A metal pot holding boiling water has a handle made of an uninsulated hollow, stainless steel tube (k = 20 W/m K) with inner and outer diameters of 1.6 cm and 2.0 cm, respectively, and is 25 cm long. The ambient temperature is 22°C, and the convective heat transfer coefficient is h = 10 W/m² K.

(a) If the maximum safe temperature is 50°C, at what distance from the pot can we safely grab the handle with bare hands? (b)

Repeat your calculations in

(a) if the handle is made of an un-insulated solid cylinder of the same material and outside diameter and length as the hollow handle.

(c) Repeat the calculations in

(b) if the solid handle is covered with a 2-mm-thick layer of an insulating material with k = 0.02 W/m K. For all three cases, assume steady-state conditions.