Prediction of the Heat Rejection from Uniform Annular Fins by the Finite-Difference Method with a Reduced System of Algebraic Equations

An ordinary differential equation of second order with variable coefficients, called the modified Bessel equation of zero order, governs the radial temperature variation along annular fins of uniform thickness and constant properties. This educational paper addresses a simplistic finite-difference procedure for solving this kind of Bessel equation relying on a reduced system of algebraic equations. Approximate temperature distributions and heat transfer rates have been obtained by hand and also with a symbolic algebra software, such as Maple V or Mathematica on a personal computer. Students of heat transfer courses may benefit from this alternative computational procedure that seeks to circumvent the use and operations with Bessel functions and still produce numerical results of good quality. Rudimentary knowledge of numerical techniques is the only mathematical background that students need to have in order to implement the computational scheme.