matlab project 406

8/2/2019 Matlab Project 406

1/16

1 Term Project

King Saud University

College of Engineering

Chemical Engineering Department

ChE 406: Computational Techniques

Term Project

By

Jassim Mohammed AlDraisi 428101168


2/16

2 Term Project

Study the heat conduction in cylindrical metallic rod extended surface

Part1: Steady State Analysis

Steady state systems:

This can be discretized by find it difference AND WE CAN DEFAINE A SYSTEM OF LINEAR EQUATIONS:

THE OBGCTOR OF THE GIVEN MATLAB PROGRAM IS TO DEFINE THR

MATRIX "A"

AND THE VECROT "B" THEN SOLVE FOR "T"


3/16

3 Term Project

A=ZERO(npoints, npoints)

B=-b * ONE(npoints,1)

=-b *

FOR LOOP

i = 1 - 4

j =1 4IF i=j

=, A(i,j) = -a = -(2+( )) = - (2+ )Else if j=i+1 or j=i-1A(i,j)=1

Else if

A(i,j)=0


4/16

4 Term Project

A=

B(1)=-b- =-112.5

B(end)= -b-

B=

=

(

)

Commend to slove TT=A\B


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5 Term Project

Matlab Codes

% working out problems of midterm one spring 2012% solution of prblem

% A Matlab program to solve a system of %linearequations toobtain

% the temperature profile in a metallic %rodsubject toabasetemperatureof%100deg-C% Define all known parameters%(1.2)Obtain and plot the solution for npoints=20 and for (k=50W/m/K) for natural

convection (h=5W/m2/K) when d=2mm, L=50cm

Too=25;To=100;TL=Too;h=5;k=50;L=0.5;D=0.002;P=0.15;S=0.002;

% calculate defined parametersnpoints=20;m=h*P/(k*S);Dx=L/(npoints+1);a=2+(m*Dx^2);b=(m*Dx^2)*Too;A=zeros(npoints,npoints);B=-b*ones(npoints,1);% Define the system: matrix A and vector B%for i=1:npointsfor j=1:npointsif i==j

A(i,j)=-a;elseif j==i+1 | j==i-1A(i,j)=1;

elseA(i,j)=0;endendendB(1)=-b-To;B(end)=-b-TL;%% Compute the solution T=[T1 T2 T3 T4]%T=A\B;

%% Display the result in a graphic form%plot([0:Dx:L],[To;T;TL],'*b')xlabel('Position in (m)');ylabel('Temperature in deg-C');


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6 Term Project


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7 Term Project

%(1.3) Obtain and plot the solution for various thermal conductivities (k=[50])

Too=25;To=100;TL=Too;h=5;k=50;L=0.5;D=0.002;P=0.15;

S=0.002;% calculate defined parametersnpoints=20;m=h*P/(k*S);Dx=L/(npoints+1);a=2+(m*Dx^2);b=(m*Dx^2)*Too;A=zeros(npoints,npoints);B=-b*ones(npoints,1);% Define the system: matrix A and vector B%for i=1:npointsfor j=1:npointsif i==jA(i,j)=-a;elseif j==i+1 | j==i-1A(i,j)=1;




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8 Term Project


9/16

9 Term Project


Too=25;To=100;TL=Too;h=5;k=100;L=0.5;D=0.002;

P=0.15;S=0.002;% calculate defined parametersnpoints=20;m=h*P/(k*S);Dx=L/(npoints+1);a=2+(m*Dx^2);b=(m*Dx^2)*Too;A=zeros(npoints,npoints);B=-b*ones(npoints,1);% Define the system: matrix A and vector B%for i=1:npointsfor j=1:npointsif i==jA(i,j)=-a;elseif j==i+1 | j==i-1A(i,j)=1;

elseA(i,j)=0;endendendB(1)=-b-To;B(end)=-b-TL;%% Compute the solution T=[T1 T2 T3 T4]%

T=A\B;%% Display the result in a graphic form%plot([0:Dx:L],[To;T;TL],'*b')xlabel('Position in (m)');ylabel('Temperature in deg-C');


10/16

10 Term Project


11/16

11 Term Project


Too=25;To=100;TL=Too;h=5;k=150;L=0.5;D=0.002;P=0.15;

S=0.002;% calculate defined parametersnpoints=20;m=h*P/(k*S);Dx=L/(npoints+1);a=2+(m*Dx^2);b=(m*Dx^2)*Too;A=zeros(npoints,npoints);B=-b*ones(npoints,1);% Define the system: matrix A and vector B%for i=1:npointsfor j=1:npointsif i==jA(i,j)=-a;elseif j==i+1 | j==i-1A(i,j)=1;




12/16

12 Term Project


13/16


14/16

14 Term Project

%(1.4) For a value of k=500 (highly conductive metal) natural convection (h=5)

Too=25;

To=100;TL=Too;h=5;k=500;L=0.5;

D=0.002;P=0.15;S=0.002;% calculate defined parametersnpoints=20;m=h*P/(k*S);Dx=L/(npoints+1);a=2+(m*Dx^2);b=(m*Dx^2)*Too;A=zeros(npoints,npoints);B=-b*ones(npoints,1);% Define the system: matrix A and vector Bfor i=1:npointsfor j=1:npointsif i==jA(i,j)=-a;elseif j==i+1 | j==i-1A(i,j)=1;

elseA(i,j)=0;endendend


15/16

15 Term Project

B(1)=-b-To;B(end)=-b-TL;%% Compute the solution T=[T1 T2 T3 T4]T=A\B;% Display the result in a graphic formplot([0:Dx:L],[To;T;TL],'*b')xlabel('Position in (m)');ylabel('Temperature in deg-C');


16/16

16 Term Project

Refrance

Bathe K.J., Finite Element Procedures In Engineering Analysis, Prentice-Hall,1982

matlab project 406

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