Transporte de Calor en Una Placa-Isamar y Brenda Rios

8/16/2019 Transporte de Calor en Una Placa-Isamar y Brenda Rios

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DIFERENCIAS FINITAS 2D - TRANSPOR

REFERENCIA DE NODOS

"0,3" "1,3" "2,3" "3,3" Delta X

"0,2" "1,2" "2,2" "3,2" Delta Y

"0,1" "1,1" "2,1" "3,1"

"0,0" "0,1" "0,2" "0,3"

Temperatura iniciale !Aumia#

20 20

$0 %0 10 &

$0 &0 30 &

%0 %0


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E DE CALOR EN UNA PLACA

2

1'1$$$$$$(

)rimera Iteraci*n Se+una

20 20

$0 3& 2%'3$&2& & $0

$0 %1'2$-%301 2&'$3%(1& & $0

%0 %0

Err.r 1/ Iteraci*n

0 0 0 0 0

0 & 1%'3$&2& 0 0

0 '(30&$--& %'3$&2%-( 0 0

0 0 0 0 0


3/37

Iteraci*n Tercera Iteraci*n

20 20 20

33'&$$&(23 22'1020$-- & $0 32'3($$$

3'&0002( 2-'&&003 & $0 3'&%&--

%0 %0 %0

Err.r 2/ Iteraci*n Err.r 3/

0 0 0 0 0

1'%33%2((% 2'2$321&12 0 0 1'1-3$3

2'%1-%2(3( %'2&0(&2$ 0 0 0'00%&(21

0 0 0 0 0


4/37

Cuarta Iteraci*n

20 20 20

23'&0&-1% & $0 32'&&$(0$ 22'-2&2-21

2'(3%0$2( & $0 3'2$%(-& 2-'2&3%(

%0 %0 %0

Iteraci*n Err.r %/ Iteraci*n

0 0 0 0 0

1'%0321&& 0 0 0'1001(3% 0'&0&--2$

1'1&1%3($1 0 0 0'&-00$13$ 0'&2%3220%

0 0 0 0 0


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uinta Iteraci*n

20 20

& $0 32'2$2($% 23'1%3(%$1 &

& $0 3'3-&1%3 2'-$$3- &

%0 %0

Err.r &/ Iteraci*n

0 0 0 0 0

0 0 0'2-32-&3 0'21%&3-& 0

0 0 0'133(1&(% 0'2-1&00( 0

0 0 0 0 0


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Seta Iteraci*n

20 20

$0 32'3%0%-12 22'--((001 &

$0 3'2&1-&1 2-'0$&3&% &

%0 %0

Err.r $/ Iteraci*n

0 0 0 0

0 0'0(($1%(- 0'1%$0%$01 0

0 0'1%$$1-1& 0'0-%(00& 0

0 0 0 0


7/37

Septima Iteraci*n Octaa I

20 20

$0 32'2$(2&%% 23'0%%2(( & $0

$0 3'2-33& 2'--22&2 & $0

%0 %0

Err.r (/ Iteraci*n

0 0 0 0 0

0 0'0(323$2 0'0%$&($ 0 0

0 0'0%1%&%3 0'0(30-&($ 0 0

0 0 0 0 0


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teraci*n $0 N.ena Itera

20 20 20 20

32'2$33% 23'00((21- & $0 32'2(033(&

3'2&$(%-& 2-'01%-00% & $0 3'2$(&--3

%0 %0 %0 2('%$113-- %0

$0

Err.r / Iteraci*n Err.r -/

0 0 0 0 0

0'0213(- 0'03$&$&(- 0 0 0'012-&%

0'03$$00& 0'022$%223 0 0 0'010%-&

0 0 0 2('%$113-- 0


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i*n & $0 Decima Iteraci*n

20 $'-%300&1 20 %-'%%&&-$ 20 20

23'012$ & $0 32'2(&01- 23'00-(3(-

2'--$$131 & $0 3'2&%&2& 2-'0021&%1

%0 12'020(2&% %0 &%'-222(- %0 %0

& $0

Iteraci*n Err.r 10/ Iteraci*n

0 $'-%300&1 %-'%%&&-$ 0 0

0'0111$0(& 0 0 0'00&%$%3- 0'00-1%%(3

0'012(3 0 0 0'00-1%$% 0'00&&%0-1

0 12'020(2&% 2('%$113-- 0 0


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& Se+una Iteraci*n

'02-01$ 20 20 20

& $0 32'2(122 23'012%-( &

& $0 3'2$11-%% 2'--(&1% &

13'$010% %0 %0 %0

&

Err.r 2/ Iteraci*n

1'$&2%-( %-'%%&&-$ 0 0 '02-01$

0 0 0'00%&(31& 0'002($0(% 0

0 0 0'002(%1-1 0'00%&(2$3 0

1'$&2%-( &%'-222(- 0 0 13'$010%


11/37

Se+una Iteraci*n

20 20

$0 32'2(2$021 23'0102123 &

$0 3'2&-0(- 2'---&-% &

%0 %0

Err.r 2/ Iteraci*n

0 0 0 0

0 0'0013(33& 0'0022$3 0

0 0'0022$&1 0'0013((- 0

0 0 0 0


12/37

Se+una Iteraci*n

20 20

$0 32'2(1%&- 23'010-00( &

$0 3'2&-&-&1 2'--(1$2 &

%0 %0

Err.r 2/ Iteraci*n

0 0 0 0

0 0'0011%32% 0'000$% 0

0 0'000$(2$ 0'0011%321 0

0 0 0 0


13/37


20 20 20 20

$0 31'-%300&2 2'13%(1& 2'13%(1& 2$'$&2&

$0 3'1(3&(&1 3%'2&3$ 3& 32'-%%&$$0 %0'%1-$-1 3('3$01 3('$2$-%3 3$'$&2&

$0 %&'$%2%( 3-'2&3$ %1'$113-- %0'%%%&$

$0 %$'2$-%301 %%'($1$& %%'3$&2& %%'1113--

$0 %('1$&031 %2'&3$01 %%'%0%1%&1 %3'13%(1&

%0 %0 %0 %0


20 20 20 20

$0 32'-01%%( 2('$$23 2('& 2$'011%31

$0 3'-$020 33'(320%- 33'0$23( 31'3-1(1&2

$0 %3'$30-( 3('3300$2$ 3'00$%2-( 3&'-2%00

$0 %%'-3-&$ %1'(22---3 %0'(0---- 3-'$(3%0%

$0 %('-21&%1& %2'01(--2 %3'3(0&133 %1'&0$3$-3

$0 %&'20000&% %3'2%&0-3 %2'3%(20 %1'--1%($

%0 %0 %0 %0


20 20 20 20

$0 33'1%-&%-& 2('(11&0&2 2$'$%&(3(1 2&'%&0%($0 %0'%%&%$1 33'%$&%&% 32'(0%(3%1 30'&001-%-

$0 %3'$&%(-$% 3'&12$12% 3$'231&3- 3%'-&-(11

$0 %('0$(32 %0'%(%2$1% %0'$-1&$& 3'1-0$3$(

$0 %$'&((((1$ %3'2$2-3 %1'&&(23 %0'%-&-3$

$0 %&'-0&-& %1'(113&1 %1'-22-$% %0'$00%0($

%0 %0 %0 %0


20 20 20 20

$0 33'$3-$%1 2('&3$2&$$ 2$'%1&23 2&'02(&(3$0 %0'&1(1%$ 33'--12(&- 31'(-(&0$ 2-'(($%$

$0 %&'1&2(%&2 3('(--%2& 3$'(0(21- 33'2(30&

$0 %$'%1$3-&% %1'$&$231- 3-'23001& 3('31-$$0(

$0 %('(-&$$ %1'&2031 %1'%&&&(3$ 3-'0(%&$13

$0 %&'20---22 %2'220002 %0'$0-3- %0'0%(&(2

%0 %0 %0 %0


20 20 20 20

$0 33'$%(%& 2('((0--$$ 2&'--$032& 2%'(((%1%$0 %1'3%2120- 33'&&3-33 31'$&$2122 2-'1%131

$0 %% %$1$ 3 $12%&3 3& &---%2 33 2&-$3--


14/37

$0 %('&(-$% %0'&(-1&1 3-'1%3$ 3$'11-$00-

$0 %('1112$(( %2'$20%$$( %0'1$3-1-1 3'%3%103$

$0 %&'(2-%$ %1'%$%($$ %0'3&&& 3-'3&%-&$&

%0 %0 %0 %0


20 20 20 20

$0 3%'02$0213 2('&&&2 2&'-%13$& 2%'%2%0-$

$0 %1'1(3-21 3%'031%% 30'-3%$$3 2'(-123$$

$0 %&'$-10$3% 3('(12022 3&'&&1%0-( 32'333-%$

$0 %('0(%303$ %1'31$$02 3'001(031 3&'&$$-10%

$0 %('3$%022 %1'$-3021 %0'1%1%- 3('%$301&

$0 %&'3(((10% %1'10-0-( %0'1$&20-& 3-'0&$$%%3

%0 %0 %0 %0


15/37

Delta X 2

Delta Y 1'1$$$$$$(

20 20

21'$113-- 1$'230&$-- &

2& 13'&0(((2 &2-'%-222 1('& &

32'-%%&$ 21'11-1(1 &

3$'$&2& 2%'1113-- &

3-'2&3$ 2-'-$113-- &

%0 %0

20 20

22'2&221 1&'(%3-( &

2%'-$$%2$ 1$'3-1(1&2 &

2'&32(--& 1('2-$3(0% &

32'&(&23- 20'3%&2%% &

3&'$0-%2& 2%'3(03(2% &

3('-&%13-( 2-'&3%-2(1 &

%0 %0

20 20

22'101&1$3 1('03$%322 &2&'013(%0& 1$'10123& &

2'222&0 1('-$1(%- &

31'&%2&1 20'313--3 &

3%'$(%0$% 23'($32%%% &

3('2(2%$ 2-'%$$&%&2 &

%0 %0

20 20

22'1-0-3%1 1$'-3(&-$ &2%'$--&-( 1$'$$3&0( &

2('1 1('31(-2& &

30'-0-&% 20'20&3%- &

33'3$30 23'$0(32%% &

3$'(&21-- 2-'1&&3-%( &

%0 %0

20 20

22'002$21 1('20%-%- &2%'&-033($ 1$'(%111-( &

2( 30321- 1( --&-&$ &


16/37

30'303%-&2 20'01&2&0& &

33'1-1(&$( 23'3%%%3& &

3$'33%--2 2-'02-30( &

%0 %0

20 20

21'-$%10&2 1('13%3333 &

2%'21-31(3 1$'2%12 &

2$'-&0(1% 1('12( &

2-'$-%000$ 1-'-03$% &

32'(022(2& 23'1%%&-1$ &

3&'-&$00( 2'(2$0- &

%0 %0


17/37

0 20 %0 $0 0 100 30'%0

30'%&

30'&0

30'&&

30'$0

30'$&

&4 30'%

°C Vs N° Nodo

/C

N° De Nodos

°C


18/37

2x2

20 20

$0 32'2( 23'01 &

$0 3'2$ 2-'00 &

%0 %0

Err.r It

0 0

0 -E0&

0 1E0%0 0

N/ e N.. /C

% 30'$3

1$ 30'&2

3$ 30'%

$% 30'%

100 30'%


19/37


20/37

Delta X 2

Delta Y 1'1$$$$$$(

20 20

$0 32'2( 23'01 & $0

$0 3'2$ 2-'00 & $0

%0 %0 $0

$0

raci.n5

0 0

1E0% 0

-E0& 00 0

$0

$0

$0

$0

$0

$0

$0$0


21/37


22/37

4x4

20 20 20 20

33'%111$3( 2$'2$13%2( 22'($3&& 1'00$(%( &

%0'203200$ 31'2&(33 2&'-%-13& 1'2%(0%% &

%3'2--202 3&'0031(3 2-'(&2%11% 21'-1&2% &

%3'&01((-( 3('-00(%3& 3%'3-(2(& 2'100$%% &

%0 %0 %0 %0

Err.r Iten

0 0 00 0'00 0'00

0 0'00 0'00

0 0'00 0'00

0 0'00 0'00

0 0 0

20 20 20 20 20 20

3%'00(%&3 2('0(3%2( 2%'3-0 22'-($&( 21'-33$101 20'1&($3

%1'&2&&%2% 32'(320(-2 2'3$$1$3- 2&'1-&2$ 23'-32((2 21'2%&$3

%&'(%$%$% 3$'(21%- 31'(0($1&1 2'%&&1%-$ 2&'-2(-& 23'1312(%

%'133%(1 3-'(%2%233 3%'%01-121 30'%%1(22 2('-$3(-2 2%'(-%%$1$

%-'3%$%231 %1'&(&-$%$ 3$'%(1&2- 33'00(1$-( 30'1200$(& 2$'($$1%%

%-'&(&01(2 %2'%-1$0% 3'00%((($ 3%'-&%(0- 32'%0202- 2-'%23(-1

%'$$2&-&- %2'&2$221 3-'0311%1 3$'(%(00- 3%'1$0%&& 32'%-3%%2%&'-13- %1'$&$$-1$ 3-'$%123$ 3'%0$$2 3('3$$21-1 3$'0$$&&(-

%0 %0 %0 %0 %0 %0

0 0

0 0'00

0 0'00

0 0'00

0 0'00


23/37

0 0'00

0 0'00

0 0'00

0 0'00

0 0


24/37

20 20 20 20

$0 33'%0-%--2 2$'2$3&33 22'($11$ 1'002&$ &

$0 %0'20&%%1- 31'21&11$ 2&'-&2(&-2 1'220033 &

$0 %3'2-$&0-$ 3&'03-%2 2-'(%0%% 21'-1(%(2 &

$0 %3'&031$%- 3('-0%( 3%'%000$(% 2'0--1-& &

%0 %0 %0 %0

raci.n5 3

0 0 00'00 0'00 0

0'00 0'00 0

0'00 0'00 0

0'00 0'00 0

0 0 0

Delta X 2

Delta Y 1'1$$$$$$(

20 20 20

1-'1%10%-( 1&'(1&&$- & $0 3%'00($$2-

1'(((2( 13'-102&- & $0 %1'&2%%%((

1-'2-$(- 13'%%(&111 & $0 %&'(%$-2-

20'%03$1%( 13'$%( & $0 %'13$$$--

22'232($(- 1&'0(&2 & $0 %-'3%(0122

2%'-20103 1('2(%0102 & $0 %-'&(3&%23

2'$$-211& 21'0%3$& & $0 %'$$2-0%33'(11-22& 2('$(0(( & $0 %&'-00(&

%0 %0 %0

0 0 0 0 0 0

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00


25/37

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0 0 0 0 0 0


26/37

Delta X 2

Delta Y 1'1$$$$$$(

20 20 20 20

$0 33'2312( 2$'2&22%3 2%'0%-1- 22'300&2$$

$0 %1'121&30& 32'20-13(1 2('(&3(%% 2%'$-(-$1

$0 %&'02%222$ 3$'010$ 30'-(%%$(- 2('23(1(11

$0 %$'((%0(% 3'$3(&1&& 33'(3$3(1 2-'--13%%&

$0 %('0$3&3%( %0'0$3(02$ 3$'0-23-2 33'03%&13-

$0 %&'2321((% %0'%&12--( 3'1%3%1$ 3$'3-0$203

%0 %0 %0 %0

0

0

0

0

0

0

0

0

20 20 20 20 20 20

2('0$2%$( 2%'3-$01& 22'-(%-01$ 21'-3%13 20'1(0$& 1-'1%1%1

32'(32(-- 2'3$333& 2&'20-3-- 23'-0100& 21'2&&03 1'(&(-0(

3$'$-3(3 31'(0-13% 2'%&001 2&'-%2%$ 23'120&&1 1-'2-((2%

3-'(%3&2$ 3%'3-($&22 30'%&31 2('-&-2& 2%'(-&-03 20'%00%2%

%1'&(20( 3$'%(-$2-2 33'00231%& 30'121(1-& 2$'(232%( 22'23330-

%2'%-2&(3( 3'001031$ 3%'-&--3& 32'3-((%- 2-'%2&0&$ 2%'-1(2-(

%2'&2%2223 3-'0321%(( 3$'(%33-- 3%'1(123- 32'%-0$%21 2'$$--0&3%1'$&(0(%$ 3-'$%$$%%1 3'%0(%%0$ 3('3$%&2- 3$'0$(0&& 33'(101%(

%0 %0 %0 %0 %0 %0

0 0

0'00 0

0'00 0

0'00 0

0'00 0


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0'00 0

0'00 0

0'00 0

0'00 0

0 0


28/37

6x6

20 20 20

20'2(%103- 1$'%0%1(1- & $0 33'23$$-%

21'1(0$- 1&'3$-$2$3 & $0 %1'11-$02

22'&&&(( 1&'-$-%3 & $0 %&'02&%%12

2&'%120&- 1('(3-%3$ & $0 %$'(&32%$

2-'02($$2- 21'31%3-& & $0 %('0$%&12

33'-02-3% 2('11$-11 & $0 %&'2312&0&

%0 %0 %0

Err.r

0 0 0 0 0 0

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0 0 0 0 0 0

20

1&'(1%--$( & 20 20

13'-10$2$$ & $0 3%'1013202 2('233(1(

13'%%$01$( & $0 %1'(2&($0& 33'03$&-&

13'$&%%12 & $0 %$'0-%$&( 3('3&2$2-2

1&'0(3&-& & $0 %'$-00$13 %0'%&1%%&

1('2(%&0&& & $0 &0'2%$--2 %2'&-&-((

21'0%((2(3 & $0 &1'0(3--% %3'-&%-&132('$-032 & $0 &1'323$2% %%'$30320&

%0 $0 &0'1-0(( %%'$2-0$

$0 %-'%$$%&$ %3'3%$0&

$0 %$'3$%&(1 %2'31(&$

%0 %0


29/37


30/37

20 20 20 20 20

2$'23&&(% 2%'0&10(3 22'2-%$1 20'2(&0&(% 1$'%032&(2 &

32'210-02 2('(&01%01 2%'$-1-&2$ 21'1(&0-2- 1&'3(0&(&% &

3$'0((3%1& 30'-((1($% 2('232&2-( 22'&((202 1&'($3- &

3'$3-(01( 33'(31(1&2 2-'--%033$ 2&'%1%%-%- 1('(%0$222 &

%0'0$0$--1 3$'0-%&$%- 33'030(-1 2-'02-31 21'312(%13 &

%0'%&22(2( 3'1%13%3$ 3$'3-11( 33'-012$ 2('1221( &

%0 %0 %0 %0 %0

0

0

0

0

0

0

0

0

Delta X

Delta Y

20 20 20 20 20 20

2%'&(%(&&$ 23'211&-%2 22'3%(20-$ 21'$&&-202 20'-%% 20'01%-0&

2'(0&($( 2$'2&%-113 2%'$31-(1 23'3201%3% 21'-$0-%3$ 20'2221-%

32'1--$&(1 2-'0102$3 2$'13--- 2%'--3&-( 23'10-&&& 20'(20&13&

3&'011&-2 31'%31$%- 2'&3% 2$'$-31-(( 2%'%1-%%-- 21'&$%&1&1

3('212110& 33'%-(3 30'($-1 2'%11$%1 2&'-32%2-$ 22'((&&-%1

3'30(-$ 3&'233(-2 32'&3&%0% 30'1-%$0$% 2('$$20%-1 2%'3--&%13-'-3%03&& 3$'$&1&(11 3%'1-%0-& 32'022$21 2-'$%&1-0 2$'%(&&&(

%0'&%($2$- 3('(-32-&% 3&'(%0(- 33'-2&3(% 31'(1302 2-'0(2%---

%0'(12-- 3'$(&3 3('21112%% 3&'-&&32( 3%'3-(020( 32'22$3%(3

%0'%3%023 3-'3-((3-1 3'$1-%1( 3('-30&133 3('12-230( 3&'-2&0%-

%0 %0 %0 %0 %0 %0

0

0


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0

0

0

0

0

0

00

0

0


32/37

2

1'1$$$$$$(

20 20 20

1'&23122- 1&'3$1&&(% & $0 3%'100-&$&

1('$12%13 13'1(3&$1 & $0 %1'(2$0((

1('32&(22 12'2&%3-33 & $0 %$'0%-

1('$0%2$3& 12'0(-2$-$ & $0 %'$-0&-$(

1'%10132 12'%2-$20$ & $0 &0'2%&(11%

1-'((-$03& 13'2(1--1 & $0 &1'0(-221'($&-(% 1%'(11031 & $0 &1'322%&0$

2%'&--1$& 1('0%332$ & $0 &0'23&2&

2'%$133% 20'-131-2& & $0 %-'%$&(&

33'$0$-3$1 2('$2&3$(1 & $0 %$'3$%(3($

%0 %0 %0

0 0 0 0 0 0

0'00 0'00 0'00 0'00 0'00 0'00


33/37

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'000'00 0'00 0'00 0'00 0'00 0'00

0'00 0'00 0'00 0'00 0'00 0'00

0 0 0 0 0 0


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35/37

0'00 0'00 0'00 0'00 0

0'00 0'00 0'00 0'00 0

0'00 0'00 0'00 0'00 0

0'00 0'00 0'00 0'00 0

0'00 0'00 0'00 0'00 0

0'00 0'00 0'00 0'00 0

0'00 0'00 0'00 0'00 00'00 0'00 0'00 0'00 0

0'00 0'00 0'00 0'00 0

0 0 0 0 0


36/37

20 20 20

20'01&3$0% 1'&223(03 1&'3$1(2($ &

20'2201-%$ 1('$130%3 13'1(211- &

20'(21(32- 1('323($32 12'2&%%-$ &

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2-'0$-$- 2%'$000$1 1('0%(2(&% &

32'22(21-$ 2'%&--%1 20'-13&1- &

3&'-2%00&$ 33'$0(2$21 2('$2%-(3 &

%0 %0 %0


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Documents

Transporte de Calor en Una Placa-Isamar y Brenda Rios