1d Unsteady
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%VJTI Phd_Mechanical %VIJAY DHADKE 169020009 %CFD 1D Unsteady clc; clear; n=input('number of grid points of control volume= '); L=input('Enter the length of bar='); K=input('Enter the value of thermal conductivity='); C=input('Enter the value of volumetric heat capacity ='); T_initial = input('Enter value of initial tenmperature (at Time=0) ='); T_b=input('Boundry temperature='); x=L/n; Time_initial = input ('Enter starting time = '); Time_final = input ('Enter final time = '); method = input('Explicit Method = 1 Crank-Nicolson Method = 2 Implicit Method = 3.... Method= '); y(1)=0; y(2)=x/2; for i=3:n+1; y(i)=y(i-1)+x; end for i=1:n+1 T(i)=T_initial; end T(n+2)=T_b; y(n+2)=L; aw(2)=2*K/x; ae(2)=K/x; aw(n+1)=K/x; ae(n+1)=2*K/x; for i=3:n; aw(i)=K/x; ae(i)=K/x; end if method==1 delT=C*(x^2)/(4*K); for i=1:delT:Time_final; Told=T; ap_old=C*x/delT; ap=ap_old; T(n+2)=0; for j=2:n+1; T(j)=((aw(j).*Told(j-1))+(ae(j).*Told(j+1))+((ap_old-aw(j)ae(j))*Told(j)))/ap; disp (T); end T(1)=T(2); end elseif method==2 delT=C*(x^2)/(2*K); for i=1:delT:Time_final; Told=T; ap_old=C*x/delT; a(1)=1; b(1)=0; c(1)=0; d(1)=-1;
for j=2:n+1 ap(j)=ap_old+(aw(j)/2)+(ae(j)/2); a(j)=ae(j)/2; b(j)=aw(j)/2; c(j)=-((b(j)*Told(j-1))+(a(j)*Told(j+1))+((ap_old-a(j)-b(j))*Told(j))); d(j)=-ap(j); end a(n+2)=0; b(n+2)=0; c(n+2)=T_b; d(n+2)=1; e(1)=d(1); f(1)=c(1); for j=2:(n+2); e(j)=d(j)-((a(j-1).*b(j))./e(j-1)); f(j)=(c(j)-((b(j).*f(j-1))./e(j-1))); end T(n+2)=f(n+2)./e(n+2); for j=(n+1):-1:1; T(j)=(f(j)-(a(j).*T(j+1)))./e(j); disp (T); end end elseif method==3; delT=input('suitable time interval='); for i=1:delT:Time_final; Told=T; ap_old=C*x/delT; a(1)=1; b(1)=0; c(1)=0; d(1)=-1; for j=2:n+1 ap(j)=ap_old+(aw(j))+(ae(j)); a(j)=ae(j); b(j)=aw(j); c(j)=-((ap_old)*Told(j)); d(j)=-ap(j); end a(n+2)=0; b(n+2)=0; c(n+2)=T_b; d(n+2)=1; e(1)=d(1); f(1)=c(1); for j=2:(n+2); e(j)=d(j)-((a(j-1).*b(j))./e(j-1)); f(j)=(c(j)-((b(j).*f(j-1))./e(j-1))); end T(n+2)=f(n+2)./e(n+2); for j=(n+1):-1:1; T(j)=(f(j)-(a(j).*T(j+1)))./e(j); disp (T); end end end
Output Explicit Output number of grid points of control volume= 5 Enter the length of bar=0.02 Enter the value of thermal conductivity=10 Enter the value of volumetric heat capacity =10^6 Enter value of initial tenmperature (at Time=0) =200 Boundry temperature=0 Enter starting time = 0 Enter final time = 2 Explicit Method = 1 Crank-Nicolson Method = 2 Implicit Method = 3.... Method= 1 200 200 200 200 200 200 0 200 200 200 200 200 200
0
200 200 200 200 200 200
0
200 200 200 200 200 200
0
200 200 200 200 200 100
0
200 200 200 200 200 100
0
200 200 200 200 200 100
0
200 200 200 200 200 100
0
200 200 200 200 175 100
0
200 200 200 200 175 75
0
200 200 200 200 175 75
0
200 200 200 200 175 75
0
200.0000 200.0000 200.0000 193.7500 175.0000 75.0000
0
200.0000 200.0000 200.0000 193.7500 156.2500 75.0000
0
200.0000 200.0000 200.0000 193.7500 156.2500 62.5000
0
Crank-Nicolson Method number of grid points of control volume= 5 Enter the length of bar=0.02 Enter the value of thermal conductivity=10 Enter the value of volumetric heat capacity =10^6 Enter value of initial tenmperature (at Time=0) =200 Boundry temperature=0 Enter starting time = 0 Enter final time = 2 Explicit Method = 1 Crank-Nicolson Method = 2 Implicit Method = 3.... Method= 2 200.0000 200.0000 200.0000 200.0000 200.0000 82.8427 0 200.0000 200.0000 200.0000 200.0000 179.8989 82.8427
0
200.0000 200.0000 200.0000 196.5507 179.8989 82.8427
0
200.0000 200.0000 199.4053 196.5507 179.8989 82.8427
0
200.0000 199.8811 199.4053 196.5507 179.8989 82.8427
0
199.8811 199.8811 199.4053 196.5507 179.8989 82.8427
0
199.8811 199.8811 199.4053 196.5507 179.8989 58.5785
0
199.8811 199.8811 199.4053 196.5507 147.3077 58.5785
0
199.8811 199.8811 199.4053 186.0766 147.3077 58.5785
0
199.8811 199.8811 196.7463 186.0766 147.3077 58.5785
0
199.8811 199.1590 196.7463 186.0766 147.3077 58.5785
0
199.1590 199.1590 196.7463 186.0766 147.3077 58.5785
0
Implicit Method number of grid points of control volume= 5 Enter the length of bar=0.02 Enter the value of thermal conductivity=10
Enter the value of volumetric heat capacity =10^6 Enter value of initial tenmperature (at Time=0) =200 Boundry temperature=0 Enter starting time = 0 Enter final time = 2 Explicit Method = 1 Crank-Nicolson Method = 2 Implicit Method = 3.... Method= 3 suitable time interval=0.5 200.0000 200.0000 200.0000 200.0000 200.0000 133.3333 0 200.0000 200.0000 200.0000 200.0000 186.6665 133.3333
0
200.0000 200.0000 200.0000 197.3325 186.6665 133.3333
0
200.0000 200.0000 199.4624 197.3325 186.6665 133.3333
0
200.0000 199.8720 199.4624 197.3325 186.6665 133.3333
0
199.8720 199.8720 199.4624 197.3325 186.6665 133.3333
0
199.8720 199.8720 199.4624 197.3325 186.6665 96.2961
0
199.8720 199.8720 199.4624 197.3325 170.3692 96.2961
0
199.8720 199.8720 199.4624 192.2910 170.3692 96.2961
0
199.8720 199.8720 198.0800 192.2910 170.3692 96.2961
0
199.8720 199.4453 198.0800 192.2910 170.3692 96.2961
0
199.4453 199.4453 198.0800 192.2910 170.3692 96.2961
0
199.4453 199.4453 198.0800 192.2910 170.3692 74.6905
0
199.4453 199.4453 198.0800 192.2910 154.9338 74.6905
0
199.4453 199.4453 198.0800 185.7840 154.9338 74.6905
0
199.4453 199.4453 195.8116 185.7840 154.9338 74.6905
0
199.4453 198.5801 195.8116 185.7840 154.9338 74.6905
0
198.5801 198.5801 195.8116 185.7840 154.9338 74.6905
0
for j=2:n+1 ap(j)=ap_old+(aw(j)/2)+(ae(j)/2); a(j)=ae(j)/2; b(j)=aw(j)/2; c(j)=-((b(j)*Told(j-1))+(a(j)*Told(j+1))+((ap_old-a(j)-b(j))*Told(j))); d(j)=-ap(j); end a(n+2)=0; b(n+2)=0; c(n+2)=T_b; d(n+2)=1; e(1)=d(1); f(1)=c(1); for j=2:(n+2); e(j)=d(j)-((a(j-1).*b(j))./e(j-1)); f(j)=(c(j)-((b(j).*f(j-1))./e(j-1))); end T(n+2)=f(n+2)./e(n+2); for j=(n+1):-1:1; T(j)=(f(j)-(a(j).*T(j+1)))./e(j); disp (T); end end elseif method==3; delT=input('suitable time interval='); for i=1:delT:Time_final; Told=T; ap_old=C*x/delT; a(1)=1; b(1)=0; c(1)=0; d(1)=-1; for j=2:n+1 ap(j)=ap_old+(aw(j))+(ae(j)); a(j)=ae(j); b(j)=aw(j); c(j)=-((ap_old)*Told(j)); d(j)=-ap(j); end a(n+2)=0; b(n+2)=0; c(n+2)=T_b; d(n+2)=1; e(1)=d(1); f(1)=c(1); for j=2:(n+2); e(j)=d(j)-((a(j-1).*b(j))./e(j-1)); f(j)=(c(j)-((b(j).*f(j-1))./e(j-1))); end T(n+2)=f(n+2)./e(n+2); for j=(n+1):-1:1; T(j)=(f(j)-(a(j).*T(j+1)))./e(j); disp (T); end end end
Output Explicit Output number of grid points of control volume= 5 Enter the length of bar=0.02 Enter the value of thermal conductivity=10 Enter the value of volumetric heat capacity =10^6 Enter value of initial tenmperature (at Time=0) =200 Boundry temperature=0 Enter starting time = 0 Enter final time = 2 Explicit Method = 1 Crank-Nicolson Method = 2 Implicit Method = 3.... Method= 1 200 200 200 200 200 200 0 200 200 200 200 200 200
0
200 200 200 200 200 200
0
200 200 200 200 200 200
0
200 200 200 200 200 100
0
200 200 200 200 200 100
0
200 200 200 200 200 100
0
200 200 200 200 200 100
0
200 200 200 200 175 100
0
200 200 200 200 175 75
0
200 200 200 200 175 75
0
200 200 200 200 175 75
0
200.0000 200.0000 200.0000 193.7500 175.0000 75.0000
0
200.0000 200.0000 200.0000 193.7500 156.2500 75.0000
0
200.0000 200.0000 200.0000 193.7500 156.2500 62.5000
0
Crank-Nicolson Method number of grid points of control volume= 5 Enter the length of bar=0.02 Enter the value of thermal conductivity=10 Enter the value of volumetric heat capacity =10^6 Enter value of initial tenmperature (at Time=0) =200 Boundry temperature=0 Enter starting time = 0 Enter final time = 2 Explicit Method = 1 Crank-Nicolson Method = 2 Implicit Method = 3.... Method= 2 200.0000 200.0000 200.0000 200.0000 200.0000 82.8427 0 200.0000 200.0000 200.0000 200.0000 179.8989 82.8427
0
200.0000 200.0000 200.0000 196.5507 179.8989 82.8427
0
200.0000 200.0000 199.4053 196.5507 179.8989 82.8427
0
200.0000 199.8811 199.4053 196.5507 179.8989 82.8427
0
199.8811 199.8811 199.4053 196.5507 179.8989 82.8427
0
199.8811 199.8811 199.4053 196.5507 179.8989 58.5785
0
199.8811 199.8811 199.4053 196.5507 147.3077 58.5785
0
199.8811 199.8811 199.4053 186.0766 147.3077 58.5785
0
199.8811 199.8811 196.7463 186.0766 147.3077 58.5785
0
199.8811 199.1590 196.7463 186.0766 147.3077 58.5785
0
199.1590 199.1590 196.7463 186.0766 147.3077 58.5785
0
Implicit Method number of grid points of control volume= 5 Enter the length of bar=0.02 Enter the value of thermal conductivity=10
Enter the value of volumetric heat capacity =10^6 Enter value of initial tenmperature (at Time=0) =200 Boundry temperature=0 Enter starting time = 0 Enter final time = 2 Explicit Method = 1 Crank-Nicolson Method = 2 Implicit Method = 3.... Method= 3 suitable time interval=0.5 200.0000 200.0000 200.0000 200.0000 200.0000 133.3333 0 200.0000 200.0000 200.0000 200.0000 186.6665 133.3333
0
200.0000 200.0000 200.0000 197.3325 186.6665 133.3333
0
200.0000 200.0000 199.4624 197.3325 186.6665 133.3333
0
200.0000 199.8720 199.4624 197.3325 186.6665 133.3333
0
199.8720 199.8720 199.4624 197.3325 186.6665 133.3333
0
199.8720 199.8720 199.4624 197.3325 186.6665 96.2961
0
199.8720 199.8720 199.4624 197.3325 170.3692 96.2961
0
199.8720 199.8720 199.4624 192.2910 170.3692 96.2961
0
199.8720 199.8720 198.0800 192.2910 170.3692 96.2961
0
199.8720 199.4453 198.0800 192.2910 170.3692 96.2961
0
199.4453 199.4453 198.0800 192.2910 170.3692 96.2961
0
199.4453 199.4453 198.0800 192.2910 170.3692 74.6905
0
199.4453 199.4453 198.0800 192.2910 154.9338 74.6905
0
199.4453 199.4453 198.0800 185.7840 154.9338 74.6905
0
199.4453 199.4453 195.8116 185.7840 154.9338 74.6905
0
199.4453 198.5801 195.8116 185.7840 154.9338 74.6905
0
198.5801 198.5801 195.8116 185.7840 154.9338 74.6905
0
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