Heat transfer enhancement in a modified straight fin of rectangular profile with enlarged round base and correlated reduced round tip

Abstract

The present study addresses the potential heat transfer enhancement in a modified straight fin of rectangularprofile with an enlarged round base compensated by a reduced round tip when compared against the standardstraight fin of rectangular profile. The straight fins of rectangular profile share the profile area (volume) and aresubject to two controlling parameters: the transverse Biot number and the aspect ratio. In the common straightfin of rectangular profile, a small fraction of material approximately equal to two thirds of the semi-thicknesssquared is removed from the tip region and is attached to the base region. Thereby, the tenuous material migrationcreates the modified straight fin of rectangular profile with an enlarged round base and a reduced roundtip.Owing that the modified straight fin with round base and round tip possesses a pronounced irregular profilearea, the one-dimensional modeling with the simplistic quasi one-dimensional heat conduction equation is inappropriate.Switching to the two-dimensional modeling, the governing two-dimensional heat conductionequation in Cartesian coordinates cannot be solved analytically and forcibly has to be done numerically with thepotent finite element method. The two-dimensional temperature distributions and the companion heat transferrates are computed for the two distinct straight fins with rectangular profile using realistic combinations of thetransverse Biot number and the aspect ratio normally used in engineering practice. At the end, the maximumheat transfer enhancement granted by the modified straight fin with round base and round tip having small-tomoderateaspect ratios can reach a favorable 12% margin.