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# Hot water passes through a copper tube, whose inner diameter is 20 mm, thickness is 3 mm, and length is 1 m.

Outside, cool air flows across the tube at T_inf = 290 K. The water flow rate is ṁ = .005 kg/s and the inlet and exit mean temperatures (or bulk temperatures) of the water flow are measured at T_m,i = 360 K and T_m,o = 330 K, respectively. Use the water properties at 345 K: c_p = 4.191 KJ/(kh*K) rho = 976.6 kg/m^3 µ = 3.89*10^-4 (N*s)/m^2 etc... Assume that the water flow within the tube is fully developed. (1) Determine the average overall heat transfer coefficient, U, with respect to the inner surface area of the tube. (2) Is the water flow laminar or turbulent? (3) If the flow rate is doubled, determine the new exit mean (bulk) temperature, T_m,o.

For the cylindrical pipe, the heat loss is given by:
= ∆ ( 2)
1
ln 2 = 401 = ( − ) = 0.005(4.191)(30) = 0.6287 26
)
20
=
= 1.041 10−4
2 (401)(1)
ln ( = − 0.6287 ∗ 1.0141 × 10−4 ≅ =...

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