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+clear;
+clc;
+
+// A Textbook on HEAT TRANSFER by S P SUKHATME
+// Chapter 2
+// Heat Conduction in Solids
+
+// Example 2.11(b)
+// Page 65
+printf("Example 2.11(b), Page 65 \n\n")
+
+D = 0.05 ; // [m]
+To = 450 ; // [degree C]
+Tf = 90 ; // [degree C]
+T = 150 ; // [degree c]
+h = 115 ; // [W/m^2 K]
+rho = 8000 ; // [kg/m^3]
+Cp = 0.42*1000 ; // [J/kg K]
+k = 46 ; // [W/m K]
+R = D/2;
+
+// (b)
+// let ratio = theta_R_0/theta_o
+ratio = (T-Tf)/(To - Tf);
+Bi = h*R/k;
+// From Table 2.5
+lambda_1_R = 0.430;
+x = 2*[sin(lambda_1_R) - lambda_1_R*cos(lambda_1_R)]/[lambda_1_R - sin(lambda_1_R)*cos(lambda_1_R)];
+
+// Substituting in equattion 2.7.29, we have an equation in variable y(=at/R^2) 
+// Solving
+function[eqn] = parameter(y)   
+eqn = ratio - x*exp(-(lambda_1_R^2)*(y));
+funcprot(0);
+endfunction
+
+y = 5; // (initial guess, assumed value for fsolve function)
+Y = fsolve(y,parameter);
+
+a = k/(Cp*rho); // alpha
+t2 = Y*(R^2)/(a); // [sec]
+t2_min = t2/60; // [min]
+printf("Time taken by the centre of the ball to reach 150 degree C if internal temperature gradients are not neglected is %f seconds i.e. %f minutes",t2,t2_min);