Aluminum nanoparticles $($radius $=40{10}^{-9}m)$ are used in nanothermite to create highly reactive solid fuels. Show that the particle may be assumed to have uniform temperature during transient cooling and compute the time required to cool a particle from $600C$ to $50C$ assuming convection occurs with $20C$ air and with a heat transfer coefficient of $h=10\frac{W}{m^2}K.$

$($a$)$ Compute the characteristic length of the Al particle:

$($b$)$ Compute Bi of the Al particle:

$($c$)$ Solve for time for the particle to reach $50C.$