Chapter 11, Problem 11.8P

Thin-walled aluminum tubes of diameter D = 10mmare used in the condenser of an air conditioner. Undernormal operating conditions, a convection coefficientof $h_i=5000{\text{ W/m}}^2\cdot \text{K}$ is associated with condensationon the inner surface of the tubes, while a coefficient of $h_o=100{\text{ W/m}}^2\cdot \text{K}$ is maintained by airflow over thetubes.
(a) What is the overall heat transfer coefficient if thetubes are unfinned?
What is the overall heat transfer coefficientbased on the inner surface, $U_i$ , if aluminum annular fins of thickness t = 1.5 mm, outer diameter $D_o=20$ mm, and pitch S = 3.5 mm are addedto the outer surface? Base your calculations on a 1-m-long section of tube. Subject to the requirements that $t\ge 1$ mm and $\left(S-t\right)\ge 1.5$ mm, explore the effect of variations in t and Son $U_i$ . What combination of t and S would yield the best heattransfer performance?