Absolute maximum heat transfer rendered by straight fins with quarter circle profile using Finite Element Analysis

• Straight fins with quarter circle profile are analyzed.
• The Biot number is the controlling parameter.
• The 2-D heat conduction equation is solved with Finite Element Analysis.
• Absolute and relative maximum heat transfer are compared.

The aim of this paper is to assess succinctly the maximum heat transfer attributes of straight optimal fins with quarter circle profile proposed by Isachenko et al. in terms of three describable parameters. There are two thermal parameters: the thermal conductivity k   and the mean convection coefficient h‾, and one geometric parameter: the semi-thickness at the base R being equal to the length R. The peculiarity of this fin is its unitary slenderness ratio S (length R  ÷÷ semi-thickness at the base R), which contrasts markedly with all standard straight fins where the length L is always much larger than the thickness δ. Through an intuitive approach, Isachenko et al. called the straight fin with a quarter circle profile fin as the optimal straight fin capable of transferring maximum heat. In order to verify this premise qualitatively, detailed mean temperature distributions were obtained solving numerically the governing two-dimensional heat conduction equation in Cartesian coordinates with Finite Element Analysis. This was done within the spectrum of representative values of the radius-based Biot number, Bi. Additionally, a comparison was carried out between the maximum heat transfer produced by the straight fin with quarter circle conceived by Isachenko et al. and the longitudinal fin of concave parabolic profile envisaged by Schmidt to decide which of the two fin profiles renders absolute maximum heat transfer or relative maximum heat transfer.