Water passes through a D =2 mm pipe that is 10 m long. The water has a mass flow

Question

Water passes through a D =2 mm pipe that is 10 m long. The water has a mass flow rate of 0.02 Kg/s. The surface of the pipe is set to a to -be -determined constant temperature. When the water enters the pipe it is fully developed both hydrodynamically and thermally. It is desired that at the outlet of the pipe, the mean temperature be equal to T m, o = 325 K, and that the pipe provide 350 W of heat to the fluid. For this to occur, what should the mean inlet temperature T m,i of the pipe be, and what should the log mean temperature difference delta T lm be? The water has the following properties: Cp = 4,178 J/KgK, ,mu = 695 x 10^-6 Ns/m^2, Pr = 4.62, and k = 606 x 10^-3 W/mK (Exam question).

Explanation / Answer

We know that

Q=mc*(Delta T)

m=0.02 kg/s

Cp=4.178 kj/kgK

Q=300 W

So Putting these value in equation,

300=0.02*4185*(325-T)

3.58=325-T

T=328.58 K (mean inlet temperature)

LMTD= 328.58-325/ln(328.58/325)=33.78 degree C

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