&$#3!(#&!3!(#HM8I 4 ( ( ( = FBF9+ r = FBFK "#$%**B*#$ &!&%#& *'##%( #'&*)!!0*C j n = FBFJ "# *&&#*3#!$ 6$&0.#'##%( #'4 () j r r r n + + ( ( ( ( ( ( =-4FBFM "#'#* 6)"#.% ###'#')%"#3#!$ 6$&!$ !& *&)$ )." "# $%#&* ,#(+#%&%#&' $%#&* ,*&! 6&' "#%#)%#(*&!*.#$&!$!&#' &#&$" #%3&!.#)%#+!,, "#3#!$ 6#; & H*##+%+#%6$%%#!& ++#' :I4

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K &! 6C $$#%& .&!&$# *+#%)%(#'&' **#' #('#!$&+%#"# *&! 6,%&' #"%,""#*6*#(4"#*&! 6 !6+!&6*& (+%&%!# "##3#)'%6B.&!*"&*&* ) $&#))#$ "#3&+%+%#**%#&"#0 $2 *%)&$#0" $"'% 3#*#3&+%& 3#%&*+%4&.!6) %"#*&(##(+#%&%#&" ,"#% *&! 6!0#%*"#3&+%+%#**%#4 *+#$ #*.&!&$#!#&'*&#;& )%'##%( "#!$&!*&! 6&#&$" + &!,"#0 $2H ,%#FBI4 *'##%( #' .6$'$ ,&&!(&**.&!&$# &'&*#+&%&#*+#$ #*(&**.&!&$#"#*&!4"#$*#%3 & )*&!$&.# 0% #&*)!!0*C ( n ( n = FBF7 *$&.#%#0% #0 ""#!$&!&!(&**)!0% &#*&'*&! 6#%(*4 ( ( ( ( = FB8 n =4FB8 3#%&!!(&**.&!&$##&$"#!#(#$&.#%#+%#*# #'4 ( ( ( = 4FB8 6+!,, ,;& *FB8&'FB8 ;& FB 8"#1"*&! 63&!#$&.# '##%( #'4() =( ( ( ( ( FB8F

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J %& '#&! -#'*6*#("#*&! 6HGI(&6.# $%# &*#'"#*&%& + .#)%#"#*&!+%#$ + &#*)*! &''%6B $$%*4;& FB8F$&.# (& +!&#'*!3#)%"#( (&!"#%# $&!n )%&, 3# !#*&! 6&' *&%& *&! 6.6&++!6 ,"#( 1 &' 1O %#*+#$ 3#!64 = n n FB88 $&.#$&!$!&#'"&0"# *& LKGH*&%& I&' LF49GH*#&0&#%I"# n ( L4K4" *&0&6#:+#% (#&!!6'##%( #"# +% (&%6$&*#)'%6B&' "0$!*#&0 $2E*+#%)%(&$#&++%&$"#* '#&!+#%)%(&$ #4)'%6B$$%*&*"# n&++%&$"#*" *( (("# (&6.#&**(#'"#0 $2"&*%#!& 3#!6 )%( *% )*&!$$#%& 4+#%)%(&$#$#) ) $ #$!'.#'#) #'0" $" $(+&%#*"#&$&!n&'%6B"#"#%# $&!( ((4"#*&%& + &!*'#+#'##(+#%&%#&'"#%#)%#%#; %#* &0B' (#* &!('#! %#*! .#+%+#%!6('#!#'&!,"#!#," )#&$"0 $24 #%,6$* '#%& *C #%,6%&*+%"%,"+%*(#' &(*&$$)% %&*)#%(#$"& *(* "%,".""#*! '(&% :&'"# #%* &!)! '4#3#%&!&**(+ ** (+! )6"# &&!6* $!' ,"##,!#$)%&' & 3##))#$*3 *$ *' ** +& &'&60%2 '#.6+%#**%#$"&,#*>M8?4

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M 6&3#%&, ,3#%"##!#(#&!3!(###%,6%& *+%"%,""#*! '(&% : $&.#%#+%#*##'&*)!!0*C()() ()()! n j j r j+ = FB89 "###%,6%&*+%"%,""#! ; '+"&*# *%#+% #*##'&*)!!0*C 4() ()! n j j r r j+ = + 4FB8K 2##%(*&%#&''#'&' *&**(#'"&"##(+#%& %#*)"#*! '&')! &%#&#; .% (0 &, 3##!#(#&!3!(# &'"&"#&$'$ "#*! &'! ; '+"&*#*&2#*+!&$# +&%&!!#!HM8I4() () () n j r r r j+ + = + + =FB8J %*#&'6B*&#+#%& 0 "-#% #%&!"#&, ##%& "#%# *&.&!&$# .#0##$3#$ %&*+%"#!#)&'' ))* 3# %&*+%"#% ,"4() () + = + r rFB8M %'#%)(&, '#*$&!#&&!6* ** ,"#.&*#$&*# *+#$ ) $& *, 3#* $!&% 6"# (+%&#%(*4)#%+!,, &! !"#&++%+% &!#*"#)!!0 %'#%)(&, '#*&%#)')%#&$"#%(C HFIOHKILHKIOHI4FB87 "#'( &##%(*%#+%#*#&.&!&$#.#0##"#$ 3#$ 3#%&*+% "# 3#% $&!' %#$ &'"#' ))* 3#%&*+% "#" % -&!' %#$ 4" %#+%#*#& 3#)&$!&** $&!**#!&&!6* *)%)!0"% ,"&+%*(#' (4"#

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7 $(+! $& &% *#*0 ""#.'&%6$' *#$#**&%6 &$&!!6*!3#)%& **#!(.#%&*"#6&%## "#%&$*&)!: %$*&#(+#%&%#.%&"#% +&%)&$(+!#:*6*#()#;& *%#+%#*# ,"# &%&*)#%"%,""## %# *6*#("&(*.#*!3#'* (!&#*!64" *(&2#*) '&(#&!$&!$!& )"# **#!(.#%&!(* (+** .!#&'* 0 !!.#!#) )%#(+ % $&!'##%( & !&#%#:+#% (#&!#))%*4 !#"#**#!(.#%0 !!.#$&!$!&#'#:&$ !6*(# (+%& )%(& $&.#'#'$#')%(&+"#(#!, $&!&% ,(#4*)! '##%*"# 3!(##!#(#&*(#(#&#(+#%&%#H ( I *"#&#'&!,"#' ))#%# &! !#,"�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n D = 4FB9 "##"&!+6#%(*$&.#%#0% # #%(*)$*& +%#**%#*+#$ ) $"#&&' #(+#%&%#)%."1&'1O4 = 4FB9 "#&!##%,6%&*)#%%#'"#3&+%*+&$# $!'# *&%&' & #%(&#%(0" $"

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F &$$*)%."$3#$ %$'$ &'&+%& #%(4"#60 !!.# $3#%#' (%#'#& "#&+%+&$#*#$ 4 ) @&**.&!&$#C "#(&**.&!&$#&$%**"#3&+%*+&$# ** (+!6&.&!&$#. #0##"#(&** #3&+%&#')%("#0 $2&'"&$'#*#'&"#$' #*& ) !(*"0&*( r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nrn ( nrn ( nrn ( ( n FB98 "#' ))* )!: *'% 3#.6"#&%&!!,)" #' (#* !#**$$#%& %& 4"#$$#%& %& *0% # #%(*) "#&!*6*#(+%#**%#&'"# +&% &!+%#**%#*&$$%' ,& '#&!,&*&**(+ & '"#&!('#!>MK?4"#

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F +&% &!+%#**%#*&"#0 $2H0I *&)$ )." #(+#%&%#&'*&! 60" !#& "#$'#*& ) !(H$)I *)#(+#%&%#!6' # .# ,&+%#*.*&$#4 &+%*+&$###%,6.&!&$##%(*C *(# #'&.3#"#%#&%#"%##+% (&%6(#$"& *( *)%"#%(&!%&*+% &$%**"#3&+%*+&$#4"#) %* *%&' & 4 ( ) ( ) ( ( ( + D =e e s 4FB99 3&+%& 3#%&*+%)!&###%,6 *%#!&#' "#' ))* (&**)!: (! +! #'.6"#!&#"#&)3&+% -& H" !3 I4 ( ) D = = ( ( nrn ( nrn ( nrn ( ( ( ( ( n FB9K '$ "%,""#3&+%*+&$# *('#!#'4 ( ) ( ) ( ( n D =4FB9J (' ) #%" *$'$ #%($&.#&++! #'& $$)%$3#$ 3# %&*+%&$%**"#3&+%*+&$#'# #%*+#$ #*' )) 4"#(' ) #% *&'+#' )%("#0%2)@$& >MJ?4"#&&!6* *'#3#!+#' )%(&((#((&**&' ##%,6.&!&$#.#0##03#% $&!0&!!*&*"#&*+#$ %& &++%&$"#* ) 64"# &++! $& 0&*% &!!6)%.& ,&(%#&$$%& #('#!)##%,6&'(&** %&*+%0 "#( *& %,&+)&. !' ,0&!! 4 "#@$& #%($&#))#$ 3#!6.#%#&#'&*&**#! (.#%4"#*# 6 ('#!*$'$ &!#0" $" *&$(((# "')%*6*#(*0 "3#%6

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FF *(&!!,&+B*+&$ ,.0"# $!'#' %#+%#*#*"##) )#$)$3#$ 3#%&*+%4 "#$3#$ %&*+% *$&*#'.6$#%B' ))* ) "#B$'#*&.!#,&*#* )%("#$'#*#%0&%'"##3&+%&%.&!&$# "#3&+%(&**)!: "# ++* #' %#$ 4&!$!& **"0"& %#'$#* "#"#&%&*)#%$(+&%#'"&) +%#$'$ .6&++%: (&#!6G4"#%#)%# 0 !'"&3#&#,! .!# (+&$ "##3&+%& 3#%&*+%"%,""#3&+%*+&$#4 3#"#&'' &!$(+!#: 6 &''*"#('#!&'"##,! .!# (+&$"#+% #!6$'$ 3#('#! *&'+#'4 "#$&!$!& $!'#')%%#)#%#$#4"#$'$ #;& *(' ) #'&* *"0.#!00 "&(' )6 ,$#)) $ #H @$& I4 ( ) ( ) D = ( ( % n FB9M "#$#)) $ # *'#) #'&*)!!0*C() n r + + = ", % 4FB97 "#.!0 ,(.#% *&' (#* !#**$$#%& ,%&' # #%(*)"#(&** )%&$ V&#&$"*%)&$#4 = ( ( ( w w w FBK "#3&+%#0 *(.#% *&' (#* !#**%& .#0## $'$ 3#"#%(&!%&*+% &'$3#$ 3#"#%(&!%&*+%.6"#' ))* ) (&**4 r= FBK

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F8 "n@&**.&!&$#&') !(" $2#**C (&**.&!&$#*"0*"&"#$"&,# (&**)!0%&#&! ,"#$'#*& *%)&$# *'#+#'#"#$'#*& %�" $" *#; &!"##3&+%& % "#&!)!0 *-#%&"#+)"#$'#*#%&' $%#&*#*&!,"#!#," "#.(0"#%# *#;&!*"#&!' !!&#+%'$ %&#)%"&#))#$4 + = ( ( ( FBK $!&** $&!**#! #,%&!&&!6* **#'('#!"#" #&%&*)#%"%," "#) !()$'#*&#"&$!!#$*"#$'#*#%4 ((#(.&!&$#"# !&( &%) !(, 3#*"#3#!$ 6+%) !#)"#0 $20" $" $!'#*,%&3 6.'6)%$#*&' 3 *$* 6.#,!#$* #% &#))#$*.6"#3&+%4"# 3#!$ 6+%) !# #,%&#')%( "#0&!!.'&%6" $2#** $) .& "#(&**)!0%"##;& $&"# .#%#&%%&,#'*!3#)%"#.'&%6" $2#**0 "& 3#(&**)!0%&#H)%("# 1B#!#(#I&')! '+%+#% #*>K?4 () =( ( nr r r mFBKF *) !(" $2#**H $) I0" $"$"&,#*&!,"#!#,")"#$'#*#%+%3 #* "#%#* *&$#$'$ 3#"#&%&*)#%&$%**"#) !( &**"0.#!04 ( ) ( ) +D = ( ( ( n FBK8 *0&6"#%#* *&$#"#"#&%&*)#% $%#&*#* &!,"#3#% $&!' %#$ )"#$'#*#%*%)&$#&*"#" $2#**)"#) !(,%0*4 "#,%0"%&#)"#) !(

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n"*#0&$$*)%"#'#,%# #)3&+%*+#%"#&.6 (' )6 ,"#!&#"#&#%(&*)!!0*>K?C

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FJ '#*$% .#' (%#'#& "&+#%84" *'# "###')%"##$#**&%6 .&$2,%'.#'#3#!+#'$%#&#&&%,(#)% "# %*.*& &!.##) 4 '' &!!6"#+#%)%(&$#%#*!*&%#, 3#&*#& $"(#"' %'$#'46*#( &,%&(*&'"##;& *'#3#!+#')%('#! ,#&$" *6*#(&%#, 3#"#%#4 %0 &##&n#$+#%& HnI *&$$(+! *"#'* ,& $!*#'$&3 6"#& #:$"&,#%"#) &!+&% )%"#&%#1#$ & *++*#'&(. #& %H ,%#FB 9I4"#*++!6.% # *%&*+%#'"%,"" *"#& #:$"&,#%)%("#+"# .()"#+&% )%+%#"#& ,.#)%#.# *% .#'#&$"#))#$4 "#*#* .!#"#& ,)"#)!0 *#;&!"###%, 6$3#$#')%("#) &! +&% &#&$"3#% $&! $%#(#4 ( ,( =FBJ "#$3#$#'##%,6 *.&*#'"#"#&%&*)#%$#) ) $ #H" n I4 ( ) ( ) ( ,( ,( D = 4FBJF "#"#&%&*)#%$#)) $ # *'##%( #'.6"#** #!(.#%&'%#!&#'"# *"&+#)&$%HI&'"#"#%(&!$'$ 3 6)"# )! 'H2 .% I4 ,,* = FBJ8 "#**#!(.#% *#;&!84MK0" $" **#!#$#')% !&( &%)!0"%,"& %#$&,!&%$&3 6>MM?4 "#*#* .!#"#& ,$&*#*&#(+#%&%# $%#&*#&!, "# #%3&!0" $" &++%: (&#'.6* ,&*+#$ ) $"#&3&!#4

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FM ( ) ( ,( ,( ( ,r =+4FBJ9 #0#(+#%&%#H n1O I *$&!$!&#'&*"#!620&'.#$(#*"# .'&%6$' %#; %#'$&!$!&#"#"#&%&# &"##: #%3&!4" %#+#&#')%("#+)"#*6*#(0"#%#"##%6 #(+#%&%##;&!*"#*%$# #(+#%&%#"#.()"#*6*#(0"#%#"##: #(+#%&%#.#$(#*"# *6*#(E* !##(+#%&%#40 "#*#$'0&6 0" $"0&*#"#&$&.#%#$+#%&#' )%("#*6*#( *& "##: )"#$$#%&#'.% #&'+%'$' !!& #(&**)!0*&(#!6#* .!# #&n#$+#%& HnI4" *$$#+0&*'#*$% .#' "&+#%&!,0 "& *&(+!#$&!$!& 4"#*6*#(#: "#*#(&**)!0*"& 3#.##"#&#'"# ,"#*#(+#%&%#)"#*6*#(&'%#+%#*#&!&%, #&()0&*#'"#&!#** %#$+#%&#'&')#'.&$2 "#*6*#(4 "##&* #*0&6 (+!#(#n *"%,"&* ,!#B* &,#$#%B)!0"#& #:$"&,#%0"#%#"#.% #&'' !!&#)!0)%(#& $"#))#$&%#$!!#$#' & $(((& )!'.#)%###% ,"#n"#&#:$"&,# %H ,%#FBKI4" *0 !!.# %#)#%%#'&* ,!#B*&,##* .!##&n#$+#%& HnI4 "#"#&%#$+#%&#')%+%#"#& ,"#*++!6.% # *%#!&#'"#*() "#%(&!##%,6$& #' "##: ,%#1#$.% # &'+%'$' !!&#(&**)!0*4 #%B)!0"#&#:$"&,#%#))#$ 3##** *'#) #' &$$)%0"&+% )"# (&: ((+# &!0&*#"#& *&$&!!6%#$+#%&#'4 n -. = FBJK "#(&: (("#&%#$+#%&#' &n*6*#( *%#+%# *##'.6&*((& )

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F7 "#0&*#"#&$& #' #&$"(&**)!0&* )"##(+ #%&%#0&*%#'$#'# %#!6 "#*%$##(+#%&%#H *%$# I&'#"&!+6)!0*&%#&++%: (&#'* ,*+#$ ) $ "#&3&!#*4()() = = + = r n n n r n n n n =FBJJ"#"#& ,)"#*++!6.% # *%#+%#*##'.6"# $%#&*#)%("#*%$# #(+#%&%#H *%$# I"#*++!6 !##(+#%&%#"#*6*#(H *++!6 I4 ( ) r = r r FBJM !#%& 3#!6n$&.#&$$(+! *"#' &(! +!#B* &,#$) ,%& 0"#%# "#.% #&'' !!&#E**#* .!###%,6)#&$"#))#$ **#+&%&#!6%#$+#%&#'0 "#*++!6(&**)%"&#))#$H ,%#FBJI4" *$ ) ,%& 0 !!.#%#)#%%#'&* @! +!#B*&##* .!##&n#$+#%& H@nI4 *(%#$*!6&'$(+!#:"# n."&**! ,"!6" ,"#%+#%)%(&$#,& *4 ( !&%!6"#@n*6*#("#"#&%#$+#%&#')% +%#"#& ,"#*++!6 .% #)%#&$"#))#$ *%#!&#'"#*()"#%(&!##%,6$& #' "##: %#1#$.% #&'+%'$' !!&#(&**)!0*)%"& #))#$4#%B)!0"#& #:$"&,#%#))#$ 3##** *'#) #'&$$)%0"&+ % )"#(&: ((+# &! 0&*#"#& *&$&!!6%#$+#%&#')%(#&$"#))#$4 n %-. ==)%#LCFBJ7 "#(&: (("#&%#$+#%&#')%(#&$"#))#$ &@ n*6*#( *%#+%#*##'.6 "#*()"#0&*#"#&$& #' "#%#1#$.% #&'+%'$' !!&#(&**)!0* &* )"##(+#%&%#0&*%#'$#'# %#!6"#*% $##(+#%&%#H *%$# I4

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a nn & #* 6>MM?C ( ) ( ) [ ] { } + + = r 0"#%# r .% "&* *)2,A( F &' **&! 6 ,A2,&' *#(+#%&%# T4 #&&+&$ 6>M7?C ( ) + = "#%#$ +.% "&* *)NA2,4r&' **&! 6 ,A2,&' *# (+#%&%# r4 "#%(&!'$ 3 6>7?C ( ) + = "#%#2 .% "&* *)A(4r&' *#(+#%&%# T4 &+%%#**%#>7?C ( ) n r + + + + + = $ ( "#%#+ *"#3&+%+%#**%#)"#*&! #0&#%%+ %#0&#%HLI & #(+#%&%# r&' **&! 6 ,A2,4 = = = ( = = = = = &L948FFKM = =

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F r& #* 6>7?C + + + =r0"#%# r "&* *)2,A( F &' *#(+#%&%# T4 6&( $ *$* 6>7?C n r + + = $ m 0"#%# m "&* *)*A( &' *#(+#%&%# r4 +#$ ) $#&>7?C ( ) + + = 0"#%#$ +! "&* *)NA2,4r&' *#(+#%&%# T4 "#%(&!'$ 3 6>7?C + = 0"#%#2 "&* *)A(4r&' *#(+#%&%# r4 &##&)&+% -& >7?C ( ) = "#%#" !3 "&* *)NA2,&' *#(+#%&%# r4 0n1 #* 6>M7?C n r = r "#%# r "& "&* *)2,A( F +HI *"#+&% &!+%#**%#)3&+% *"#&! +%#**%#&' *#(+#%&%# r4

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8 #)) $ #) &%6 ))* >M7?C = "#%# "&* *)( A*&' *#(+#%&%# r4 "#%(&!'$ 3 6>7?C / / + + + = 0"#%#2 "& "&* *)A(4r&' *&)$ )"#"#%(&!$ '$ 3 #*)"#& % &'3&+%0# ,"#'.6"#%#*+#$ 3#(&**%& *&'& )$ 0" $" *&)$ )"#3 *$* #*&'a0" $"%#+%#*#*(!&%$$#%& *4 n r + = / m m n r + = / m m w + = w w + = = w

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9 1 "#%(&!$'$ 3 6>7?C + = 0"#%#2 "& "&* *)A(4r&' *#(+#%&%# r4 6&( $3 *$* 6>7?C + =m 0"#%# m "&* *)*A( &' *#(+#%&%# r4 &) "#%(&!$'$ 3 6>7?C + + = 0"#%#2 "& "&* *)A(4r&' *#(+#%&%# r4 6&( $3 *$* 6>7?C + + =m 0"#%# m "&* *)*A( &' *#(+#%&%# r4 #* 6>7?C() = r 0"#%# r 3 "&* *)2,A( F &' *#(+#%&%# r4 +#$ ) $#&>M7?C + = 0"#%#$ +3 "&* *)NA2,4&' *#(+#%&%# r4

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K a @ M.file #1 %%%%%%Parametric Control Panel%%%%%% Description: Outermost loop for parametrically vary ing parameters and solving for PR %Parametrically vary second parameter for r=1:1 %eps_w=0.9-(r-1)*.25; %eps_cf=0.9-(r-1)*.25; %FR=1.2+(r-1)*0.4; %FR_r(r)=FR; %t_vs=0.000+r*0.002; %Gap-spacing %t_vs_r(r)=t_vs; %Q_in=300+r*100; %Q_in_r(r)=Q_in; %k_s=0.06+(r-1)*4; %k_s_r(r)=k_s; %T_inf = 273.16+20+(r-1)*5; %T_inf_r(r)=T_inf; %S_supply=20+(r-1)*5; %S_supply_r(r)=S_supply; %u_a = 1+(r-1)*1; %Cooling velocity %u_a_r(r)=u_a; %eps_p=.1+(r-1)*.8; %eps_p1=.1+(r-1)*.8; %Solve system across domain t for t=1:15 %m=0+t; %m_t(t)=m; %u_a = 2.1-.2*t; %Cooling velocity %u_a_t(t)=u_a; %eps_w=1.1-t*.1; %wick emissivity %eps_w_t(t)=eps_w; %eps_cf=1.1-t*.1; %condenser emissivity %eps_cf_t(t)=eps_cf; N=0+t; %number of effects N_t(t)=N; %FR=1.5+t*.1; %FR_t(t)=FR; %Parameters Q_in = 800; %heat flux of radiation source (W/m ^2) %N = 5; %Number of effects m = 5; %Resolution (if m=1, then must change md ot_evap_sum_temp equation to without the sum term) S_supply = 1; %Inlet Salinity (g/kg)

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J %mdot_supply = [.0004088 .0003386 .0002825 .000 2389 .0002059 .0001813 .0001629 .0001486 .0001359]; %flow rate of supply to each effect FR=2; %System Dimensions W=1; %system width (meters) L=1; %system height (meters) %Component Dimensions t_vs=0.01; %gap-spacing (m) t_p=0.0005; %panel thickness (m) t_w=0.0005; %wick thickness (m) t_ag = 0.01; %air gap between glazing and absor ber t_hr = .02; %thickness of heat recuperator %Component Properties k_p=15; %thermal conducitivity of panel (W/mK) k_g=1; %thermal conducitivity of glass when ap plicable (W/mK) k_s=0.06; %thermal conducitivity of wick materi al (W/mK) Nu_w1 = 1; %Nusselt number of wick flow phi = 0.6; % (V/V) porosity as volume of total air space divided by volume of matrix %k_a = 0.06; %thermal conductivity of air in ai r gap(W/mK) %Radiation constants eps_g = 0.9; %emissivity of glass eps_p1 = 0.2; %emissivity of absorber plate eps_p = 0.9; %emissivity of last panel surface for heat rejection eps_w = 0.9; %emissivity of wick surface eps_cf = 0.9; %emissivity of condenser surfaces tau_g = 0.9; %transmissivity of glazing(constan t or changes with incident angle) alpha_g = 0.1; %aborptivity of glazing alpha_p = 0.9; %absorptivity of absorber plate %Heat Rejection u_a = 1; %velocity of ambiant air on last panel (m/s) %Sensible Heat Recuperation eff=.8; %heat exchanger effectiveness %SHR=1; %choose one or the other turns on SHR with thermal mixing all effects to one equilibrium temperature SHR=2; %turns on SHR with mixing at each effect to an equilibrium temperature for each effect %Latent Heat Recuperator Nu_hr=4.86; %constant T and insulated (Shah and London) %Nu_hr=1; D=4*(t_hr*W)/(2*t_hr+2*W); %characteristic diam eter of heat recuperator (area/perimeter) %Environment Temperatures T_inf = 30+273.16; %(K) Temperature of ambient air T_surr = 30+273.16; %(K) Temperature of sky fo r reradiation T_source = 30+273.16; %(K) Temperature of supp ly brine %T_source = T_inf %System Pressure P=101325; %(Pa or N/m^2) %Run Program

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M Revision2_single_solution_outline; %Calculate Results for 1st set of parameters t T_w_t(:,:,t)=T_w; %T_cf_t(:,:,t)=T_cf; %mdot_evap_t(:,:,t)=mdot_evap(:,:); if m==1 mdot_evap_sum_t(:,t)=mdot_evap; mdot_evap_sum_sum_t(t)=sum(mdot_evap); PR_net(:,t) = (sum(h_lv_j.*(mdot_evap)))/(m *Q_supply); else mdot_evap_sum_t(:,t) = sum(mdot_evap(:,:)); mdot_evap_sum_sum_t(t) = sum(sum(mdot_evap)); PR_net(:,t) = (sum(h_lv_j.*sum(mdot_evap)))/(m* Q_supply); end if r==1 save ('temp','PR_net','S_supply','T_source','t','r' ) clear all load ('temp','PR_net','S_supply','T_source','t','r' ) else save ('temp','PR_net','PR_net_r','S_supply','T_sour ce','t','r') clear all load ('temp','PR_net','PR_net_r','S_supply','T_sour ce','t','r') end end %Save results for 2nd set of parameters r PR_net_r(r,:)=PR_net; end return %Display %Heat Rate Ratios % Q_e_HRR = Q_e./(Q_d); %ratio of evaporative heat rate to total heat rate through the partition of that effect % Q_r_HRR = Q_r./(Q_d); %ratio of radiation heat ra te to total heat rate through the partition of that effect % Q_s_HRR = Q_s./(Q_d); %ratio of conductive heat r ate to total heat rate through the partition of that effect % Q_w_f_HRR = Q_w_f./(Q_d); %ratio of conductive he at rate to total heat rate through the partition of that effect % %Overall Percentages % Q_refl_HRR_tot = Q_refl/(Q_supply*m); % Q_r_ga_HRR_tot = sum(Q_r_ga)/(Q_supply*m); % Q_c_ga_HRR_tot = sum(Q_c_ga)/(Q_supply*m); % Q_r_pna_HRR_tot = sum(Q_r_pna)/(Q_supply*m); % Q_c_pna_HRR_tot = sum(Q_c_pna)/(Q_supply*m); % for i=1:n %percentages within each effect % Q_e_HRR_tot(i) =sum(Q_e(:,i))/(Q_supply*m); % Q_r_HRR_tot(i) =sum(Q_r(:,i))/(Q_supply*m); % Q_s_HRR_tot(i) =sum(Q_s(:,i))/(Q_supply*m); % Q_w_f_HRR_tot(i) =sum(Q_w_f(:,i))/(Q_supply*m); % Q_cf_f_HRR_tot(i) =sum(Q_cf_f(:,i))/(Q_supply*m);

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7 M.file #2 %%%%%%Solver Operator: Heat Recuperation algorithm s, FR iteration, Vertical Resolution Loop, calls solver and property data generator%%%%%% n=N; %number of effects delta_y=L/m; %increment size A = W*delta_y; %area of increment Q_supply = Q_in*A; % Watts T_guess (1:4*(n-1)+7)= 303.16; %(K) first temperatu re guess for fsolve %Latent heat recuperation from the final condenser for q=1:1 %must be at least 4 or the heat added by LHR is overestimated and m must be at least 5 if q==1 T_lhr_out=T_source; else T_lhr_out =real((Q_lhr(m,n)+(sum(mdot_supply_final))*Cp_br_j( n)*T_lhr(m,1))/((su m(mdot_supply_final))*Cp_br_j(n))); %calculates the final LHR temp based on the previous T_lhr and Q_lhr end T_lhr_out_temp(q,:)=T_lhr_out; %shows itera tions of T_lhr_out %Sensible heat recuperation iteration of T_supply f rom energy rejected in massstreams (p=3 is suggested for convergence) for p=1:1 if p==1 T_shr_out(1:n) = T_lhr_out; else if SHR==1; T_shr_out(1:n) =(eff.*(sum(mdot_w(m+1,:).*Cp_br(m,:).*(T_w(m,:)-T_lhr_out))+sum(mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m, :)T_lhr_out)))+sum(mdot_supply_final).*Cp_br(1,1).*T_ lhr_out)./(sum(mdot _supply_final).*Cp_br(1,1)); %thermal mixing of all effects elseif SHR==2; T_shr_out = (eff.*(mdot_w(m+1,:).*Cp_br( m,:).*(T_w(m,:)T_lhr_out)+mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m,:)-T_ lhr_out))+ mdot_supply_final.*Cp_br(1,1).*T_lhr_out)./(mdot_su pply_final(1,:).*Cp _br(1,1)); %thermal mixing at each effect seperatel y end end T_shr_out_temp(p,:)=T_shr_out; %show iteration s of T_shr_out %mdot_supply iteration based on FR (must be higher for low vertical %resolution / suggest value of at least 4 for conve rgence) for l=1:6 if q==1 && p==1 && l==1 for i=1:n %initial guess for m_dot supply mdot_supply(l,i) = 0.00035-(i^1.1*0.00002); %(k g/s)

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end elseif l==1 %but system has already been solved for q or p mdot_supply(l,:)=FR.*mdot_evap_sum_temp(l,:); else mdot_supply(l,:)=FR.*mdot_evap_sum_temp(l-1,:); end %y direction step through for j=1:m; if j==1; T(j,:) = T_guess; %T(j,4*(n-1)+7) = T_shr_out(n); mdot_w(j,:) = mdot_supply(l,:); mdot_cf(j,1:n) = 0.000000001; t_cf(j,1:n) = 0.000001; %use function call for rest of equation S(j,1:n) = S_supply; T_w_in(j,:) = T_shr_out; T_cf_in(j,:) = T_shr_out; T_lhr(j,1) = T_source; % if q==1 % T_lhr(j,1) = T_source; %guess at average reje ction temperature of first element so as to not overpredict the heat into the recuperator % else % T_lhr(j,1) = T_source+((T_lhr_temp(2,q-1)-T_l hr_temp(1,q-1))/2); %guess based on previous temperature rises across r ecuperator % end else %mdot_evap needs calculated in j-1 results mdot_w(j,:) = mdot_w(j-1,:) mdot_evap(j-1,:); mdot_cf(j,:) = mdot_cf(j-1,:) + mdot_evap(j-1,: ); t_cf(j,:) = 0.000001; S(j,:) = S(j-1,:).*mdot_w(j-1,:)./(mdot_w(j-1,: )-mdot_evap(j1,:)); T_w_temp(j,:) = T_sol(j-1,:); T_cf_temp(j,:) = T_sol(j-1,:); T_lhr(j,1)= (Q_lhr(j-1,n)+(sum(mdot_supply(l,:)))*Cp_br_j(n)*T_lhr(j-1))/((sum(mdot_supply(l,:)))*Cp_br_j(n)); for i=1:n; T_w_in(j,i) = T_w_temp(j,4*(i-1)+4); T_cf_in(j,i) = T_cf_temp(j,4*(i-1)+5); end end mdot_w_j=mdot_w(j,:); T_w_in_j = T_w_in(j,:); T_cf_in_j = T_cf_in(j,:); T_lhr_j=T_lhr(j,1); mdot_cf_j=mdot_cf(j,:); S_j=S(j,:); t_cf_j = t_cf(j,:);

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%Temperature dependent property convergence Revision2_single_master; %properties are solved at T_temp at j T0 = T; %Starting point for fsolve %options=optimset('Display','iter') % Option to d isplay output %run solver (takes properties at T_temp, T0, mdot_w (j,:), mdot_cf(j,:), t_cf, and S and gives new T [T]=Revision2_single_solver(N,alpha_g,Q_supply,tau_ g,alpha_p,A,sigma,e ps_p1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu_ w1,k_w_j,t_w,k_g,md ot_w_j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j, a,b,c,d,e,f,g,h,k,S _j,eps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j, Cp_l_j,T_cf_in_j,ep s_p,T0); %with rejection to ambient %[T]=Revision2_single_solver(N,alpha_g,Q_supply,tau _g,alpha_p,A,sigma, eps_p1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu _w1,k_w_j,t_w,k_g,m dot_w_j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j ,a,b,c,d,e,f,g,h,k, S_j,eps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j ,Cp_l_j,T_cf_in_j,N u_hr,D,k_br_j,T_lhr_j,eps_p,T0); %system is solved with properties at T_temp at j to give new T Revision2_single_master; %properties are solved at T_temp at j T0 = T; %Starting point for fsolve %options=optimset('Display','iter') % Option to d isplay output %run solver (takes properties at T_temp, T0, mdot_w (j,:), mdot_cf(j,:), t_cf, and S and gives new T [T]=Revision2_single_solver(N,alpha_g,Q_supply,tau_ g,alpha_p,A,sigma,e ps_p1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu_ w1,k_w_j,t_w,k_g,md ot_w_j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j, a,b,c,d,e,f,g,h,k,S _j,eps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j, Cp_l_j,T_cf_in_j,ep s_p,T0); %with rejection ambient %[T]=Revision2_single_solver(N,alpha_g,Q_supply,tau _g,alpha_p,A,sigma, eps_p1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu _w1,k_w_j,t_w,k_g,m dot_w_j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j ,a,b,c,d,e,f,g,h,k, S_j,eps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j ,Cp_l_j,T_cf_in_j,N u_hr,D,k_br_j,T_lhr_j,eps_p,T0); %system is solved with properties at T_temp at j to give new T Revision2_single_master; %properties are solved at T_temp at j T0 = T; %Starting point for fsolve %options=optimset('Display','iter') % Option to d isplay output %run solver (takes properties at T_temp, T0, mdot_w (j,:), mdot_cf(j,:), t_cf, and S and gives new T [T]=Revision2_single_solver(N,alpha_g,Q_supply,tau_ g,alpha_p,A,sigma,e ps_p1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu_ w1,k_w_j,t_w,k_g,md ot_w_j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j, a,b,c,d,e,f,g,h,k,S _j,eps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j, Cp_l_j,T_cf_in_j,ep s_p,T0); %with rejection to ambient %[T]=Revision2_single_solver(N,alpha_g,Q_supply,tau _g,alpha_p,A,sigma, eps_p1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu _w1,k_w_j,t_w,k_g,m dot_w_j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j ,a,b,c,d,e,f,g,h,k, S_j,eps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j ,Cp_l_j,T_cf_in_j,N u_hr,D,k_br_j,T_lhr_j,eps_p,T0); % with heat recupe ration system is solved with properties at T_temp at j to give new T

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T_sol(j,:)=real(T); %save the final T for j int o T_sol matrix T_temp(j,:)= T; for i=1:n %location temperatures T_g(j,i)=real(T(4*(i-1)+1)); T_p1(j,i)=real(T(4*(i-1)+2)); T_p2(j,i)=real(T(4*(i-1)+3)); T_w(j,i)=real(T(4*(i-1)+4)); T_cf(j,i)=real(T(4*(i-1)+5)); T_m_vs(j,i)=real((T(4*(i-1)+4)+ T(4*(i-1)+5))/2 ); end mdot_evap(j,:)= real(((A.*D_ab(j,:).*P)./(R.*t_vs.*T_m_vs(j,:))).*l og((P(100000.*10.^(a+b./T_cf(j,:)+((c.*(T_cf(j,:).^2-g))./T_cf(j,:)).*(10.^(d.*(T_cf(j,:).^2-g).^2)-1) + e.*10.^(f.*(617.27-T_cf(j,:)).^1.25))))./(P-(100000.*10.^(a+b./T_w(j,:)+((c.*(T_w(j,:).^2-g))./T_w(j,:)).*(10.^(d.*(T_w(j,:).^2-g).^2)-1) + e .*10.^(f.*(617.27T_w(j,:)).^1.25) + h.*S(j,:) + k.*S(j,:).^2))))); for i=1:n %heat flux components(for HHR's) if i==1; Q_c_ga(j,i)= real(A*(5.7+3.8*u_a)*(T(1)-T_i nf)); Q_r_ga(j,i)= real(sigma*eps_g*A*(T(1)^4-T_s urr^4)); Q_d_p1g(j,i)= real((A*k_a_j/t_ag)*(T(2)-T(1 ))); Q_r_p1g(j,i)= real(((A*sigma)/(1/eps_p1+1/e ps_g-1))*(T(2)^4T(1)^4)); end Q_d(j,i) = real((k_p*A/t_p)*(T(4*(i-1)+2) T(4*(i-1)+3))); Q_w_f(j,i) = real((mdot_w_j(i)*Cp_br_j(i)*( T(4*(i-1)+4) T_w_in_j(i)))); Q_cf_f(j,i) = real((mdot_cf_j(i)*Cp_l_j(i)* (T(4*(i-1)+5) T_cf_in_j(i)))); Q_w(j,i) = real((Nu_w1*k_w_j(i)*A/t_w)*(T(4 *(i-1)+3)-T(4*(i1)+4))); Q_e(j,i) = real(((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m_vs_j(i) ))*log((P(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))); Q_r(j,i) = real((1/((1/eps_w)+(1/eps_cf)-1) )*A*sigma*(T(4*(i1)+4)^4-T(4*(i-1)+5)^4)); Q_s(j,i) = real((A*k_ha_j(i)/t_vs)*(T(4*(i1)+4)-T(4*(i1)+5))); % or from McBain Q_cf(j,i) = real((k_l_j(i)*A/t_cf_j(i)))*(T (4*(i-1)+5)-T(4*(i1)+6)); if i==n Q_c_pna(j,i) = real((A*(5.7+3.8*u_a)*(T(4*( i-1)+7)-T_inf))); Q_r_pna(j,i) = real(sigma*eps_p*A*(T(4*(i-1 )+7)^4-T_surr^4)); Q_d(j,i) = real((k_p*A/t_p)*(T(4*(i-1)+6) T(4*(i-1)+7))); %for recuperator on back plate

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F % if j==1 % Q_lhr(j,i) = .1*(Nu_hr*k_br_j(n)*A)/(D)*( T(4*(i-1)+7)T_lhr_j); % else Q_lhr(j,i) = (Nu_hr*k_br_j(n)*A)/(D)*(T(4*( i-1)+7)-T_lhr_j); % end end end end %calculate total mdot_evap to calculate mdot_supply based on FR if m==1 mdot_evap_sum_temp(l,:)=(mdot_evap); %need vect or, if resolution is one, then the sum is not needed else mdot_evap_sum_temp(l,:)=sum(mdot_evap); %turns matrix into vector end end %calculate final mass flow rates at bottom of syste m for heat recuperation mdot_w(j+1,:) = mdot_w(j,:) mdot_evap(j,:); mdot_cf(j+1,:) = mdot_cf(j,:) + mdot_evap(j,:); mdot_supply_final=mdot_supply(l,:); S(j+1,:) = S(j,:).*mdot_w(j,:)./(mdot_w(j,:)-mdot_e vap(j,:)); T_lhr_temp(:,q)=T_lhr; end end %Total system energy balance %Total system energy in Q_net_in = alpha_g*(Q_supply)*m + (Q_supply*tau_g*a lpha_p)*m %Q_refl = Q_supply*m Q_net_in; %Without recuperation Q_net_out = (sum(mdot_w(m+1,:).*Cp_br(m,:).*(T_w(m, :)T_inf))+sum(mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m,:)-T _inf))) + sum(Q_d(:,n)) + sum(Q_c_ga)+sum(Q_r_ga) %With latent heat recuperation on final condenser Q_net_out_lhr = (sum(mdot_w(m+1,:).*Cp_br(m,:).*(T_ w(m,:)T_lhr_out))+sum(mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m, :)-T_lhr_out))) + sum(Q_d(:,n)) + sum(Q_c_ga)+sum(Q_r_ga) %With sensible heat recuperation from mass flows wi th total mixing %Q_net_out_SHR1 = (1-eff).*(sum(mdot_w(m+1,:).*Cp_b r(m,:).*(T_w(m,:)T_lhr_out))+sum(mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m, :)-T_lhr_out))) + sum(Q_d(:,n)) + sum(Q_c_ga)+sum(Q_r_ga) %With sensible heat recuperation from mass flows wi th individual mixing %Q_net_out_SHR2 = sum((1-eff).*(mdot_w(m+1,:).*Cp_b r(m,:).*(T_w(m,:)T_lhr_out)+mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m,:)-T_ lhr_out))) + sum(Q_d(:,n)) + sum(Q_c_ga)+sum(Q_r_ga) %With latent and SHR1 Q_net_out_LHR_SHR1 = (1-eff).*(sum(mdot_w(m+1,:).*Cp_br(m,:).*(T_w(m,:)-

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8 T_lhr_out))+sum(mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m, :)-T_lhr_out))) + sum(Q_d(:,n)) + sum(Q_c_ga)+sum(Q_r_ga) %With latent and SHR2 Q_net_out_LHR_SHR2 = sum((1-eff).*(mdot_w(m+1,:).*Cp_br(m,:).*(T_w(m,:)-T_lhr_out)+mdot_cf(m+1,:).*Cp_l(m,:).*(T_cf(m,:)-T_ lhr_out))) + sum(Q_d(:,n)) + sum(Q_c_ga)+sum(Q_r_ga) %Net performance ratio %if m==1 %PR_net = (sum(h_lv_j.*(mdot_evap)))/(m*Q_supply) %else %PR_net = (sum(h_lv_j.*sum(mdot_evap)))/(m*Q_supply ) %end M.file #3 %%%%%%Equation set generator and solver engine%%%%% % function [T,fval] = Revision2_single_solver(N,alpha_g,Q_supply,tau_g,al pha_p,A,sigma,eps_p 1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu_w1,k _w_j,t_w,k_g,mdot_w _j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j,a,b, c,d,e,f,g,h,k,S_j,e ps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j,Cp_l _j,T_cf_in_j,eps_p, T0); %with rejection to air %function [T] = Revision2_single_solver(N,alpha_g,Q_supply,tau_g,al pha_p,A,sigma,eps_p 1,eps_g,k_a_j,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu_w1,k _w_j,t_w,k_g,mdot_w _j,Cp_br_j,T_w_in_j,h_lv_j,D_ab_j,P,R,T_m_vs_j,a,b, c,d,e,f,g,h,k,S_j,e ps_w,eps_cf,k_ha_j,t_vs,k_l_j,t_cf_j,mdot_cf_j,Cp_l _j,T_cf_in_j,Nu_hr, D,k_br_j,T_lhr_j,eps_p,T0); %with rejection to heat recuperator %function [T,fval] = Revision2_single_solver(alpha_g,Q_supply,tau_g,alph a_p,A,sigma,eps_p1, eps_g,k_a,t_ag,T_surr,u_a,T_inf,k_p,t_p,Nu_w1,k_w_j ,t_w,k_g,mdot_w_j,C p_br_j,T_w_in,h_lv_j,D_ab_j,P,R,T_m_vs_j,a,b,c,d,e, f,g,h,k,S_j,eps_w,e ps_cf,k_ha_j,t_vs,mdot_cf_j,Cp_l_j,k_l_j,t_cf_j,T_c f_in,eps_p,T0); [T,fval] = fsolve(@nestedfun,T0); % Nested function that computes the objective funct ion function y = nestedfun(T) n=N; for i=1:n; %equation builder GC = alpha_g*(Q_supply)+(((A*sigma)/(1/eps_p1+1/eps _g-1))*(T(2)^4T(1)^4))+((A*k_a_j/t_ag)*(T(2)-T(1)))-(sigma*eps_g* A*(T(1)^4T_surr^4))-(A*(5.7+3.8*u_a)*(T(1)-T_inf)); %GC = alpha_g*(Q_supply)/(tau_g*alpha_p)+(((A*sigma)/(1/e ps_p1+1/eps_g1))*(T(2)^4-T(1)^4))+((A*k_a_j/t_ag)*(T(2)-T(1)))-(sigma*eps_g*A*(T(1)^4-T_surr^4))-(A*(5.7+3.8*u_a)* (T(1)-T_inf)); %Tanaka model %Q_r_p1g(j,:)= ((A*sigma)/(1/eps_p1+1/eps_g-1))*(T( 2)^4-T(1)^4); %Q_d_p1g(j,:)= (A*k_a/t_ag)*(T(2)-T(1));

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9 %Q_r_ga(j,:)= sigma*eps_g*A*(T(1)^4-T_surr^4); %Q_c_ga(j,:)= A*(5.7+3.8*u_a)*(T(1)-T_inf); AB = (Q_supply*tau_g*alpha_p) (((A*sigma)/(1/eps_ p1+1/eps_g1))*(T(2)^4-T(1)^4)) ((A*k_a_j/t_ag)*(T(2)-T(1))) ((k_p*A/t_p)*(T(2) T(3))); %AB = (Q_supply) (((A*sigma)/(1/eps_p1+1/eps_g-1) )*(T(2)^4-T(1)^4)) ((A*k_a_j/t_ag)*(T(2)-T(1))) ((k_p*A/t_p)*(T(2) T(3))); %Tanaka Model %Q_d(j,1) = (k_p*A/t_p)*(T(2) T(3)); P1_e(i,:)= ((k_l_j(i)*A/t_cf_j(i)))*(T(4*(i-1)+5)-T (4*(i-1)+6))((k_p*A/t_p)*(T(4*(i-1)+6) T(4*(i-1)+7))); %P1_e(1)= ((k_l_j(i).*A/t_cf_j(i)))*(T(6)-T(7))-((k _g*A/t_p)*(T(7) T(8))); %P1_e(2)= ((k_l_j(i).*A/t_cf_j(i)))*(T(11)-T(12))-( (k_g*A/t_p)*(T(12) T(13))); %Q_cf(j,i) = ((k_l_j(i)*A/t_cf_j(i)))*(T(4*(i-1)+5) -T(4*(i-1)+6)); %Q_d(j,i) = ((k_p*A/t_p)*(T(4*(i-1)+6) T(4*(i-1)+ 7))); P2_e(i,:)= ((k_p*A/t_p)*(T(4*(i-1)+2) T(4*(i-1)+3 )))((Nu_w1*k_w_j(i)*A/t_w)*(T(4*(i-1)+3)-T(4*(i-1)+4)) ); %P2_e(1)= ((k_p*A/t_p)*(T(2) T(3)))-((Nu_w1.*k_w_ j(i).*A/t_w)*(T(3)T(4))); %P2_e(2)= ((k_p*A/t_p)*(T(7) T(8)))-((Nu_w1.*k_w_ j(i).*A/t_w)*(T(8)T(9))); %Q_w(j,i) = ((Nu_w1*k_w_j(i)*A/t_w)*(T(4*(i-1)+3)-T (4*(i-1)+4))); %P2_en = ((k_p*A/t_p)*(T(4*(n-1)+6) T(4*(n-1)+7)) ) ((Nu_hr*k_br_j(n)*A)/D)*(T(4*(n-1)+7)-T_lhr_j); %wi th rejection to heat recuperator P2_en = ((k_p*A/t_p)*(T(4*(n-1)+6) T(4*(n-1)+7))) (A*(5.7+3.8*u_a)*(T(4*(n-1)+7)-T_inf)) (sigma*eps _p*A*(T(4*(n1)+7)^4-T_surr^4)); %with rejection to ambient air from Tanaka %Q_d(j,n) = ((k_p*A/t_p)*(T(4*(n-1)+6) T(4*(n-1)+ 7))); %Q_c_pna = (A*(5.7+3.8*u_a)*(T(4*(n-1)+7)-T_inf)); %Q_r_pna = (sigma*eps_p*A*(T(4*(n-1)+7)^4-T_surr^4) ); %WCV(i,:)= ((Nu_w1.*k_w_j(i)*A/t_w)*(T(5*(i-1)+3)-T (5*(i-1)+4))) + (mdot_w_j(i).*Cp_br_j(i).*T_m_w_j(i)) ((mdot_w_j( i) (((A.*D_ab_j(i).*P)/(R*t_vs.*T_m_vs_j(i)))*log((P-(100000*10^(a+b/T(5*(i-1)+6)+((c*(T(5*(i-1)+6)^2-g) )/T(5*(i1)+6))*(10^(d*(T(5*(i-1)+6)^2-g)^2)-1) + e*10^(f*(6 17.27-T(5*(i1)+6))^1.25))))/(P-(100000*10^(a+b/T(5*(i-1)+5)+((c *(T(5*(i-1)+5)^2g))/T(5*(i-1)+5))*(10^(d*(T(5*(i-1)+5)^2-g)^2)-1) + e*10^(f*(617.27T(5*(i-1)+5))^1.25) + h*S_j(i) + k*S_j(i)^2))))))*C p_br_j(i)*T(5*(i1)+4)) ((Nu_w2*k_w_j(i)*A/t_w)*(T(5*(i-1)+4) T( 5*(i-1)+5))); %WCV(i,:)= ((Nu_w1*k_w_j(i)*A/t_w)*(T(5*(i-1)+3)-T( 5*(i-1)+4))) + (mdot_w_j(i).*Cp_br_j(i)*T_m_w_j(i)) (mdot_w_j(i) *Cp_br_j(i)*T(5*(i1)+5)) ((Nu_w2*k_w_j(i)*A/t_w)*(T(5*(i-1)+4) T( 5*(i-1)+5)));

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K %WCV(1)= ((Nu_w1.*k_w_j(i)*A/t_w)*(T(3)-T(4))) + (mdot_w_j(i).*Cp_br_j(i).*T_m_w_j(i)) ((mdot_w_j( i) (((A.*D_ab_j(i).*P)/(R*t_vs.*T_m_vs_j(i)))*log((P-(100000*10^(a+b/T(6)+((c*(T(6)^2-g))/T(6))*(10^(d*( T(6)^2-g)^2)-1) + e*10^(f*(617.27-T(6))^1.25))))/(P-(100000*10^(a+b/T (5)+((c*(T(5)^2g))/T(5))*(10^(d*(T(5)^2-g)^2)-1) + e*10^(f*(617.27 -T(5))^1.25) + h*S_j(i) + k*S_j(i)^2))))))*Cp_br_j(i)*T(4)) ((Nu_w2*k_w_j(i)*A/t_w)*(T(4) T(5))); %WCV(2)= ((Nu_w1.*k_w_j(i)*A/t_w)*(T(8)-T(9))) + (mdot_w_j(i).*Cp_br_j(i).*T_m_w_j(i)) ((mdot_w_j( i) (((A.*D_ab_j(i).*P)/(R*t_vs.*T_m_vs_j(i)))*log((P-(100000*10^(a+b/T(11)+((c*(T(11)^2-g))/T(11))*(10^( d*(T(11)^2-g)^2)-1) + e*10^(f*(617.27-T(11))^1.25))))/(P-(100000*10^(a+b/T(10)+((c*(T(10)^2-g))/T(10))*(10^( d*(T(10)^2-g)^2)-1) + e*10^(f*(617.27-T(10))^1.25) + h*S_j(i) + k*S_j(i)^2))))))*Cp_br_j(i)*T(9)) ((Nu_w2*k_w_j(i )*A/t_w)*(T(9) T(10))); W(i,:)= ((Nu_w1*k_w_j(i))*A/t_w)*(T(4*(i-1)+3) T( 4*(i-1)+4)) mdot_w_j(i)*Cp_br_j(i)*(T(4*(i-1)+4) T_w_in_j(i)) (((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m_vs_j(i)))*l og((P(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))) ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(4*(i-1)+4) ^4-T(4*(i-1)+5)^4)) ((A*k_ha_j(i)/t_vs)*(T(4*(i-1)+4)-T(4*(i-1)+5))); %WCS(1)= ((Nu_w2*k_w_j(i))*A/t_w)*(T(4) T(5)) (((A*h_lv_j(i)*D_ab_j(1)*P)/(R*t_vs*T_m_vs_j(i)))*l og((P(100000*10^(a+b/T(6)+((c*(T(6)^2-g))/T(6))*(10^(d*( T(6)^2-g)^2)-1) + e*10^(f*(617.27-T(6))^1.25))))/(P-(100000*10^(a+b/T (5)+((c*(T(5)^2g))/T(5))*(10^(d*(T(5)^2-g)^2)-1) + e*10^(f*(617.27 -T(5))^1.25) + h*S_j(i) + k*S_j(i)^2))))) ((1/((1/eps_w)+(1/eps_ cf)1))*A*sigma*(T(5)^4-T(6)^4)) ((A*k_ha_j(i)/t_vs)* (T(5)-T(6))); %WCS(2)= ((Nu_w2*k_w_j(i))*A/t_w)*(T(9) T(10)) (((A*h_lv_j(i)*D_ab_j(1)*P)/(R*t_vs*T_m_vs_j(i)))*l og((P(100000*10^(a+b/T(11)+((c*(T(11)^2-g))/T(11))*(10^( d*(T(11)^2-g)^2)-1) + e*10^(f*(617.27-T(11))^1.25))))/(P-(100000*10^(a+b/T(10)+((c*(T(10)^2-g))/T(10))*(10^( d*(T(10)^2-g)^2)-1) + e*10^(f*(617.27-T(10))^1.25) + h*S_j(i) + k*S_j(i )^2))))) ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(10)^4-T(11 )^4)) ((A*k_ha_j(i)/t_vs)*(T(10)-T(11))); %Q_w_f(j,i) = mdot_w_j(i)*Cp_br_j(i)*(T(4*(i-1)+4) T_w_in(i)); %Q_e(j,i) = (((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m _vs_j(i)))*log((P(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i-

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J 1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))) %Q_r(j,i) = ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*( T(4*(i-1)+4)^4T(4*(i-1)+5)^4)); %Q_s(j,i) = ((A*k_ha_j(i)/t_vs)*(T(4*(i-1)+4)-T(4*( i-1)+5))); % or from McBain %CF(i,:)=(((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m_vs _j(i)))*log((P(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))) + ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(4*(i-1)+4) ^4-T(4*(i-1)+5)^4)) + ((A*k_ha_j(i)/t_vs)*(T(4*(i-1)+4)-T(4*(i-1)+5))) (k_l_j(i)*A/t_cf_j(i))*(T(4*(i-1)+5) T(4*(i-1)+6) ) mdot_cf_j(i)*Cp_l_j(i)*(T(4*(i-1)+5)-T_cf_in_j(i)); % include heating of CF flow CF(i,:)=(((A*(h_lv_j(i)+Cp_br_j(i).*(T(4*(i-1)+4)-T (4*(i1)+5)))*D_ab_j(i)*P)/(R*t_vs*T_m_vs_j(i)))*log((P-(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))) + ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(4*(i-1)+4) ^4-T(4*(i-1)+5)^4)) + ((A*k_ha_j(i)/t_vs)*(T(4*(i-1)+4)-T(4*(i-1)+5))) (k_l_j(i)*A/t_cf_j(i))*(T(4*(i-1)+5) T(4*(i-1)+6) ) mdot_cf_j(i)*Cp_l_j(i)*(T(4*(i-1)+5)-T_cf_in_j(i)); % include superheat and heating of CF flow %CF(i,:)= (((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m_v s_j(i)))*log((P(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))) + ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(4*(i-1)+4) ^4-T(4*(i-1)+5)^4)) + ((A*k_ha_j(i)/t_vs)*(T(4*(i-1)+4)-T(4*(i-1)+5))) (k_l_j(i)*A/t_cf_j(i))*(T(4*(i-1)+5) T(4*(i-1)+6) ); %does not include either superheat or heating the incoming CF flow %CF(i,:)=(((A*(h_lv_j(i)+Cp_br_j(i).*(T(4*(i-1)+4)T(4*(i1)+5)))*D_ab_j(i)*P)/(R*t_vs*T_m_vs_j(i)))*log((P-(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27-

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M T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))) + ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(4*(i-1)+4) ^4-T(4*(i-1)+5)^4)) + ((A*k_ha_j(i)/t_vs)*(T(4*(i-1)+4)-T(4*(i-1)+5))) (k_l_j(i)*A/t_cf_j(i))*(T(4*(i-1)+5) T(4*(i-1)+6) ); % include superheat %CF(j,i)= (((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m_v s_j(i)))*log((P(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))) + ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(4*(i-1)+4) ^4-T(4*(i-1)+5)^4)) + ((A*k_ha_j(i)/t_vs)*(T(4*(i-1)+4)-T(4*(i-1)+5))) + ((((A*D_ab_j(i)*P)/(R*t_vs*T_m_vs_j(i)))*log((P-(100000*10^(a+b/T(4*(i-1)+5)+((c*(T(4*(i-1)+5)^2-g) )/T(4*(i1)+5))*(10^(d*(T(4*(i-1)+5)^2-g)^2)-1) + e*10^(f*(6 17.27-T(4*(i1)+5))^1.25))))/(P-(100000*10^(a+b/T(4*(i-1)+4)+((c *(T(4*(i-1)+4)^2g))/T(4*(i-1)+4))*(10^(d*(T(4*(i-1)+4)^2-g)^2)-1) + e*10^(f*(617.27T(4*(i-1)+4))^1.25) + h*S_j(i) + k*S_j(i)^2))))))*C p_l_j(i)*(T(4*(i1)+4)-T(4*(i-1)+5)) mdot_cf_j(i)*Cp_l_j(i)*(T(4*( i-1)+5) T_cf_in(i)) (k_l_j(i)*A/t_cf_j(i))*(T(4*(i-1)+5) T(4*(i1)+6));%includes both superheat and heating the inc oming wall flow %CF(j,i)= (((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m_v s_j(i)))*log((P(100000*10^(a+b/T(5*(i-1)+6)+((c*(T(5*(i-1)+6)^2-g) )/T(5*(i1)+6))*(10^(d*(T(5*(i-1)+6)^2-g)^2)-1) + e*10^(f*(6 17.27-T(5*(i1)+6))^1.25))))/(P-(100000*10^(a+b/T(5*(i-1)+5)+((c *(T(5*(i-1)+5)^2g))/T(5*(i-1)+5))*(10^(d*(T(5*(i-1)+5)^2-g)^2)-1) + e*10^(f*(617.27T(5*(i-1)+5))^1.25) + h*S_j(i) + k*S_j(i)^2))))) + ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(5*(i-1)+5) ^4-T(5*(i-1)+6)^4)) + ((A*k_ha_j(i)/t_vs)*(T(5*(i-1)+5)-T(5*(i-1)+6))) + (mdot_cf_j(i)*Cp_l_j(i)*T_cf_j(i)) (mdot_cf_j(i)* Cp_l_j(i)*T(5*(i1)+6)) ((k_l_j(i)*A/t_cf_j(i))*(T(5*(i-1)+6) T( 5*(i-1)+7))); %CF(j,i)= (((A*h_lv_j(i)*D_ab_j(i)*P)/(R*t_vs*T_m_v s_j(i)))*log((P(100000*10^(a+b/T(5*(i-1)+6)+((c*(T(5*(i-1)+6)^2-g) )/T(5*(i1)+6))*(10^(d*(T(5*(i-1)+6)^2-g)^2)-1) + e*10^(f*(6 17.27-T(5*(i1)+6))^1.25))))/(P-(100000*10^(a+b/T(5*(i-1)+5)+((c *(T(5*(i-1)+5)^2g))/T(5*(i-1)+5))*(10^(d*(T(5*(i-1)+5)^2-g)^2)-1) + e*10^(f*(617.27T(5*(i-1)+5))^1.25) + h*S_j(i) + k*S_j(i)^2))))) + ((1/((1/eps_w)+(1/eps_cf)-1))*A*sigma*(T(5*(i-1)+5) ^4-T(5*(i-1)+6)^4)) + ((A*k_ha_j(i)/t_vs)*(T(5*(i-1)+5)-T(5*(i-1)+6))) + (mdot_cf_j(i)*Cp_l_j(i)*T_cf_j(i)) ((mdot_cf_j(i)+(((A*D_ab_j(i)*P)/(R*t_vs*T_m_vs_j(i )))*log((P(100000*10^(a+b/T(5*(i-1)+6)+((c*(T(5*(i-1)+6)^2-g) )/T(5*(i1)+6))*(10^(d*(T(5*(i-1)+6)^2-g)^2)-1) + e*10^(f*(6 17.27-T(5*(i1)+6))^1.25))))/(P-(100000*10^(a+b/T(5*(i-1)+5)+((c *(T(5*(i-1)+5)^2g))/T(5*(i-1)+5))*(10^(d*(T(5*(i-1)+5)^2-g)^2)-1) + e*10^(f*(617.27T(5*(i-1)+5))^1.25) + h*S_j(i) + k*S_j(i)^2)))))))* Cp_l_j(i)*T(5*(i1)+6) ((k_l_j(i)*A/t_cf_j(i))*(T(5*(i-1)+6) T(5 *(i-1)+7)));

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7 %Q_cf(j,i) = (k_l_j(i)*A/t_cf_j(i))*(T(4*(i-1)+5) T(4*(i-1)+6)); end y = [GC; AB; P1_e; P2_e; P2_en; W; CF]; end end %T_g = T(1) %T_p1(1) = T(2) %T_p2(1) = T(3) %T_w(1) = T(4) %T_cf(1) = T(5) %T_p1(2) = T(6) %T_p2(2) = T(7) M.file #4 %%%%%%Temperature dependent property data generator %%%%%% T_temp(j,:)= T; n=N; for i=1:n %Temperature guesses for property calculation cal culates T_w and T_cf %vectors as T_temp vector as input T_w(j,i)=T_temp(j,4*(i-1)+4); z_w(j,i)=T_w(j,i)273.16; T_w_j(i)= T_temp(j,4*(i-1)+4); T_cf(j,i)=T_temp(j,4*(i-1)+5); z_cf(j,i)=T_cf(j,i) 273.16; T_cf_j(i)=T_temp(j,4*(i-1)+5); T_m_vs(j,i)=(T_temp(j,4*(i-1)+4)+ T_temp(j,4*(i-1)+ 5))/2; T_m_vs_j(i)=(T_temp(j,4*(i-1)+4)+ T_temp(j,4*(i-1)+ 5))/2; end T_m_a(j,1)=(T_temp(j,1)+T_temp(j,2))/2; T_m_a_j(1)=(T_temp(j,1)+T_temp(j,2))/2; %Air gap constants k_a(j,:)=0.000851+0.00009555.*T_m_a(j,:)-0.00000003 75.*T_m_a(j,:).^2; %thermal conductivity of air in air gap(W/mK) k_a_j=k_a(j,:); %Film / Wick constants Cp_br(j,:) = 3958 52.3.*(S(j,:).*.1) + 0.837.*T_w (j,:); Cp_br_j = Cp_br(j,:); k_br(j,:) = (577 + 1.522.*(T_w(j,:)-273.16) 0.005 81.*(T_w(j,:)273.16).^2).*10.^(-3); %(W/mK) thermal conductivity of liquid within matrix (source Shalabh pg67)

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k_br_j=k_br(j,:); k_w(j,:) = (1-phi).*k_s + phi.*k_br(j,:); % (W/mK) effective conductivity of parallet heat transfer through wick matrix and liquid k_w_j=k_w(j,:); %rho_br(j,:)=1000*(1+0.805*(S(j,:)*1000)-0.0000065* (T_w(j,:)4+220*(S(j,:)*1000))^2): %not used yet (Holzbecher ) %Latent transfer constants D_ab(j,:) = 0.000000000187.*T_m_vs(j,:).^(2.072); % D_ab_j=D_ab(j,:); R = 461.5; %(J/kgK) h_lv(j,:) = 1000.*(3146 2.36.*T_w(j,:)); %(J/kg) latent of vaporization at wick temperature h_lv_j=h_lv(j,:); a = 5.432368; %constants for calculation of partial pressure b = -2005.1; c = 0.00013869; d = 0.000000000011965; e = -0.0044; f = -0.0057148; g = 293700; h = -0.0002169; k = -0.00000035012; sigma=0.0000000567; %W/m^2K^4 %Condensation Film constants mu_l(j,:) = 0.001*(10.^(-10.2158 + 1792.5./T_cf(j,: ) + 0.01773.*T_cf(j,:) 0.000012631.*T_cf(j,:).^2)); % (mNs/m^2) dynamic viscosity of liquid water (Shalabh) %z_cf = T_cf 273.16; rho_l(j,:) = (999.83952 + 16.945176.*(T_cf(j,:)-273 .16) 0.0079870401.*(T_cf(j,:)-273.16).^2-0.000046170461. *(T_cf(j,:)273.16).^3+0.00000010556302.*(T_cf(j,:)-273.16).^4)./(1+0.016879850.*(T_cf(j,:)-273.16)); % (kg/m^3) density of liquid water (Shalabh) gv = 9.81; % (m/s^2) gravity P_cf(j,:) = 100000.*10.^(a+b./T_cf(j,:)+((c.*(T_cf( j,:).^2g))./T_cf(j,:)).*(10.^(d.*(T_cf(j,:).^2-g).^2)-1) + e.*10.^(f.*(617.27-T_cf(j,:)).^1.25)); % (N/m^2) pa rtial pressure of water vapor of condensor film surface with x(T) and y(T) plugged in P_w(j,:) = 100000.*10.^(a+b./T_w(j,:)+((c.*(T_w(j,: ).^2g))./T_w(j,:)).*(10.^(d.*(T_w(j,:).^2-g).^2)-1) + e .*10.^(f.*(617.27T_w(j,:)).^1.25)+ h.*S(j,:) + k.*S(j,:).^2); P_m_vs(j,:)=(P_cf(j,:)+P_w(j,:))./2; rho_ha(j,:) = (352.6*(1-0.378.*P_cf(j,:)/P))./T_cf( j,:); %(kg/m^3) density of humid air used for momentum balance on c ondenser film (Tanaka) t_cf(j,:) = ((3.*mdot_cf(j,:).*mu_l(j,:))./(gv*W.*rho_l(j,:).*( rho_l(j,:)rho_ha(j,:)))).^(1/3); %thickness of condenser film based on mass flow rate and laminar condensing film assumptions (sourc e: Carey) t_cf_j=t_cf(j,:);

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Cp_l(j,:) = 1000.*(4.2174 0.003720283.*(T_cf(j,:) -273.16) + 0.0001412855.*(T_cf(j,:)-273.16).^2 0.00000265438 7.*(T_cf(j,:)273.16).^3 + 0.00000002093236.*(T_cf(j,:)-273.16).^ 4); % (kJ/kgK) specific heat of liquid water (Source: Shalabh) Cp_l_j=Cp_l(j,:); k_l(j,:) = -0.2758 + 0.004612.*T_cf(j,:) 0.000005 5391.*T_cf(j,:).^2; % (W/mK) thermal conductivity of liquid water (Sour ce: Shalabh) k_l_j=k_l(j,:); %Vapor space thermal conductivity calculation k_v(j,:)=-0.003537+0.0000654755.*T_m_vs(j,:)+0.000000017446.* T_m_vs(j,:).^2; k_a2(j,:)=0.000669881+0.0000942482.*T_m_vs(j,:)-0.0000000327450.*T_m_vs(j,:).^2; mu_v(j,:)=-0.00000097494+0.0000000359061.*T_m_vs(j,:)+0.000000 000000241612.*T_m_v s(j,:).^2; mu_a(j,:)=0.00000143387+0.0000000656244*T_m_vs(j,:) 0.000000000029905.*T_m_vs(j,:).^2; X_v(j,:)=(0.622.*(P_m_vs(j,:)./(P-P_m_vs(j,:))))./(0.62197058+(0.622.*(P_m_vs(j,:)./( P-P_m_vs(j,:))))); X_a(j,:)=1./(1+1.607793.*(0.622.*(P_m_vs(j,:)./(P-P _m_vs(j,:))))); G_v(j,:)=0.277609.*(1+1.12605.*(mu_v(j,:)./mu_a(j,: )).^0.5).^2; G_a(j,:)=0.2189366.*(1+0.8880603.*(mu_a(j,:)./mu_v( j,:)).^0.5).^2; k_ha(j,:)=k_v(j,:)./(1+G_v(j,:).*(X_a(j,:)./X_v(j,: )))+k_a2(j,:)./(1+G _a(j,:).*(X_v(j,:)./X_a(j,:))); k_ha_j=k_ha(j,:); % %McBain: % %rho_v(j,:)=1./((460.5.*T_m_vs(j,:))./P_w(j,:)-0. 02); %Shalabh % rho_v(j,:)=0.0022*P_w(j,:)./T_m_vs(j,:); % Cp_v(j,:)=3399.476-10.83929.*T_m_vs(j,:)+0.019166 67.*T_m_vs(j,:).^2; %Tanaka % Le_v(j,:)=k_v(j,:)./(rho_v(j,:).*Cp_v(j,:).*D_ab( j,:)); % w_cf(j,:)=0.622.*(P_cf(j,:)./(P-P_cf(j,:))); % w_w(j,:)=0.622.*(P_w(j,:)./(P-P_w(j,:))); % B(j,:)=(w_w(j,:)-w_cf(j,:))./(w_cf(j,:)-1); % Nu_vs(j,:)=log((P-P_cf(j,:))/(P-P_w(j,:))).*(1./( Le_v(j,:).*(((PP_cf(j,:))/(P-P_w(j,:))).^(1./(Le_v(j,:)))-1))); %M cBain modifier of conduction % Nu_vs_j=Nu_vs(j,:);

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