What is Biot number?

For a solid of size $L$ exchanging with a fluid, the Biot number

compares the two. If $\mathrm{Bi} \ll 1$ the solid is uniform in temperature at every instant and cools as a whole, exponentially with the time constant $\tau = \rho c V/hS$; if $\mathrm{Bi} \gg 1$ the surface is at the fluid temperature and the interior conducts at its own pace $L^2/a$.