How to code heat transfer expansion of erf ?

%mainp3
clear all 
clc
k=30;%Wm^-1K^-1
p=3950;%kg m^-3
c = 880; %J kg^-1 K^-1
L = 0.10;%m
Tin = 1200;%K
Tout = 300;%k
ti=0;

N0=1;
nsteps = 5;

N = zeros(1,nsteps+1);
N(1) = N0;
ap=0.1;
x=1;
for (tf=10:50)
  tf= tf+1;
  t = linspace(ti, tf, nsteps);
[Theta] = InfConduct(x,ap,t)
pause(0.5)
plot(t,Theta)
end
hold off
figure(2)
plot(t, Theta)

In this problem I dont understand why we defined all the variables in the top portion if my InfConduct function from the last problem uses the right side of equation 3?

function [Theta] = InfConduct(x,ap,t)
    tfh = @(t) erfc(x./sqrt(4 .*ap.*t));
  Theta = tfh(t(1));
  for k = 2:numel(t)-1
    Theta(k+1) = Theta(k) + tfh(t(k+1))
  end
end

[Henry B.]

I didn't include the output because its changing in periods of 0.5.

[Torsten]

Because you are supposed to calculate alpha from k, rho and cp in the calling program and to call InfConduct with this value of alpha.