How to create a function handle for thermodyna​mics(semi-​infinite heat conduction) using erfc with multiple variables?

%So my initial guess would be to create arrays or vectors for t, x, and alpha and try to pass those values through function handle something like :

thetafh = @(x,t,alpha) erfc(x/sqrt(4*alpha*t))

This is part of my final and any help is greatly appreciated please and thank you.

[Walter Roberson]

You used a tag "octave". This is not an octave resource. octave is a different programming language. The stated intent of the Free Software Foundation is that they provide the software free with the expectation that you will pay for help if you need help.

It is sort of like the way that printer costs fell drastically but the price for toner or ink rose a lot: the economic model of octave is specifically that you get the software free and are expected to pay and pay for assistance.

Octave assistance is not here.

[Henry B.]

good to know I thought they were the same coding language as my class is taught as octave/matlab.

[Henry B.]

function [Theta] = InfConduct(x,t,alpha)
  tfh = @(x,t,alpha) erfc(x./sqrt(4 .*alpha.*t))
  Theta=0;
  for k = 1:size(t)
    Theta(k+1) = Theta(k) + tfh(k+1)
  end
  end

This is the code I have tried and when I try to use the example code in the command line it generates a function handle error.

Answer 1

[Torsten]

Use ./ instead of / in your definition of thetafh.

But you are asked to write a function, not a function handle.

[Henry B.]

good call most my issues come from being a poor direction translator. Thank you for the help!

[Henry B.]

function [Theta] = InfConduct(x,t,alpha)
  tfh = @(x,t,alpha) erfc(x./sqrt(4 .*alpha.*t))
  Theta=0;
  for k = 1:size(t)
    Theta(k+1) = Theta(k) + tfh(k+1)
  end
  end

This is the code I have tried and when I try to use the example code in the command line it generates a function handle error.

[Walter Roberson]

You create tfh as a function handle that expects x, t, and alpha as inputs, but when you call tfh you pass in only k+1

I would suggest

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

[Henry B.]

%main for InfConduct
ti=0;
tf=10;
N0=1;
nsteps = 5;
t = linspace(ti, tf, nsteps+ 1)
N = zeros(1,nsteps+1);
N(1) = N0;
alpha=0.1;
x=1;
[Theta] = InfConduct(x,t,alpha)

I tried it with this as my main and it generates a error saying x is undefined, but as we see its defined in my main and for some reason isnt being passed to the function .

[Walter Roberson]

%main for InfConduct
ti=0;
tf=10;
N0=1;
nsteps = 5;
t = linspace(ti, tf, nsteps+ 1)

t = 1×6

0 2 4 6 8 10

N = zeros(1,nsteps+1);
N(1) = N0;
alpha=0.1;
x=1;
[Theta] = InfConduct(x,t,alpha);

Theta = 1×2

0 0.1138

Theta = 1×3

0 0.1138 0.3774

Theta = 1×4

0 0.1138 0.3774 0.7387

Theta = 1×5

0 0.1138 0.3774 0.7387 1.1679

Theta = 1×6

0 0.1138 0.3774 0.7387 1.1679 1.6474

plot(t, Theta)

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

[Henry B.]

thank you so much its matching with inputs listed and match the erfc function values

[Torsten]

I wonder why you sum up the theta values.

A call to your function handle with t(i) already gives you the dimensionless temperature.

The fact that you get dimensionless temperatures that exceed the value of 1 show that your summation must be wrong.