I suggest to consider the plot of the gradient of temperature that is a vector field

@ Mohammad Amir Ghasemian Moghaddam

If you have the analytical solution of T(x), then derive it w.r.t (x) and multiply it by (k, thermal conductivity) you will get the heat flux, q(x), then plot it with 'Grapher 9' software. But, if you don't have the analytical solution of T(x) and you have only the numerical solution of T(i) which is shown in the figure above, then this is another case and needs simple FORTRAN code using either Forward, Backward or Central difference techniques (with delta x) All of these techniques need an output file of your numerical results of T(i) and you have to save this file as data file then open it with FORTRAN code . You have to specify your question to get accurate answer. thank you.

@Mishaal A Abdulkareem

Thanks for your help, I have the numerical solution of T(i) (in a .txt file), Is there any paper or website or any books you could recommend so I could learn how to write the code you are mentioning?

(I solved the problem with a C code with Finite Difference method and this is how I got the numerical results of temperature)

In your 2D case, I suggest to write the numerical solution in a 2D array T(1:n,1:m) and load it in Matlab where you can easily do the vector plot of the computed gradient

@ Mohammad Amir Ghasemian Moghaddam

1- Change your file extension from .txt to .dat in order to be compatible with FORTRAN code.

2- Write the value of dx with units (1D)

3- Write the value of k, (thermal conductivity with units)

4- Attach your .dat file and I will code it for you (using FORTRAN 77) and selecting the central difference scheme for its accuracy

5- Don't forget to recommend all my answers to this discussion.

The heat flux is normal to isotherm. At each points, trace a perpendicular and you see the heat flux.