A long iron rod (r 5 7870 kg/m3, cp 5 447 J/kg·K, k 5 80.2 W/m·K, and a 5 23.1 3 10–6 m2/s) with diameter of 25 mm is initially heated to a uniform temperature of 700°C. The iron rod is then quenched in a large water bath that is maintained at constant temperature of 50°C and convection heat transfer coefficient of 128 W/m2·K. Determine the time required for the iron rod surface temperature to cool to 200°C. Solve this problem using analytical one-term approximation method (not the Heisler charts).