Chapter 3, Problem 3.137P

Circular copper rods of diameter $D=1\text{mm}$ and length $L=25\text{mm}$ are used to enhance heat transfer from a surface that is maintained at $T_{s,1}=100°\text{C}\text{.}$ One end of the rod is attached to this surface (at $x=0.)$ while the other end $\left(x=25\text{mm}\right)$ is joined to a second surface, which is maintained at $T_{s,2}=0°\text{C}\text{.}$ Air flowing between the surfaces (and over the rods) is also at a temperature of $T_{\infty }=0°\text{C,}$ and a convection coefficient of $h=100{\text{W/m}}^{\text{2}}\cdot \text{K}$ is maintained.

(a) What is the rate of heat transfer by convection from a single copper rod to the air?
(b) What is the total rate of heat transfer from a $1\text{m}\times 1\text{m}$ section of the surface at $100°\text{C,}$ if a bundle of the rods is installed on 4-mm centers?