### Enhancement of Algorithm and Investigation of Heat Transfer Through Fins

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#### Abstract

Finite Element Method (FEM) and Differential Quadrature Method (DQM) are two very important numerical solution techniques to solve engineering and physical science problems. Usually elements are sub-divided uniformly in FEM (Conventional FEM, CFEM) to obtain temperature distribution behavior in a fin or plate. Hence, extra computational complexity is needed to obtain a fair solution with required accuracy. In this paper, non-uniform sub-elements are considered to enhance the CFEM algorithm to reduce the computational complexity. The proposed algorithm is known as Efficient FEM (EFEM).This EFEM is applied for the solution of one-dimensional heat transfer problem in convection-tip thin rectangular fin. Exact solutions are also obtained for comparison purpose. The obtained results are compared with CFEM and Efficient DQM (EDQM), with non-uniform mesh generation. It is found that the EFEM exhibits more accurate results than CFEM, EDQM and agrees with exact solution showing its potentiality *Copyright © 2013 Praise Worthy Prize - All rights reserved.*

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