A long cylinder of 30-mm diameter, initially at a uniform temperature of 1000 K, is suddenly quenched in a large, constant-temperature oil bath at 350 K. The cylinder properties are k = 1.7 W/m · K, c = 1600 J/kg · K, and ρ = 400 kg/m3, while the convection coefficient is 50 W/m2 · K.
(a) Calculate the time required for the surface of the cylinder to reach 500 K.
(b) Compute and plot the surface temperature history for 0 ≤ t ≤ 300 s. If the oil were agitated, providing a convection coefficient of 250 W/m2 · K, how would the temperature history change?