Analysis of a Parabolic Fin via Matrix Method

Abstract

Heat is not lost equally by each element of the fin but is lost mostly near the base of the fin. Thus there would be wastage of the material if a uniform fin is used. Due to this reason fins of varying cross-sections like hyperbolic fins or parabolic fins are constructed. The parabolic fin of varying cross-section is usually analyzed by ordinary calculus approach. The paper analyses parabolic fin of varying cross-section to find the rate of conduction of heat through it via the application of matrix method. The matrix method has been applied successfully in science and engineering problems and also comes out to be very effective tool to find the temperature distribution and rate of conduction of heat through a parabolic fin.