Hedge's Ultimate Numerical Technique (HUNT) for Steady State Diffusion Problem

Abstract

A more realistic numerical technique hereafter known as Hegde's Ultimate Numerical Technique (HUNT) is developed and demonstrated on a one dimensional and a two dimensional steady state diffusion problem of heat transfer. The available numerical methods developed are based on finite difference technique neglecting the contribution of higher order terms in Taylor series expansion of the function leading to an approximation and the error in the solution. In the present effort of the HUNT, the optimization of the partial derivatives leads to the elimination of the error and justifies the stability and the convergence of the solution. The HUNT procedure based on the interface theory developed by the author, is capable of providing the ultimate optimum solution to all the partial derivatives considered as decision vectors. Even though the HUNT is demonstrated on one dimensional and two dimensional steady state diffusion equations, it does not require rigorous efforts to apply it to three dimensional problems of fluid flow and heat transfer. As pilot exercises the HUNT is demonstrated on a one dimensional circular fin and a two dimensional plate to obtain the temperature distribution. The result is compared with the analytical method and the finite volume method for which the results are available in the literature. To the knowledge of the authors, HUNT is both different and a unique example of its kind.