A pure aluminum bar has a diameter of 15 cm and a length of 1.25m. The rod is initially uniform in temperature at 300?C. The bar isnow suddenly exposed to a convection environment at 50?C with h =1250 W/m K. How long does it take the center to cool to atemperature of 80?C? (a) Determine if a lumped capacitance analysisis or is not appropriate. (b) Determine the cooling time assumingthe lumped capacitance model is valid. (c) Finally, determine thetime required for a point 0.5 cm from the surface to drop to275?C
