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A heat exchanger consists of a bundle of steel tubes each of 25.4mm outside diameter and with a wall thickness of 3mm. Cooling water flows through the tubes with a Reynolds number of 10,000 and a mean temperature of 40'C. Scale deposited on the tube inner surface contributes a thermal resistance of 2 x 10

^{-4}m

^{2}KW

^{-1}. A process gas flows over the tubes, with a film heat transfer coefficient to the tube outer surface of 57Wm

^{-2}K

^{-1}. Using an appropriate correlation, determine the film heat tranfer coefficient from the water to the inside surface of the tubes, and thus determine the overall heat transfer coefficient.

Density of water = 992 kgm

^{-3}

Specific heat capacity of water at 40'C = 4810Jkg

^{-1}K

^{-1}

Thermal conductivity of water at 40'C= 0.632Wm

^{-1}K

^{-1}

Viscosity of water at 40'C = 6.51x10

^{-4}kgm

^{-1}s

^{-1}

Thermal conductivity of steel = 70Wm

^{-1}K

^{-1}

I have used Dittus-Boelter correlation because water is not viscous and used n=0.4 because the water is being heated.

I have found Prandtl number to be: Pr=4.31

I substituted into get: Nu=65.39

I then rearranged Nu = hD/k to find h: h=271171Wm

^{-2}K

^{-1}

From here I don't know how to find the overall heat transfer coefficient and I think I should have included the thermal resistance of the scale deposited on the inner surfaces of the walls.

would I use stanton number to find the heat tranfer coeffient?