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Re: analytical solution laminar flow in rectangular microchannel
Posted:
Dec 6, 2012 2:33 AM
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> I understand the concept but I having difficulty to
> set the array elements.
>
> Can you show me example for 0.53mm/s in a 100um
> x100um x50mm (width x height x length)?
>
> my coding:
> h=100e-6;
> w=100e-6;
> Q=0.00025;
> z=0;
> i=0;
> y=0;
> while(i<1000)
> n = 1;
> ans=0;
> term=0;
> while (n<1000)
> a=(1/n^3)*(1-(cosh(n*pi*y/h))/(cosh(n*pi*w/(2*h))))*si
> n(n*pi*z/h);
> b=1-(((192*h)/(n^5*pi^5*w))*tanh(n*pi*w/(2*h)));
> term=(48*Q*a)/(pi^3*h*w*b);
> ans=ans+term;
> n=n+2;
> end
> i=i+1;
> result((i+1),1)=ans;
> result((i+1),2)=z;
> z=h/999*i;
> end
> xlswrite('Figure6.xlsx',result)
> width = xlsread('Figure6.xlsx', 'B:B')
> avevelocity = xlsread('Figure6.xlsx', 'A:A')
> figure(1);
> plot(width,avevelocity);
>
> figure(2);
> x_array=[0.0: 10e-6:200e-6];
> y_array=[0.0:10e-6:100e-6];
> velocity_array=[0:1e-6:10e-6];
> n=length(x_array);
> m=length(y_array);
>
> x_quiver_array=zeros(m*n);
> y_quiver_array=zeros(m*n);
> x_velocity_quiver_array=zeros(m*n);
> y_velocity_quiver_array=zeros(m*n);
>
> for i=1:n
> for j=1:m
> x_quiver_array((i-1)*m+j)=x_array(i);
> y_quiver_array((i-1)*m+j)=y_array(j);
> x_velocity_quiver_array((i-1)*m+j)=velocity_array(j);
> y_velocity_quiver_array((i-1)*m+j)=0.0;
> end
> end
> quiver(x_quiver_array,y_quiver_array,x_velocity_quiver
> _array,y_velocity_quiver_array);
>
> Best regards,
> Anne
Your formula to calculate the velocity profile at the channel entrance are still wrong.
Look up formula (3.48), page 120, in
http://www.google.de/url?sa=t&rct=j&q=&esrc=s&frm=1&source=web&cd=1&ved=0CDkQFjAA&url=ftp%3A%2F%2Fftp.demec.ufpr.br%2FCFD%2Fbibliografia%2Fviscous_fluid_flow_frank_m_white_second_edition.pdf&ei=REnAUNSeJ4HbtAaqtoCgDg&usg=AFQjCNFU1bp4sP63L7py2hK8SDLFJCq1eQ&sig2=5sO3Ydf0ikNyewvndZUYsw
for the correct one.
But to understand how to make a vector plot from the results, you can try this:
h=100e-6;
w=100e-6;
Q=0.00025;
z=0;
i=0;
y=0;
while(i<1000)
n = 1;
ans=0;
term=0;
while (n<1000)
a=(1/n^3)*(1-(cosh(n*pi*y/h))/(cosh(n*pi*w/(2*h))))*sin(n*pi*z/h);
b=1-(((192*h)/(n^5*pi^5*w))*tanh(n*pi*w/(2*h)));
term=(48*Q*a)/(pi^3*h*w*b);
ans=ans+term;
n=n+2;
end
i=i+1;
result((i+1),1)=ans;
result((i+1),2)=z;
z=h/999*i;
end
xlswrite('Figure6.xlsx',result)
width = xlsread('Figure6.xlsx', 'B:B')
avevelocity = xlsread('Figure6.xlsx', 'A:A')
figure(1);
plot(width,avevelocity);
figure(2);
x_array=[0.0];
y_array=results(:,1);
velocity_array=results(:,2);
n=length(x_array);
m=length(y_array);
x_quiver_array=zeros(m*n);
y_quiver_array=zeros(m*n);
x_velocity_quiver_array=zeros(m*n);
y_velocity_quiver_array=zeros(m*n);
for i=1:n
for j=1:m
x_quiver_array((i-1)*m+j)=x_array(i);
y_quiver_array((i-1)*m+j)=y_array(j);
x_velocity_quiver_array((i-1)*m+j)=velocity_array(j);
y_velocity_quiver_array((i-1)*m+j)=0.0;
end
end
quiver(x_quiver_array,y_quiver_array,x_velocity_quiver_array,y_velocity_quiver_array);
Best wishes
Torsten.
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