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| author | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
|---|---|---|
| committer | prashantsinalkar | 2017-10-10 12:27:19 +0530 |
| commit | 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 (patch) | |
| tree | dbb9e3ddb5fc829e7c5c7e6be99b2c4ba356132c /534/CH5/EX5.9/5_9_Finite_Difference1.sce | |
| parent | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (diff) | |
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initial commit / add all books
Diffstat (limited to '534/CH5/EX5.9/5_9_Finite_Difference1.sce')
| -rw-r--r-- | 534/CH5/EX5.9/5_9_Finite_Difference1.sce | 56 |
1 files changed, 56 insertions, 0 deletions
diff --git a/534/CH5/EX5.9/5_9_Finite_Difference1.sce b/534/CH5/EX5.9/5_9_Finite_Difference1.sce new file mode 100644 index 000000000..b527b3273 --- /dev/null +++ b/534/CH5/EX5.9/5_9_Finite_Difference1.sce @@ -0,0 +1,56 @@ +clear;
+clc;
+printf('FUNDAMENTALS OF HEAT AND MASS TRANSFER \n Incropera / Dewitt / Bergman / Lavine \n EXAMPLE 5.9 Page 305 \n'); //Example 5.9
+// Temperature distribution 1.5s after a change in operating power
+
+//Operating Conditions
+
+L = .01; //[m] Metre
+Tsurr = 250+273; //[K] Temperature
+h = 1100; //[W/m^2.K] Heat Convective Coefficient
+q1 = 10^7; //[W/m^3] Volumetric Rate
+q2 = 2*10^7; //[W/m^3] Volumetric Rate
+k = 30; //[W/m.K] Conductivity
+a = 5*10^-6; //[m^2/s]
+
+delx = L/5; //Space increment for numerical solution
+Bi = h*delx/k; //Biot Number
+//By using stability criterion for Fourier Number
+Fo = (2*(1+Bi))^-1;
+//By definition
+t = Fo*delx^2/a;
+printf('\n As per stability criterion delt = %.3f s, hence setting stability limit as .3 s.',t)
+// Using Finite time increment of .3s
+delt = 1*.3;
+Fo1 = a*delt/delx^2;
+x = [0 delx delx*2 delx*3 delx*4 delx*5];
+
+//At p=0 Using equation 3.46
+for i = 1: length(x)
+T(1,i) = q1*L^2/(2*k)*(1-x(i)^2/L^2)+Tsurr + q1*L/h -273 ;
+end
+//System of Equation in Finite Difference method
+for j = 2:6
+ T(j,1)=Fo1*(2*T(j-1,2)+q2*delx^2/k) + (1 -2*Fo1)*T(j-1,1);
+ T(j,2)=Fo1*(T(j-1,1)+T(j-1,3)+q2*delx^2/k) + (1 -2*Fo1)*T(j-1,2);
+ T(j,3)=Fo1*(T(j-1,2)+T(j-1,4)+q2*delx^2/k) + (1 -2*Fo1)*T(j-1,3);
+ T(j,4)=Fo1*(T(j-1,3)+T(j-1,5)+q2*delx^2/k) + (1 -2*Fo1)*T(j-1,4);
+ T(j,5)=Fo1*(T(j-1,4)+T(j-1,6)+q2*delx^2/k) + (1 -2*Fo1)*T(j-1,5);
+ T(j,6)=2*Fo1*(T(j-1,5)+Bi*(Tsurr-273)+q2*delx^2/(2*k)) + (1 -2*Fo1-2*Bi*Fo1)*T(j-1,6);
+end
+//At p=infinity Using equation 3.46
+x = [0 delx delx*2 delx*3 delx*4 delx*5];
+for i = 1:length(x)
+T(7,i) = q2*L^2/(2*k)*(1-x(i)^2/L^2)+Tsurr+q2*L/h-273;
+end
+
+for j= 1:6
+Tans(j,:) = [j-1 delt*(j-1) T(j,:)];
+end
+
+printf("\n\n Tabulated Nodal Temperatures \n\n p t(s) T0 T1 T2 T3 T4 T5\n");
+format('v',6);
+disp(Tans);
+printf(" inf inf %.1f %.1f %.1f %.1f %.1f %.1f",T(7,1),T(7,2),T(7,3),T(7,4),T(7,5),T(7,6));
+
+//END
\ No newline at end of file |