A steel ball of 20 mm diameter (k = 60 W/m·ºC, α = 177×10-6 m2/s, rho = 7854 kg/m3) is dropped in a large tank of water. The sphere ball is initially isothermal at 360 K and drops until the center temperature is 320 K, and the temperature of the water is 280 K. The sphere ball may be assumed to quickly reach the terminal velocity of 1.3 m/s in the water. Determine the height of the water tank required to cool the sphere ball to 320 K. Use analytical one-term approximation method for the conduction heat transfer.