A solid shaft for a power generator is produced from aluminum plus $1\%$ copper alloy.

The shaft makes one revolution per minute during operation with applied load of

$125001$b$.$ The design requirements calls for continuous safe operation for one$-$year

under the fatigue loading. Based on above imposed conditions, the length of this shaft

should be $96$ in long and with $4\mathrm{.}39$ in $,$ in diameter. In order to avoid the premature

fatigue failure it is required to manufacture this shaft with uniform structure. Based on

this we need to maintained the plane front casting during the processing of the shaft. As

a casting engineer suppose you can maintained $360\frac{C}{c}m$ temperature gradient $(G_L)$

during casting for your heat flow in liquid. Calculate the required growth rate moving

this shaft through the fumace in order to maintain plane front and avoid dendritic

growth.

$K=0\mathrm{.}1,m_L=4,CO=0\mathrm{.}01$CaI,$D_L=3{10}^{-6}$