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Topic: Duct Temperature Distribution
Replies: 10   Last Post: Dec 1, 2011 4:08 AM

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Green Sal

Posts: 48
Registered: 10/15/10
Re: Duct Temperature Distribution
Posted: Nov 29, 2011 12:59 PM
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Thanks Torsten,

but am afraid i don't understand exactly what you are saying, could you please elaborate more?

Thank you!

Torsten <Torsten.Hennig@umsicht.fraunhofer.de> wrote in message <ae366e8e-d9b5-4f49-818c-773ef2a31292@i8g2000vbh.googlegroups.com>...
> On 29 Nov., 09:22, "Green Sal" <cyberr...@hotmail.com> wrote:
> > Hello guys, i am trying to find the temperature distribution in a dukt that is insulated from both sides, constant temperature on one side, and const. heat flux from the top. in the inner duct steam flows at constant temperature.  The following is the code that i used but i know something is not working. I am trying to validate my code by changing the values of the heat flux but the temperature distribution seems to stay the same. Also, if i run the code at 10 seconds and 100 seconds, the results are the same. If anybody understand such problems please help. Thank you.
> >
> > clear
> > clc
> >
> > T = zeros(20,20);
> > % Initial condition
> > % Set all material to 20C ambient temp
> > for y = 1:20;
> >     for x = 1:20;
> >         T(y,x) = 20;
> >     end
> > end
> > h=[1000000;0;0;0];
> > dt = .1;  %(Time increment, Seconds)
> > p = 9000; %(Density of Copper, kg/m^3)
> > Cp = 380; %(Specific heat of Copper, J/kg*K)
> > qT = 500; %(Solar heat flux, W/m^2)
> > TL = 50;  %(Temperature of the left side of the block, Celsius)
> > Tsteam = 400; % (Temperature of steam inside the duct, Celsius)
> > l = 0.005; % 0.005 Meters
> > K = 400; % (Thermal conductivity of Coppy,W/m*C)
> > Alpha = K/(p*Cp); % (Thermal diffusivity)
> > Fo = (Alpha*dt)/(l^2); % Seconds
> > Bi=(h*l)/K;
> > b(1)=det(T);
> > fprintf('Enter Time (s):\n')
> > t = input(' ');
> >
> > A=t/dt; %time/step increment size
> > %instant steam at center
> > for y = 6:15;
> >     for x = 6:15;
> >         T(y,x) = Tsteam;
> >     end;
> > end;
> > %for whole matrix
> > for n = 1:A
> >
> > % BOUNDRY CONDITIONS
> >     % Node 1 - Top left node
> >     T(1,1) = T(1,1)*(1-4*Fo)+2*Fo*(T(1,2) + T(2,1) + (2/K)*TL+ qT*l/K);
> >
> >     % Node 21 - Top right node
> >
> >     T(1,20) = T(1,20)*(1-4*Fo)+2*Fo*(T(1,19) + T(2,20)+ qT*l/K);
> >
> >     % Left nodes - Left side BC
> >     for x = 1;
> >         for y = 2:19;
> >             T(y,x) = TL;
> >         end
> >     end
> >
> > % Right nodes - Right surface BC (Insulated section (no qT))
> >
> >     for x = 20;
> >         for y = 3:19;
> >             T(y,x) = T(y,x)*(1-4*Fo) + Fo*(T(y-1,x) + T(y+1,x) + 2*T(y,x-1));
> >         end;
> >     end;
> >
> >     % Bottom left Node - insulated with left BC
> >
> >     T(20,1) = T(20,1)*(1-4*Fo) + 2*Fo*(T(19,1) + T(20,2) + (2*TL)/K);
> >
> >     % Bottom right Node - insulated with right BC
> >
> >     T(20,20) = T(20,20)*(1-4*Fo) + 2*Fo*(T(19,20) + T(20,19));
> >
> >     % Top nodes calcs - Top surface (Heat Flux addition)
> >     for y = 1;
> >         for x = 2:19;
> >             T(y,x) = T(y,x)*(1-3*Fo) + Fo*((qT*l/K) + T(y,x-1) + T(y,x+1) + T(y+1,x));
> >         end;
> >     end;
> >
> > % Calculating the in between nodal temperatures at each delta(time)
> >     for y = 2:19; %inside left slab and right slab
> >         for x = [2:5,16:19]
> >             T(y,x) = T(y,x)*(1-4*Fo) + Fo*(T(y,x-1) + T(y,x+1) + T(y-1,x) + T(y+1,x));
> >         end;
> >     end;
> >  %central nodes
> >     for x = 6:19;%center slab portions above and below duct
> >         for y = [2:5,16:19];
> >             T(y,x) = T(y,x)*(1-4*Fo) + Fo*(T(y,x-1) + T(y,x+1) + T(y-1,x) + T(y+1,x));
> >         end;
> >     end;
> >
> >  % Bottom Nodes - Insulated section (no qT)
> >
> >     for y = 20;
> >         for x = 2:19;
> >             T(y,x) = T(y,x)*(1-4*Fo) + Fo*(T(y,x-1) + T(y,x+1) + 2*T(y-1,x));
> >         end;
> >     end;
> >
> > %this part below kills the initial for loop if the duct has reached steady
> > %state, and displays the time in seconds
> >     b(n+1)=det(T);
> > if b(n)== b(n+1);
> >     s=(n-1)*.1;
> >     fprintf('The Duct reached Steady State at: %4.1f seconds \n',s);
> > break
> > end
> > end;
> >
> > Tfinal = flipud(T);
> >
> > % Graphing the temperature isotherm
> >
> > Spacing = (20:5:400);
> > [C,h]=contourf(Tfinal,Spacing);
> > clabel(C,h)
> >
> > [val,ind] = max(Tfinal(:));
> > [max_x,max_y] = ind2sub(size(Tfinal),ind);

>
>
> Use two arrays T and T_new for the old (at time level t) and new (at
> time level t+deltat)
> temperatures.
> With your settings above, you get a garbage mixture of the
> temperatures at both time levels.
>
> Best wishes
> Torsten.




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