A counterflow double pipe heat exchanger is used to cool the lubricating oil for a large industrial gas turbine engine. The flow rate of cooling water through the inner tube is m_c = 0.2 kg/s, while the flow rate of oil through the outer annulus is m_h = 0.4 kg/s. The oil and water enter at temperatures of 60°C and 30°C, respectively. The heat transfer coefficient in the annulus is calculated to be 8 W/m ? K. The inner diameter of the tube and the annulus are 25 and 45 mm, respectively. The outlet temperature of the oil is 40°C. Take c_p = 4,178 J/kg ? K for water and c_p = 2,006 J/kg ? K for oil.

a. Calculate the heat transfer coefficients in the inner tube.

b. Neglect the wall resistance and the curvature of the tube wall (assume a flat plate surface), and calculate the overall heat transfer coefficient assuming the water used is the city water with a fouling factor of 0.000176 m² ? K/W inside the tube. The oil side is clean.