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+//Exa 4.12
+clc;
+clear;
+close;
+//given data
+D=10*10^-2;// in m
+b=D/2;
+h= 100;// in W/m^2 degree C
+T_o=418;// in degree C
+T_i=30;// in degree C
+T_infinite=1000;// in degree C
+
+disp(" (A) For copper cylinder ");
+k=350;// in W/mK
+alpha=114*10^-7;// in m^2/s
+Bi= h*b/k;
+theta_0_t = (T_o-T_infinite)/(T_i-T_infinite);
+Fo=18.8;
+// Formula Fo= alpha*t/b^2
+t=Fo*b^2/alpha;
+disp("Time required to reach for the cylinder centreline temperature 418 degree C : "+string(t)+" seconds or "+string(t/3600)+" hours")
+
+// (2) Temperature at the radius of 4 cm
+theta_0_t = 0.985;
+// Formula theta_0_t = (T-T_infinite)/(T_o-T_infinite)
+T= theta_0_t*(T_o-T_infinite)+T_infinite;// in degree C
+disp(T,"Temperature at the radius of 4 cm ") 
+disp("It has very less temperature gradients over 4 cm radius")
+
+disp(" (B) For asbestos cylinder ");
+k=0.11;// in W/mK
+alpha=0.28*10^-7;// in m^2/s
+Bi= h*b/k;
+theta_0_t = (T_o-T_infinite)/(T_i-T_infinite);
+Fo=0.21;
+// Formula Fo= alpha*t/b^2
+t=Fo*b^2/alpha;
+disp("Time required to reach for the cylinder centreline temperature 418 degree C : "+string(t)+" seconds or "+string(t/3600)+" hours")
+
+// (2) Temperature at the radius of 4 cm
+theta_x_t = 0.286;
+// Formula theta_x_t = (T-T_infinite)/(T_o-T_infinite)
+T= theta_x_t*(T_o-T_infinite)+T_infinite;// in degree C
+disp(T,"Temperature at the radius of 4 cm ") 
+disp("It has large temperature gradients")