So$,$ you could solve the egg example with just charts.

Try this one with very high $h.$

An ordinary egg can be approximated as a $5-$cm$-$diameter sphere $($Fig$.18-20).$ The egg is initially at a uniform temperature of $5C$ and is dropped into boiling water at $95C.$ Taking the convection heat transfer coefficient to be $h={10}^{10}W{m}^{-2}{K}^{-1}$ determine how long it will take for the center of the egg to reach $94$ degree $C.$

$k=0\mathrm{.}627W{m}^{-1}{k}^{-1}$

$=0\mathrm{.}151{10}^{-6}{m}^2{s}^{-1}$

$=\frac{t}{r_o^2}$

$11$