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

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 Torsten Hennig Posts: 2,419 Registered: 12/6/04
Re: analytical solution laminar flow in rectangular microchannel
Posted: Oct 29, 2012 7:00 AM

>May I know what is the term "eps"?

Since you can not sum up to n=infinity, you
stop evaluating the series coefficients when both terms are smaller than eps.

> I would like to plot u_x vs width(y).

Try this:

eps=1e-8;

For i = 1:21
y(i) = 5*(i-1);
term1 = 1.0;
term2 = 1.0;
n = 1;
a = 0;
b = 0;
While (term1 > eps) | (term2 > eps)
term1 = 1/n^3 [1-(cosh(n*pi* y/h))/(cosh(n*pi* w/h))]* sin(n*pi* z/h);
term2 = 192*h/(n^5* pi^5* w)*tanh(n*pi*w/h)
a=a+term1;
b=b+term2;
n=n+2;
end
b=1-b;
ux(i)=48*Q/(pi^3*h*w)*a/b;
end

Now you can plot ux versus y.

In the 3d-case, you will have to add a for-loop
above to loop over the z-component, too.

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
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12/3/12 Anne
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12/4/12 Torsten Hennig
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12/4/12 Torsten Hennig
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12/5/12 Torsten Hennig
12/5/12 Anne
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12/6/12 Torsten Hennig
3/21/13 Anne