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In a straight tube of 60 mm diameter, water is flowing at a velocity of 12 m/s.

The tube surface temperature is maintained at 70℃ and the flowing water is heated from the inlet 15℃ to an outlet temperature of 45℃. Calculate the following.

(i)The heat transfer coefficient from the tube surface of the water

(ii)The heat transfer and

(iii)The length of the tube. Take the physical properties of water at its mean bulk temperature of 30℃.ρ=995.7 Kg/m3 ,Cp=(4.174KJ)/Kgk,k=61.718×10(2) W/mK,v=0.805×10(6) m2s,Pr=5.42

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Let us first determine the type of flow

Re=UDv=(12×0.06)(0.805×10(6))=8.94×105

Since Re > 8.94×105, the flow is turbulent

Nu=0.023 Re.8 Pr(1/3)

Nu=hDk=0.023×(8.94×105).8× 5.42(1/3)=2330.58

h=2330.58×61.718P0.06=23.973×$103$ W(m2K) h=23973 W(m2K) Heat Transfer, Q=mCP(ToutTin)=UρACP(ToutTin)

=12×995.7×π4×0.062×4174(45-15)

Q=4.2303×106 W

We know that

Q=hA∆T

=h×π×D×L×(TsTmean)

4.2303×106=23973×π×0.06×L×(70-30)

L=23meter

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