Chapter 6, Problem 6.10P

Experiments have been conducted to determine local heat transfer coefficients for flow perpendicular to a long, isothermal bar of rectangular cross section. The bar is of width c parallel to the flow, and height d normal to the flow. For Reynolds numbers in the range ${10}^4\le {\mathrm{Re}}_d\le 5\times {10}^4,$ the face-averaged Nusselt numbers are well correlated by an expression of the form
${\overline{Nu}}_d=\bar{h}d\text{/}k=C{R}_d^m{\mathrm{Pr}}^{1/3}$
The values of C and m for the front face, side faces, and back face of the rectangular rod are found to be the following:

Determine the value of the average heat transfer coefficient for the entire exposed surface (that is, averaged over all four faces) of a $c=40\text{-mm-}$ wide, $d=30\text{-mm-}$ tall rectangular rod. The rod is exposed to air in cross flow at $V=10\text{m/s,}{T}_{\infty }=300\text{K}\text{.}$ Provide a plausible explanation of the relative values of the face-averaged heat transfer coefficients on the front, side, and back faces.