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Topic: analytical solution laminar flow in rectangular microchannel
Replies: 29   Last Post: Mar 21, 2013 4:58 AM

 Messages: [ Previous | Next ]
 Torsten Hennig Posts: 2,419 Registered: 12/6/04
Re: analytical solution laminar flow in rectangular microchannel
Posted: Dec 6, 2012 2:33 AM

> 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)
> 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
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)
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.

Date Subject Author
10/28/12 Anne
10/29/12 Torsten Hennig
10/29/12 Anne
10/29/12 Torsten Hennig
10/29/12 Anne
10/30/12 Torsten Hennig
10/31/12 Torsten Hennig
11/3/12 Anne
11/3/12 Torsten Hennig
11/4/12 Anne
11/5/12 Torsten Hennig
11/16/12 Anne
11/16/12 Torsten Hennig
11/16/12 Anne
11/19/12 Torsten Hennig
11/19/12 Torsten Hennig
12/3/12 Anne
12/4/12 Torsten Hennig
12/4/12 Anne
12/4/12 Torsten Hennig
12/4/12 Anne
12/4/12 Torsten Hennig
12/4/12 Anne
12/4/12 Torsten Hennig
12/4/12 Anne
12/5/12 Torsten Hennig
12/5/12 Anne
12/5/12 Anne
12/6/12 Torsten Hennig
3/21/13 Anne