Water must be heated from 15 to 50°C in a simple double-pipe heat exchanger at a rate of 3,500 kg/h. The water is flowing inside the inner tube with steam condensing at 110°C on the outside. The tube wall is so thin that the wall resistance may be neglected. Assume that the steam-film coefficient h_∘ is 11 kW/m²·°C. What is the length of the shortest heat exchanger that will heat the water to the desired temperature? Average properties of water are as follows: 

ρ = 993 kg/m³         k = 0.61 W/m·°C       μ = 0.78 cP         c_p = 4.19 J/g ·°C