4-41 A steel cylinder 10 cm in diameter and 10 cm long is initially at 300°C. It is suddenly immersed in an oil bath that is maintained at 40°C, with h = 280 W/m2 .°C. Find (a) the temperature at the center of the solid after 2 min and (b) the temperature at the center of one of the regular faces after 2 min.

A metallic sphere of radius R is heated in an oven to a temperature of 600 ° F throughout, and then removed from the oven and allowed to cool in ambient air to T∞ = 75 ° F, by convection and radiation (see attached figure). The thermal conductivity of the ball material is known to vary linearly with temperature. Assuming that the ball is uniformly cooled starting from the entire outer surface, obtain the differential equation that describes the change in temperature in the sphere during cooling. Note: In the image, the translation would be: metallic sphere

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