function mnhf_fin3(n,Bi)
%MNHF_FIN3 solves for the 1D temperature distribution in a cooling fin 
% of variable cross-sectional area subject to Dirichlet BCs.
%
% n -  number of interior grid points.
% Bi - modified Biot number.
%
% Usage  mnhf_fin3(100,1e-1)

% Set grid spacing, i.e. define \delta \xi.
dxi = (1.0-0.0)/(n+1);
 
%% Initialize arrays.
xi = linspace(dxi,1.0-dxi,n); 
maindiag = -2.0*(2.0-xi+Bi*dxi^2.0);                 % Main diagonal.
supdiag = 2.0-xi(1:end-1)-0.5*dxi;                   % Super diagonal.
subdiag = 2.0-xi(2:end)+0.5*dxi;                     % Sub diagonal.
T = diag(maindiag,0)+diag(supdiag,1)+diag(subdiag,-1); % Put it together.
b = zeros(n,1);                                      % Define RHS vector.
b(1) = -1.0*(2.0-xi(1)+0.5*dxi);

% Solve linear system using Thomas's algorithm then plot solution.
theta = mnhf_thomas(T,b); theta = [1.0 theta' 0.0];
xi = linspace(0.0,1.0,n+2);
figure(1); hold on; box on; set(gca,'fontsize',14)
plot(xi,theta,'k--','linewidth',2);

%% Add axis labels and a title to the figure.
xlabel('{\it \xi=x/L}');
ylabel('{\it \theta=(T-T_\infty)/(T_0-T_\infty)}');
title('Cooling fin (variable cross-section, Dirichlet BCs)','fontsize',12)