A cylindrical bar of Fe $(1cm$ diameter$)$ is suspended in a small well$-$stirred manganese bath maintained at

$1300C.$ Assuming that local equilibrium is reached at the solid$-$liquid interface, calculate the time required

to increase the composition. of manganese at $1\%$ in the center of the bar. The inter$-$diffusion coefficient

of manganese in $Fe$ is given by:

$D=0\mathrm{.}49$exp$(-\frac{33200}{T})$