Numerical Analysis For Rate Of Heat Transfer And Optimal Dimensions Of A Circular Fin With Hyperbolic Profiles

摘要

The present article deals a solution to the problem of circular fin with hyperbolic profile numerically using a C programme. A fin with this type of geometry resembles the optimal circular fin of convex parabolic profile, which delivers the maximum heat transfer for a given volume of material. The circular fin of hyperbolic profile is governed by a two-term differential equation of second order with one variable coefficient which, via a transformation can be converted into a Bessel equation. Unlike adopting the conventional Bessel’s functions, the present paper discusses an easy alternative to solve the problem by using finite difference techniques for a preliminary solution which is further refined using numerical programming in C. In this method as the interval size is decreased, the solution to the problem approaches towards that of exact method. Finally a test problem is discussed to check the validity of present formulation. Temperature distribution and heat transfer rates are compared with earlier exact methods and experimental results on graphs which confirm the correctness of present formulation. Another important out come of this article is, running the programme for various values of input parameters an optimum dimension of the fin for maximum heat transfer can be decided.