A steel cube, \(2.0 \mathrm{~cm}\) on a side, is initially at a temperature of \(300^{\circ} \mathrm{C}\). The cube is dropped into a cooling bath \(\left(T_{\infty}=25^{\circ} \mathrm{C}, h=100 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\right)\) to reduce its temperature so that it can be handled.

\[k=16 \mathrm{~W} / \mathrm{m} \mathrm{K} \quad ho C_{p}=3.636 \times 10^{6} \mathrm{~J} / \mathrm{m}^{3} \mathrm{~K}\]

a. What is the temperature of the cube after it has been in the bath for \(5 \mathrm{~min}\).?

b. How much heat has the cube lost by that time?

c. What is the heat flux from the surface of the cube at that time?

d. For the conditions specified in this problem, what is the maximum stainless-steel cube size that can be analyzed by lumped capacitance?