# Help: Fluid Flow Over a Horizontal Flat Plate by Boundary Layer Eq.

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 May 20, 2011, 04:57 Help: Fluid Flow Over a Horizontal Flat Plate by Boundary Layer Eq. #1 New Member   Egemen Join Date: May 2011 Posts: 1 Rep Power: 0 Sponsored Links Hi everyone, i faced up a problem on my matlab code related to fluid flow over a horizontal plate by boundary layer theorem. I found nodal equations and wrote a script to solve it but it didnt work. I really dont understand why it did not work. I controlled it many times and i could not find any problem with code. I will be crazy. Are there someone can help me on this code? Boundary Layer Equations for Fluid Flow 1.u(du/dx)+v(du/dy)=mu(d^2u/dy^2) (momentum eq.) 2.du/dx+dv/dy=0 (continuity eq.) Code at below; clear all clc x1=0; %initial x value x2=0.1; %final x value (lenght of the domain) y1=0; %initial y value y2=0.1; %final y value dv=1.307*10^-6; %kinematic viscosity n=100; %number of volumes and also nodes g=5; %initial guess Q=g*ones(n,n); %initial Q values for each node U=g*ones(n+1,n+1); %initial U values at surfaces V=g*ones(n+1,n+1); %initial V values at surfaces Uinf=4; %U infinity m/s maxerrq=1; maxerrv=1; h=(x2-x1)/n; %dx=dy=h the number of nodes D=dv/h; %kinematic viscosity over step k=0; while maxerrq>10^-6 && maxerrv>10^-6 maxerrq=0; maxerrv=0; k=k+1; Qold=Q; for j=1:n U(1,j)=Uinf; U(j,n)=Uinf; end for i=1:n V(i,1)=0; U(i,1)=0; end Vold=V; Uold=U; for i=2:n-1 for j=2:n-1 api=(U(i+1,j)+V(i,j+1)+2*D); aei=0; awi=U(i,j); ani=D; asi=D+V(i,j); Si=0; Q(i,j)=(aei*Q(i+1,j)+awi*Q(i-1,j)+ani*Q(i,j+1)+asi*Q(i,j-1)+Si)/api; end end % corners % lower-left corner's coefficients & nodal eq. (B1) ap1=U(2,1)+V(1,2)+3*D; ae1=0; aw1=0; an1=D; as1=0; S1=U(1,1)*Uinf; Q(1,1)=(ae1*Q(2,1)+an1*Q(1,2)+S1)/ap1; %B1 % -------------------------------------------- % upper-left corner's coef. & nodal eq. (B3) ap3=U(2,n)+3*D; ae3=0; aw3=0; an3=0; as3=V(1,n)+D; S3=(U(1,n)-V(1,n+1)+2*D)*Uinf; Q(1,n)=(ae3*Q(2,n)+as3*Q(1,n-1)+S3)/ap3; %B3 % -------------------------------------------- % upper-right corner's coef. & nodal eq. (B5) ap5=U(n+1,n)+3*D; ae5=0; aw5=U(n,n); an5=0; as5=V(n,n)+D; S5=2*D*Uinf; Q(n,n)=(aw5*Q(n-1,n)+as5*Q(n,n-1)+S5)/ap5; % -------------------------------------------- % lower-right corner's coef. & nodal eq. (B7) ap7=U(n+1,1)+V(n,2)+3*D; ae7=0; aw7=U(n,1); an7=D; as7=0; S7=0; Q(n,1)=(aw7*Q(n-1,1)+an7*Q(n,2)+S7)/ap7; % -------------------------------------------- % edges % left & right edges (B2 & B6) for j=2:n-1 Q(1,j)=(D*Q(1,j+1)+(D+V(1,j))*Q(1,j-1))/(U(2,j)+V(1,j+1)+2*D); %for B2 Q(n,j)=(U(n,j)*Q(n-1,j)+D*Q(n,j+1)+(V(i,j)+D)*Q(n,j-1))/(U(n+1,j)+V(n,j+1)+2*D); %for B6 end % --------------------------------------------- % lower & upper edges (B8 & B4) for i=2:n-1 Q(i,1)=(U(i,1)*Q(i-1,1)+D*Q(i,2))/(U(i+1,1)+V(i,2)+3*D); %for B8 Q(i,n)=((V(i,n)-2*D)*Q(i,n-1)+(U(i,n)-V(i,n+1)+2*D)*Uinf)/(U(i+1,n)+3*D); %for B4 end % --------------------------------------------- for j=1:n for i=2:n U(i,j)=(Q(i-1,j)+Q(i,j))/2; %average U velocity at surfaces end end for i=1:n for j=2:n+1 V(i,j)=U(i,j-1)-U(j,i)+V(i,j-1); %continuity eq. end end for i=1:n for j=1:n errq=abs(Qold(i,j)-Q(i,j)); errv=abs(Vold(i,j)-V(i,j)); if errq>maxerrq maxerrq=errq; end if errv>maxerrv maxerrv=errv; end end end end

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