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Re: analytical solution laminar flow in rectangular microchannel
Posted:
Oct 29, 2012 7:00 AM
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>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.
> What about for 3D?
In the 3d-case, you will have to add a for-loop
above to loop over the z-component, too.
Best wishes
Torsten.
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