Consider a packed bed of spheres, each of diameter \(D=2 \mathrm{~mm}\), at an initial temperature of \(T_{i}=90^{\circ} \mathrm{C}\). Cold water at \(T_{w}=5^{\circ} \mathrm{C}\) is poured onto the bed at \(t=0\), producing a large convection coefficient about each sphere. Determine the rate (in \({ }^{\circ} \mathrm{C} / \mathrm{s}\) ) at which an individual sphere near the top surface of the bed is cooled at \(t=0.1,0.25\), and \(1 \mathrm{~s}\). The spheres have thermophysical properties similar to Pyrex.