Transient conduction in an iron slab. In this problem, we will investigate the evolution

of the temperature distribution in a semi$-$infinite slab of iron $(>99\mathrm{.}99\%)$ when one face is

instantaneously elevated from $90$ to $900$K$.$

a numerical solution assuming the iron thermal conductivity varies with

temperature itself. Mathlab$/$mathematica code that solve this problem based on the infinite method $.$ Below is the gorver equation

T$[$i$,$ j$]=$ T$[$i$,$ j $-1]+\backslash$alpha $*$ dt

dx$2*($T$[$i $+1,$ j $-1]-2*$ T$[$i$,$ j $-1]+$ T$[$i $-1,$ j $-1])$

The data given in the following table are provided for your reference. We are particularly

interested in the temperature profiles at t $=5$ min and t $=50$ min.

Temperature $($K$)$ Thermal conductivity

$($W$/$cm K$)$

$901\mathrm{.}46$

$1501\mathrm{.}04$

$2000\mathrm{.}94$

$3000\mathrm{.}803$

$4000\mathrm{.}694$

$6000\mathrm{.}547$

$8000\mathrm{.}433$

$9000\mathrm{.}38$