To protect a piece of iron $(Fe)$ material from oxidation,

a layer of chromium $(Cr)$ is coated, as shown in the diagram.

Suppose the oxidation follows Wagner's parabolic model, and

the oxidation rate constant $(K)$ for $Cr$ and $Fe$ is respectively

$2\mathrm{.}5{10}^{-8}c\frac{m^2}{sec}$ and $2{10}^{-6}c\frac{m^2}{sec}.$ It is assumed that $($i$)$ the

oxidation rate constant of iron under chromium oxide coating remains the same as when it is

in direct contact with air, and $($ii$)$ coating of $Cr$ will be oxidized $($sacrificed$)$ completely first

before the $Fe$ metal underneath undergoes oxidation to form its own oxide layer. Determine

the minimum thickness of $Cr$ coating needed to protect $Fe$ for $5$ years $(365$ days per year$),$ with

a maximum allowable thickness of $Fe$ oxidation of $2cm.$