SIMPLIFIED FORMULAS FOR SOME BESSEL FUNCTIONS AND THEIR APPLICATIONS IN EXTENDED SURFACE HEAT TRANSFER

Abstract

Bessel functions find many applications in Physics and Engineering fields. Some of these applications are in the analysis of extended surface heat transfer where the cross-sections vary. Tables of various kinds of Bessel functions are available in most handbooks of mathematics. However, the use of tables is not always convenient, particularly for applications where many values must be computed. In the applications of Bessel functions in extended surface heat transfer, graphs are also available to provide quick evaluations of the values needed. However, reading these graphs always needs interpolation; this will be cumbersome and time-consuming if there are many readings to be taken. Mathematical formulas for Bessel functions are available but they are usually complicated. Software to calculate values of Bessel functions is also available. Excel, Maple, and Mathematica can also be used to compute the values of Bessel functions. A user can write a program for an application that involves Bessel functions. However, the use of Bessel functions in Excel is limited while Maple and Mathematica are expensive commercial software. In this paper, formulas for Bessel functions of (Formula Presented) and (Formula Presented) are simplified with adequate accuracy that can be used to easily compute values needed in the extended surface heat transfer analysis. It is found that errors for (Formula Presented) and (Formula Presented) are relatively small (maximum errors are 0.004% and 0.003%, respectively) in the range of 0.05 to 3.75 while the maximum error for (Formula Presented) is 3.678% for the same range. However, the maximum error for (Formula Presented) is reduced to 0.166 if the range is from 0.25 to 3.75.