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 $900K.$

Prepare two solutions:

$(1)$ An analytical solution assuming constant thermal conductivity $(k$ at $90K).$

$(2)$ a numerical solution assuming the iron thermal conductivity varies with

temperature itself.

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.