[Amirhossein mokhtari]

If the heat generation varies linearly with position. How can i discretize that?
Problem is 1D mixed of convection and conduction.

[Rami]

Originally Posted by Amirhossein mokhtari

If the heat generation varies linearly with position. How can i discretize that?
Problem is 1D mixed of convection and conduction.

Hi Amirhossein mokhtari,

It is quite simple with the FEM. See e.g., my paper

R. Ben-Zvi, H. Scher and B. Berkowitz, Two-dimensional finite element method solution of a class of integro-differential equations: Application to non-Fickian transport in disordered media, IJNME, Vol. 112 No. 5, pp. 459-478, 2017, DOI: 10.1002/nme.5524, 2017.

in which you may drop the transient and the memory terms and insert S=Axi + B.

I hope it helps,
Rami

[lejonetfrannorden]

Hello Amirhossein,

I think you can use a linear equation, e.g. q = Ax + B where A and B are coefficients and x is the distance from your reference point.

One way of discretization that came to my mind first is setting a do or for loop starting at your reference point and then incrementing.
Assign q = B at x=0 assuming 0 is your reference position and B is the heat generation at that point. Then, since you know your final length (xmax) for nmax stepsizes you would have dx = xmax/nmax. Then it is, q = q + A*dx for all the remaining stepsizes.

Regards,
Lejonet