tarea 9 metodos

8/4/2019 tarea 9 metodos

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Ejercicios de Numerical Methods for Chemical Engineers with MATLABApplications

Ejercicio 2.1clcclear%input dataTs=input(' Temperature of steam (deg C) = ');Ta=input(' Temperature of air (deg C) = ');D1=1e-3*input(' Pipe ID (mm) = ');D2=1e-3*input(' Pipe OD (mm) = ');Ith=1e-3*input(' Insulation thickness (mm) = ');D3=(D2+2*Ith);hi=input(' Inside heat transfer coefficient(W/m2.K) = ');ho=input(' Outside heat transfer coefficient(W/m2.K) = ');Ks=input(' Heat conductivity of steel (W/m.K) = ');Ki=input(' Heat conductivity of insulation (W/m.K) = ');%Matrix of coefficientsA=[2*Ks/log(D2/D1)+hi*D1 , -2*Ks/log(D2/D1) ,0

Ks/log(D2/D1) , -(Ks/log(D2/D1)+Ki/log(D3/D2)) , Ki/log(D3/D2)0 , 2*Ki/log(D3/D2) , -(2*Ki/log(D3/D2)+ho*D3)];

%matrix of constantsC= [hi*D1*Ts ; 0 ; -ho*D3*Ta];%solving the set of equations by Gauss elimination methodT= Gauss(A , C);%show the resultsdisp(' '),disp(' Results : ')fprintf(' T1= %4.2f\n T2=%4.2f\n T3=%4.2f\n',T)

function x=Gauss(A,c)%GAUSS solves a set of linear algebraic equations by the Gausselimination%method.%GAUSS(A,C) finds unknowns of a set of linear algebraic equations.A isthe%matrix of coefficients and C is the vector of constants.%See also JORDAN,JACOBIc=(c(:).')'; %make sure it's a column vectorn=length(c);[nr nc]=size(A);%check coefficient matrix and vector of constantsif nr~=nc

error('coefficient matrix is not square,')

endif nr~=nerror('coefficient matrix and vector of constants do not have the

same length')end%check if the coefficient matrix is singularif det(A)==0

fprintf('\nRank=%7.3g\n',rank(A))error('The coefficient matrix is singular.')

end


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unit=eye(n); %unit matrixorder=(1:n); %order of unknownsaug=[A c]; %augmented matrix%Gauss eliminationfor k=1:n-1

pivot=abs(aug(k,k));prow=k;pcol=k;%locating the maximun pivot elementfor row=k:n

for col=k:nif abs(aug(row,col))>pivot

pivot=abs(aug(row,col));prow=row;pcol=col;

endend

end%interchanging the rowspr=unit;

tmp=pr(k , :);pr(k,:)=pr(prow,:);pr(prow , : ) = tmp;aug = pr*aug;%interchanging the columnspc=unit;tmp=pc(k , : );pc(k , : )=pc(pcol , : );pc(pcol , : )=tmp;aug(1 : n , 1 : n)= aug(1 : n , 1 : n)*pc;order=order*pc; %keep track of the column interchanges%reducing the elements below diagonal to zero in the column klk=unit;for m=k+1:n

lk(m,k)=-aug(m,k)/aug(k,k);endaug=lk*aug;

endx=zeros(n,1);%back substitutiont(n)=aug(n,n+1)/aug(n,n);x(order(n))=t(n);for k=n-1:-1:1

t(k)=(aug(k,n+1)-sum(aug(k,k+1:n).*t(k+1:n)))/aug(k,k);x(order(k))=t(k);

end

ResultadosTemperature of steam (deg C) = 130

Temperature of air (deg C) = 25


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Pipe ID (mm) = 20

Pipe OD (mm) = 25

Insulation thickness (mm) = 40

Inside heat transfer coefficient(W/m2.K) = 1700

Outside heat transfer coefficient(W/m2.K) = 3

Heat conductivity of steel (W/m.K) = 45

Heat conductivity of insulation (W/m.K) = 0.064

Results :

T1= 129.79

T2=129.77

T3=48.12

Ejercicio 2.2%example2_2%solution to example 2.2.this program solves the material%and energy balances equations of a steam distribution

%system using the function JORDAN.M.clcclear%matrix of coefficientsA=[1,1,1,0*(4:14)

1.17,0,0,-1,0*(5:14)0*(1:4),1,0*(6:14)0,0,1,0,1,-1,-1,-1,0*(9:12),1 , 00*(1:5),1,1,1,1,-1,-1,0*(12:14)0*(1:3),1,0*(5:12),-1,01,0*(2:3),-1,0*(5:9),1,0*(11:13),10*(1:9),4.594,0*(11:13),0.110*(1:8),1,0*(10:14)

0,1,0*(3:14)0*(1:5),1,0*(7:13),-0.01470,0,1,0*(4:11),-0.07,0,00*(1:6),1,0*(8:14)0*(1:9),1,0,-1,0,1];

%vector of constantsc=[43.93,0,95.798,99.1,-8.4,24.2,189.14,146.55,10.56,2.9056,0,0,14.6188,-97.9];%solutionX=Jordan(A,c)

function x=Jordan(A,c)c=(c(:).')';

n=length(c);[nr nc]=size(A);if nr~=nc

error('coefficient matrix is not square,')endif nr~=n

error('coefficient matrix and vector of constants do not have thesame length')end%check if the coefficient matrix is singular


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if det(A)==0fprintf('\nRank=%7.3g\n',rank(A))error('The coefficient matrix is singular.')

endunit=eye(n); %unit matrixorder=(1:n); %order of unknownsaug=[A c]; %augmented matrix%Gauss_jordan algorithmfor k=1:n

pivot=abs(aug(k,k));prow=k;pcol=k;%locating the maximun pivot elementfor row=k:n

for col=k:nif abs(aug(row,col))>pivot

pivot=abs(aug(row,col));prow=row;pcol=col;

end

endend%interchanging the rowspr=unit;tmp=pr(k , :);pr(k,:)=pr(prow,:);pr(prow , : ) = tmp;aug = pr*aug;%interchanging the columnspc=unit;tmp=pc(k , : );pc(k , : )=pc(pcol , : );pc(pcol , : )=tmp;aug(1 : n , 1 : n)= aug(1 : n , 1 : n)*pc;order=order*pc; %keep track of the column interchanges%reducing the elements below diagonal to zero in the column klk=unit;for m=1:n

if m==klk(m,k)=1/aug(k,k);

elselk(m,k)=-aug(m,k)/aug(k,k);

endendaug=lk*aug;

endx=zeros(n,1);

%solutionfor k=1:nx(order(k))=aug(k,n+1);

end

ResultadosX =


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20.6854

2.9056

20.3390

24.2020

95.7980

2.4211

14.6188-0.0010

10.5600

27.9567

8.0422

290.5565

0.0020

164.6998

Ejercicio 2.3%example2_3clcclear%input datafprintf('solution of set of linear algebraic equations by the Jacobimethod\n\n')n=input('Number of equations = ');for k=1:n

fprintf('\n Coefficients of eq. %2d= ',k)A(k,1:n)=input(' ');fprintf(' Constant of eq. %2d= ',k)c(k)=input(' ');

enddisp(' ')tol=input('Convergence criterion= ');trace=input(' Show step-bye-step path to results(0/1)? ');redo=1;while redo

disp(' ')guess=input('Vector of initial guess= ');%solutionca=Jacobi(A,c,guess,tol,trace);fprintf('\n\n Results:\n')for k=1:n

fprintf(' CA(%2d)=%6.4g\n',k,ca(k))enddisp(' ')

redo=input('Repeat the calculations with another guess (0/1)? ');disp(' ')end

function x=Jacobi(A,c,x0,tol,trace)%initializationif nargin=4 && tol==0


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tol=1e-6;endif nargin=tol

x0=x;x=c0-a0*x0;if trace

iter=iter+1;fprintf('\n Iteration no. %3d\n',iter)fprintf('%8.6g ',x)

endend

Resultadossolution of set of linear algebraic equations by the Jacobi method


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Number of equations = 4

Coefficients of eq. 1= [1100,0,0,0]

Constant of eq. 1= 1000

Coefficients of eq. 2= [1000,-1400,100,0]


Coefficients of eq. 3= [0,1100,-1240,100]


Coefficients of eq. 4= [0,0,1100,-1250]


Convergence criterion= 1e-5

Show step-bye-step path to results(0/1)? 1

Vector of initial guess= 0.06*ones(1,4)

Initial guess:

0.06 0.06 0.06 0.06

Iteration no. 1

0.909091 0.0471429 0.0580645 0.0528

Iteration no. 2

0.909091 0.653498 0.0460783 0.0510968

Iteration no. 3

0.909091 0.652642 0.583837 0.0405489

Iteration no. 4

0.909091 0.691053 0.582227 0.513776

Iteration no. 50.909091 0.690938 0.654465 0.512359

Iteration no. 6

0.909091 0.696098 0.654248 0.575929

Iteration no. 7

0.909091 0.696083 0.663952 0.575739

Iteration no. 8

0.909091 0.696776 0.663923 0.584278

Iteration no. 9

0.909091 0.696774 0.665227 0.584252

Iteration no. 10

0.909091 0.696867 0.665223 0.5854

Iteration no. 110.909091 0.696867 0.665398 0.585396

Iteration no. 12

0.909091 0.696879 0.665397 0.58555

Iteration no. 13

0.909091 0.696879 0.665421 0.58555

Iteration no. 14

0.909091 0.696881 0.665421 0.58557

Iteration no. 15


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0.909091 0.696881 0.665424 0.58557

Results:

CA( 1)=0.9091

CA( 2)=0.6969

CA( 3)=0.6654

CA( 4)=0.5856

Repeat the calculations with another guess (0/1)? 1

Vector of initial guess= 100*ones(1,4)

Initial guess:

100 100 100 100

Iteration no. 1

0.909091 78.5714 96.7742 88

Iteration no. 2

0.909091 7.56179 76.7972 85.1613

Iteration no. 3

0.909091 6.13487 13.5759 67.5816

Iteration no. 4

0.909091 1.61906 10.8923 11.9468

Iteration no. 5

0.909091 1.42738 2.39971 9.58527

Iteration no. 6

0.909091 0.820759 2.03923 2.11175

Iteration no. 7

0.909091 0.79501 0.898394 1.79452

Iteration no. 80.909091 0.713522 0.84997 0.790587

Iteration no. 9

0.909091 0.710063 0.69672 0.747973

Iteration no. 10

0.909091 0.699116 0.690215 0.613113

Iteration no. 11

0.909091 0.698652 0.669628 0.607389

Iteration no. 12

0.909091 0.697181 0.668755 0.589273

Iteration no. 13

0.909091 0.697119 0.665989 0.588504

Iteration no. 140.909091 0.696921 0.665872 0.586071

Iteration no. 15

0.909091 0.696913 0.6655 0.585967

Iteration no. 16

0.909091 0.696886 0.665485 0.58564

Iteration no. 17

0.909091 0.696885 0.665435 0.585626

Iteration no. 18


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0.909091 0.696882 0.665433 0.585583

Iteration no. 19

0.909091 0.696882 0.665426 0.585581

Results:

CA( 1)=0.9091

CA( 2)=0.6969CA( 3)=0.6654

CA( 4)=0.5856

Repeat the calculations with another guess (0/1)? 0

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