Heat Transfer: Question $4$

Hot water at $85C$ is being transported through a thin brass pipe of outer diameter of

$\frac{W}{m}K.$ The water pipe is placed inside a room where $T_{}=22C.$ Cold water at lower temperature

is required at the end of the pipe which signifies that more heat loss should occur from the pipe

surface.

For this purpose, an Engineer proposes to place $0\mathrm{.}8mm$ thick straight circular fins $($circular fins of

rectangular profile$)$ over the pipe to improve heat lost. The proposed fins are $8cm$ in diameter and

are spaced $2cm$ apart. Earlier, the Engineer has determined that convective heat transfer coefficient

will equal $20\frac{W}{m^2}.K$ on the pipe and $15\frac{W}{m^2}.K$ on the fins, when they have been added.

The employer has asked the Engineer to compute the heat loss per meter of pipe before and after

the fins are added so that he can approve the design. Please help the engineer to accurately calculate

heat lost from pipe with and without fins, and recommend to the employer if he should approve

the proposed design. Please note that heat lost must be increased to at least $2$ times more with fins

compared to that without fins in order to get necessary approvals. $($step by step solution$)$