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Re: analytical solution laminar flow in rectangular microchannel
Posted:
Dec 4, 2012 10:27 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
What do you mean by 0.53 mm/s ?
You mean the average velocity at the entry is 0.53 mm/s ?
So the volume flow rate is 0.53*10^(-3)*100*10^(-6)*100*10^(-6)=5.3*10^(-12) m^3/s ?
Best wishes
Torsten.
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