Water with a flow rate of 5200 Kg/min is flowing inside the tubes of a cross flow heat exchanger. Water makes one pass through the tubes and its inlet temperature is 20°C. Combustion gas at 450°C flowing at a rate of 2500 Kg/min outside the tubes. Tube inside and outside diameters are D_i = 20 mm and D_o =25 mm and its length is 2m. Tube bank has 2500 tubes. Use the following properties:

Water properties at an assumed average mean temperature: ρ = 987 Kg/m³, C_p = 4182 J/(KgK), μ = 5.28 x 10^-4 Ns/m², k= 0.645 W/(mK), P_r = 3.42.

Combustion Gas properties at an assumed average film temperature: ρ = 0.696 Kg/m³, C_p =1030 J/(KgK), v = 3.88x10^-5 m²/s, k = 0.041 W/(mK), Pr = 0.7.

a. If tubes are made of steel with k=70 W/(mK), h_i = 850 W/(m²K)-and an outlet temperature of 65°C is desired for water, using NTU-Effectiveness method calculate the overall heat transfer coefficient U. and then calculate the outside heat transfer coefficient h_o.

b. What is the average heat flux based on inside area of the tubes? What is the average temperature gradient in the water on the inside surface of a tube?