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Re: analytical solution laminar flow in rectangular microchannel
Posted:
Nov 19, 2012 4:03 AM
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> > This code is written by a senior. The velocity /
> flow
> > rate is set as 0.15u l/min^-1. The value is then
> > convert to form of (m/s).
> >
> > Regards,
> > Anne
>
> I don't know whether the formula you used to
> calculate
> the axial velocity in your code is correct since
> I could not find it in the literature.
> The formula I used can be found in
>
> http://www.amazon.de/Str%C3%B6mungslehre-Einf%C3%BChru
> ng-Theorie-Str%C3%B6mungen-Springer-Lehrbuch/dp/364213
> 1425
>
> Chapter 6.1.6: Strömung durch nichtkreisförmige
> Rohre
> (Flow through non-circular tubes)
>
> I enclose my attempt to translate the FORTRAN-code
> to MATLAB.
>
> Best wishes
> Torsten.
>
> %Length(Lx) and height(Ly) of the microchannel [m]
>
> %The channel is considered to be centered at (0,0) so
> that
> %velocity output is for -Lx/2 <= x <= Lx/2 and -Ly/2
> <= y <= Ly/2
> Lx = 500e-6;
> Ly = 500e-6;
> %Volume flow through the microchannel [m^3/s]
> Vpunkt = 3.0009375e-8;
> %Number of points in x- and y-direction for which
> velocity is
> %calculated (npoints_x, npoints_y <= 100)
> npoints_x = 40;
> npoints_y = 40;
> %Minimum number of series terms to be considered
>
> nmin = 10;
> %USUALLY NO CHANGES ARE REQUIRED BELOW THIS LINE
> %OUTPUT (x-coordinate, y-coordinate, velocity in
> (x,y))
> %is written to a file named 'Velocity')
> x_vector = zeros(npoints_x);
> y_vector = zeros(npoints_y);
> velocity = zeros(npoints_y,npoints_x);
> sum = 0;
> n = 0;
> reihenglied = 1.0;
> while (abs(reihenglied) > 1e-18) || (n <= nmin)
> n = n + 1;
> m = pi/Ly*(2*n-1);
> reihenglied = tanh(0.5*Lx*m)/m^5;
> sum = sum + reihenglied;
> end
> konstante =
> 4.0D0*Vpunkt/(Lx*Ly^3)/(1.0/3.0-64.0/(Lx*Ly^4)*sum)
> deltax = Lx/npoints_x;
> deltay = Ly/npoints_y;
> x = -Lx/2.0 - deltax/2.0;
> i = 0;
> While (i < npoints_x)
> i = i + 1;
> x = x + deltax;
> x_vector(i) = x;
> y = -Ly/2.0 - deltay/2.0;
> j = 0;
> While (j < npoints_y)
> j = j + 1;
> y = y + deltay;
> y_vector(j) = y;
> sum = 0.0;
> n = 0 ;
> reihenglied = 1.0;
> While (abs(reihenglied) > 1e-18) || (n <=
> (n <= nmin)
> n = n + 1;
> m = pi/Ly*(2*n-1);
> reihenglied =
> englied =
> cos(m*y)/m^3*(cosh(m*x)/cosh(0.5*m*Lx)-1.0);
> if (mod(n,2) == 1)
> reihenglied = -reihenglied;
> end
> sum = sum + reihenglied;
> end
> velocity(j,i) = konstante*4.0/Ly*sum;
> end
> end
> surf(x_vector,y_vector,velocity);
> %
> %Check whether velocity profile satisfies volume flow
> constraint
> %
> Vpunkt_check = 0.0;
> For i = 1:npoints_x
> For j = 1:npoints_y
> Vpunkt_check = Vpunkt_check + velocity(i,j);
Should read:
Vpunkt_check = Vpunkt_check + velocity(j,i);
> end
> end
> Vpunkt_check = deltax*deltay*Vpunkt_check;
>
> Vpunkt;
> Vpunkt_check;
Best wishes
Torsten.
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