%?Twodimensional?heat?conduction
%?Finite?Volume?Method
%?SOR
clear?all;
x=[];y=[];T=[];Told=[];Su=[];Sp=[];ap=[];ae=[];aw=[];as=[];an=[];
great?=?1.e20;
lambda?=?10;?%?thermal?conductivity
alfa?=?10;?%?heat?transfer?coefficient
dt?=?great;?%?Time?step.?If?great?stedy?state
density?=?6000;%?density
cp?=?500;%?heat?capacity
Lx?=?0.12;?%?length?x-direction
Ly?=?0.12;?%?length?y?-direction
Tfluid?=?20;?%?Fluid?temperature
Tinit?=?50;?%?Initial?guess?and?top-?and?bottom?tempearature
%cv_x?=?input（‘Number?of?CVs?in?x-direction?=?‘）
%cv_y?=?input（‘Number?of?CVs?in?y-direction?=?‘）
cv_x=10;cv_y=10;
ni?=?cv_x+2;?%?grid?points?x-direction
nj?=?cv_y+2;?%?grid?points?y-direction
dx?=?Lx/cv_x;
dy?=?Ly/cv_y;
x（1）?=?0;
x（2）=dx/2;
for?i?=?3:ni-1
???x（i）=x（i-1）+dx;
end;
x（ni）=Lx;
y（1）?=?0;
y（2）=dy/2;
for?j?=?3:nj-1
???y（j）=y（j-1）+dy;
end
y（nj）=Ly;
%?Initial?values?and?coefficients
for?i?=?1:ni
??for?j?=?1:nj
????T（ij）?=?Tinit;??%Initial?temperature
????Told（ij）?=?Tinit;
????T（i1）?=?50;
????T（inj）?=?50;
????Su（ij）=0;???????%Initial?indendendent?source?term
????Sp（ij）=0;???????%Initial?dependent?source?term
????ae（ij）?=?lambda*dy/dx;
????aw（ij）?=?lambda*dy/dx;
????an（ij）?=?lambda*dx/dy;
????as（ij）?=?lambda*dx/dy;
????dV?=?dx*dy;
????ap0?=?density*cp*dV/dt;
????if?i==2??%?convective?heat?transfer?boundary
???????Su（ij）?=?Tfluid/（1/alfa+dx/（2*lambda））*dy/dV;
???????Sp（ij）?=?-1/（1/alfa+dx/（2*lambda））*dy/dV;
???????aw（ij）?=?0;
????end;
????if?i==ni-1?%?insulated?boundary
???????ae（ij）?=?0;
????end
????if?j==2?%?bottom?boundary?given?temperature
???????as（ij）=2*lambda*dx/dy;
????end???
????if?j==nj-1?%?top?boundary?given?temperature
???????an（ij）=2*lambda*dx/dy;
????end???
????ap（ij）?=?ae（ij）+aw（ij）+an（ij）+as（ij）-Sp（ij）*dV+ap0;
??end;
end;
%%%%%%%%%%%
maxres?=?1.0e-6;
maxit?=?100;
time=0;
maxtime=100;
s=（cos（pi/cv_x）+（dx/dy）^2*cos（pi/cv_y））/（1+（dx/dy）^2）;
omega?=2/（1+sqrt（1-s^2））;omega=1;
while?（time??Told=T;??
?sumres?=?1;
?counter?=?0;
?while?（sumres>maxres&counter??sumres?=?0;
??for?i?=?2:ni-1
???for?j?=?2:nj-1
????T（ij）=omega*（ae（ij）*T（i+1j）+aw（ij）*T（i-1j）+an（ij）*T（ij+1）...
???????+as（ij）*T（ij-1）+Su（ij）*dV+ap0*Told（ij））/ap（ij）+（1-omega）*T（ij）;
????res?=??abs（ap（ij）*T（ij）-（ae（ij）*T（i+1j）+aw（ij）*T（i-1j）+...
??????an（ij）*T（ij+1）+as（ij）*T（ij-1）+Su（ij）*dV+ap0*Told（ij）））;
????sumres=sumres+res;
???end;
??end;
??for?i?=?2:ni-1
???for?j?=?2:nj-1
????res?=??abs（ap（ij）*T（ij）-（ae（ij）*T（i+1j）+aw（ij）*T（i-1j）+...
??????an（ij）*T（ij+1）+as（ij）*T（ij-1）+Su（ij）*dV+ap0*Told（ij）））;
????sumres=sumres+res;
???end;
??end

??sumerr=sumres
??counter?=?counter?+?1
?end;
?time?=?time?+dt;
end;?
%?Calculate?boundary?values
?for?j?=?2:nj-1
???T（1j）=（alfa*Tfluid+lambda/（dx/2）*T（2j））/（alfa+lambda/（dx/2））;
???T（nij）?=?T（ni-1j）;
end;???
%
pcolor（xyT‘）;shading?interp;xlabel（‘x‘）;ylabel（‘y‘）;title（‘Tempera

?屬性????????????大小?????日期????時間???名稱
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?????文件???????3036??2003-08-07?14:21??temperatureofoilthrustbearing\Example_3_SOR.m

?????目錄??????????0??2008-11-07?12:16??temperatureofoilthrustbearing

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?????????????????3254????????????????????3