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

[Kamuna]

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:

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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