assign and analysis velocity profile for the Poiseuille flow in a rectangular microchannel

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Anne Lee 2012-10-29

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I'm a beginner. I need to assign and analysis velocity profile for the Poiseuille flow in a rectangular microchannel. I need help on the equations below.

a= sigma_(n,odd to inf)(1/n^3) [1-(cosh(n*pi* y/h))/(cosh(n*pi* w/h))] sin(n*pi* z/h)

b= 1-sigma_(n,odd to inf)(192h/(n^5* pi^5* w) *tanh(n*pi*w/h))

u_x (y,z)=48*Q/(pi^3*h*w)*a/b

Thank you.

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Answer 1

Walter Roberson 2012-10-29

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The sum over n odd to infinity can be rewritten in terms of a sum over n, by taking each "n" in the summation and multiplying it by 2 and adding 1, and replacing the summation by sum n.

Your problem will then simply to merely calculating a countable infinite number of terms in countable infinite precision; fortunately that task can be simplified to take merely countable infinite time. Just program it up, start it going, and take a lot of coffee breaks until it finishes.