B. A large flat sheet of plate glass is cooled from 400 to 350 K by dropping it in a large vat of water at 298 K with hwater= 138.7 W/m2-K (you may look up kglass@ 300K)

F. A hot pancake at 330 K is flipped in the air at 298 K with hair= 27.4 W/m2-K You may treat the pancake as cooked cake batter – and look up k at 300 K (it’s in our appendix!). You should treat the pancake as a flat disc (i.e. a slab geometry, not a cylinder). Lc = 0.1 * 0.121 W/m-K / 27.4 W/m2-K. The temperature of the air is unimportant here. Lc = 0.000442 m The maximum thickness of a pancake to allow lumped capacitance to be valid is 2 * Lc = 0.00088 m (less than 1 mm) G. A donut hole (spherically-shaped cooked cake batter) comes out of the fryer at 400 K and is cooled by air at 298 K with hair= 27.4 W/m2-K. Lc = 0.1 * 0.121 W/m-K / 27.4 W/m2-K. The temperature of the air is unimportant here. Lc = 0.000442 m The maximum radius of a donut hole to allow lumped capacitance to be valid is 3 * Lc = 0.00132 m Max diameter = 0.00265 (2.65 mm) H. A donut hole (spherically-shaped cooked cake batter) comes out of the fryer at 400 K and is cooled by air using a fan at 298 K with hair= 88.5 W/m2-K. Lc = 0.1 * 0.121 W/m-K / 88.5 W/m2-K. The temperature of the air is unimportant here. Lc = 0.000137 m The maximum radius of a donut hole to allow lumped capacitance to be valid is 3 * Lc = 0.00410 m Max diameter = 0.00082 (0.82 mm) The fan cools faster, but reduces the thermal resistance due to convection so the max diameter is smaller.

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