Leiden frost effect a water drop that is slung onto a skillet with a temperature between 100oC and about 200oC will last about 1 s. However, if the skillet is much hotter, the drop can last several minutes, an effect named after an early investigator. The longer life time is due to the support of a thin layer of air and water vapor that separates the drop from the metal (by distance L in Fig. Let L = 0.100mm, and as same that the drop is flat with height h = 1.50 mm and bottom face area A = 4.00 x 10-6 m2. Also assume that the skillet has a constant temperature Ts = 300"C and the drop has a temperature of l00oC. Water has density p = 1000 kg/m3 and the supporting layer has thermal conductivity k - 0.026 W/m ∙ K.
(a) At what rate is energy conducted from the skillet to the drop through the drop's bottom surface?
(b) If conduction is the primary way energy moves from the skillet to the drop, how long will the drop last?