One dimensional steady state diffusion
Consider the problem of source-free heat conduction in an insulated rod whose ends are
maintained at constant temperatures of 100°C and 500°C, respectively. The one-
dimensional equation problem shown in the figure below is governed by
$\frac{d}{dx}(k\frac{dT}{dx}) = 0$
1-Divide the length of the rod into five equal control volumes, discretise the equation, write
it in the form:
$a_pT_P = a_wT_w + a_eT_e + S_u$
and give the expressions for the coefficients $a_p$, $a_w$, $a_e$ and $S_u$.
2- Write the set of algebraic equations in a matric form.
