%
% Fuel_Temp_FD2_mx.M Function file to compute the coefficient matrices (A & B)
% for the cylindrical fuel pin heat transfer problem.
%
% This routine is called from Fuel_Temp_FD2.m. Several variables are passed
% into this routine via Matlab's global statement. The position vector, r, and
% the thermal conductivity vector, K, are passed into the subroutine via input
% arguments and the resultant A and B matrices are returned.
%
% File prepared by J. R. White, UMass-Lowell (Oct. 2003)
%
function [a,b] = abmatrix(r,K)
global qqq Ts Ks h h2
%
% initialize variables
N = length(K); a = zeros(N,N); b = zeros(N,1);
%
% matrix eqns. -- interior points
for i = 2:N-1
rm = r(i)-h/2; rp =r(i)+h/2;
a(i,i-1) = rm*(K(i) + K(i-1))/2;
a(i,i) = -(rm*K(i-1) + 2*r(i)*K(i) + rp*K(i+1))/2;
a(i,i+1) = rp*(K(i) + K(i+1))/2;
b(i) = -qqq*r(i)*h2;
end
%
% matrix eqns. -- left boundary
a(1,1) = -(K(1) + K(2))/2; a(1,2) = (K(1) + K(2))/2;
b(1) = -qqq*h2/4;
%
% matrix eqns. -- right boundary
rm = r(N)-h/2; rp =r(N)+h/2;
a(N,N-1) = rm*(K(N) + K(N-1))/2;
a(N,N) = -(rm*K(N-1) + 2*r(N)*K(N) + rp*Ks)/2;
b(N) = -qqq*r(N)*h2 - Ts*rp*(K(N)+Ks)/2;
%
% end of routine
%