Repeat Prob. 4–116 for the case where the aluminum block is inserted into the furnace on a low-conductivity material so that the heat transfer to or from the bottom surface of the block is negligible.

Data from problem 116

A 20-cm-long cylindrical aluminum block (ρ = 2702 kg/m³, c_p = 0.896 kJ/kg · K, k = 236 W/m · K, and α = 9.75 × 10^-5 m²/s), 15 cm in diameter, is initially at a uniform temperature of 20°C. The block is to be heated in a furnace at 1200°C until its center temperature rises to 300°C. If the heat transfer coefficient on all surfaces of the block is 80 W/m² · K, determine how long the block should be kept in the furnace. Also, determine the amount of heat transfer from the aluminum block if it is allowed to cool in the room until its temperature drops to 20°C throughout.