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+//Eg-9.8
+//pg-413
+
+clc
+clear
+
+//After substituting alpha=lamda*R,z/L,r/R,L/R
+//Treq=T-Ta/T0-Ta
+//first three zeros are taken from appendix 9F
+
+
+alpha=[2.4048;5.5201;8.6537];
+
+a=[1;-2.2499997;1.2656208;-.3163866;.0444479;-.0039444;.00021];
+b=[.5;-.56249985;.21093573;-.03954289;.00443319;-.00031761;.00001109];
+c=[.36746691;.60559366;-.74350384;.25300117;-.04261214;.00427916;-.00024846];
+d=[-.6366198;.2212091;2.1682709;-1.31164827;.3123951;-.0400976;.0027873];
+e=[0.79788456;-.00000077;-.0055274;-.00009512;.00137237;-.00072805;.000014476];
+f=[.79788456;.00000156;.01659667;.00017105;-.00249511;.00113653;-.00020033];
+g=[-.78539816;-.04166397;-.00003954;.00262573;.00054125;-.00029333;.00013558];
+h=[-2.35619449;.12499612;.0000565;-.00637879;.00074348;.00079824;-.00029166];
+
+
+for i=1:3
+
+x=alpha(i);
+
+p=x/3*x/3;
+q=3/x;
+
+if x<3 then
+ J0(i)=a(1)+p*(a(2)+p*(a(3)+p*(a(4)+p*(a(5)+p*(a(6)+p*(a(7))))))) ;
+ J1(i)=x*(b(1)+p*(b(2)+p*(b(3)+p*(b(4)+p*(b(5)+p*(b(6)+p*(b(7)))))))) ;
+else
+ f0=e(1)+q*(e(2)+q*(e(3)+q*(e(4)+q*(e(5)+q*(e(6)+q*(e(7)))))));
+ f1=f(1)+q*(f(2)+q*(f(3)+q*(f(4)+q*(f(5)+q*(f(6)+q*(f(7))))))) ;
+ theta0=x+g(1)+q*(g(2)+q*(g(3)+q*(g(4)+q*(g(5)+q*(g(6)+q*(g(7))))))) ;
+ theta1=x+h(1)+q*(h(2)+q*(h(3)+q*(h(4)+q*(h(5)+q*(h(6)+q*(h(7))))))) ;
+ J0(i)=(1/x)^.5*f0*cos(theta0);
+ J1(i)=(1/x)^.5*f1*cos(theta1);
+end
+
+end
+for i=1:3
+
+x=alpha(i)/2;
+
+p=x/3*x/3;
+q=3/x;
+
+if x<3 then
+ JJ0(i)=a(1)+p*(a(2)+p*(a(3)+p*(a(4)+p*(a(5)+p*(a(6)+p*(a(7))))))) ;
+ JJ1(i)=x*(b(1)+p*(b(2)+p*(b(3)+p*(b(4)+p*(b(5)+p*(b(6)+p*(b(7)))))))) ;
+else
+ f0=e(1)+q*(e(2)+q*(e(3)+q*(e(4)+q*(e(5)+q*(e(6)+q*(e(7)))))));
+ f1=f(1)+q*(f(2)+q*(f(3)+q*(f(4)+q*(f(5)+q*(f(6)+q*(f(7))))))) ;
+ theta0=x+g(1)+q*(g(2)+q*(g(3)+q*(g(4)+q*(g(5)+q*(g(6)+q*(g(7))))))) ;
+ theta1=x+h(1)+q*(h(2)+q*(h(3)+q*(h(4)+q*(h(5)+q*(h(6)+q*(h(7))))))) ;
+ JJ0(i)=(1/x)^.5*f0*cos(theta0);
+ JJ1(i)=(1/x)^.5*f1*cos(theta1);
+end
+
+end
+
+Treq=0;
+
+for i=1:3
+Treq=(1/alpha(i)*JJ0(i)*sinh(.5*alpha(i))/J1(i)/sinh(2*alpha(i)))+Treq;
+end
+Tfinal=2*Treq;
+disp("values of alpha ,required bessel functions and final required value are respectively")
+disp(alpha)
+disp(JJ0)
+disp(J1)
+disp(Tfinal)
+