In a double pipe exchange (23 × 2 mm), the cold fluid (cₚ = 1 /( · K), flow rate 500 /ℎ) passes through the pipe and the hot fluid goes through the annular. The inlet and outlet temperatures of cold fluid are 20° and 80°, and the inlet and outlet temperatures of hot fluid are 150° and 90°, respectively. The ℎᵢ (heat transfer coefficient inside a pipe) is 700 W/(m² · °) and overall heat transfer coefficient ₀ (based on the outside surface of pipe) is 300 W/(m² · °), respectively. If the heat loss is ignored and the conductivity of pipe wall (steel) is taken as 45 W/(m · °), find:
(1) Heat transfer coefficient outside the pipe ℎ₀.
(2) The pipe length required for counter flow, in m.
(3) What is the pipe length required if the heating medium changes to saturated vapor (140°) which condenses to saturated liquid and other conditions keep unchanged?
(4) When the exchanger is used for a year, it is found that it cannot meet the need of production (the outlet temperature of cold fluid cannot reach 80° ), explain why.