Consider a plate of thickness 1 in, a long cylinder of diameter 1 in, and a sphere of diam...

Consider a plate of thickness 1 in, a long cylinder of diameter 1 in, and a sphere of diameter 1 in. all initially at 400°F and all made of bronze (k = 15.0 Btu/h·ft·°F and α = 0.333 ft2 /h). Now all three of these geometries are exposed to cool air at 75°F on all of their surfaces, with a heat transfer coefficient of 7 Btu/h·ft2 ·°F. Determine the center temperature of each geometry after 10 and 20 min. Explain why the center temperature of the sphere is always the lowest.