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COMBINED CONDUCTION CONVECTION ON CYLINDRICAL WALLS AND MULTIPLE CYLINDRICAL WALLS( HEAT TRANSFER)

COMBINED CONDUCTION CONVECTION ON CYLINDRICAL WALLS AND MULTIPLE CYLINDRICAL WALLS( HEAT TRANSFER)

COMBINED CONDUCTION CONVECTION ON CYLINDRICAL WALLS AND MULTIPLE CYLINDRICAL WALLS( HEAT TRANSFER)

(OP)
Hello, I am an engineering student struggling on heat transfer. So our professor gave us an activity about the topic. My question is that what is the general formula in finding the heat transfer/loss in a cylindrical wall? For reference, here is our question:

A hot-water pipe (k = 60 W/m K) in a house, made of 3/4-inch schedule 40 pipe (OD = 26.7 mm; thickness = 2.87 mm) is 15 meters long and contains water at 50 C. The air around the pipe is at 24 C. The heat transfer coefficient inside and outside the pipe are 1,135 W/m2 K and 17 W/m2 K, respectively. Insulation with thermal conductivity of 20 W/m K is to be added to the pipe. Determine the percent reduction of heat loss from the pipe due to insulation of 130 mm thick.

I was struggling because our professor gave us different formulas so which of these three is the exact formula ? Thanks in advance

Q = Ai (Ti – To)
(1/fi + ri (ln ro/ri) + (ri/ro)(1/fo)


and
Q = A2 (T1 – T4)
(r1/r4) (1/fh) + r1 (ln r2/r1) + r1 (ln r3/r2) + r1 (ln r4/r3) + (1/fc)
kA kB kC

Q = A1 (T1 – T4)
1/fh + r1 (ln r2/r1) + r1 (ln r3/r2) + r1 (ln r4/r3) + (r1/r4) (1/fc)
kA kB kC

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