A face based basis function solutions to thermal conduction problems for 3-D irregular shaped bodies using BEM

Abstract

Abstract Out of all the numerical methods available to solve the engineering problems using boundary element method, the basis functions which are used to define the unknown quantity in the mathematical formulation, are based on the combination of the shape functions as in a regular finite element procedure. Also, since the BEM is based on defining the source density functions, the kernels in the integral equations become singular, strongly singular and hyper singular for which the traditional BEM does not have a common solution procedure. In this paper, it is proposed to develop boundary element solutions for the thermal conduction problems, for 3-D irregular shaped bodies, using the indirect method i.e. by defining the source density functions. Thermal conduction problem is solved using the boundary integral equation formulation and boundary element solution method. The geometry of the body is divided into triangular patches using triangular patch modeling. A numerical solution is developed effectively by defining the basis functions on the face of the triangles generated in the triangular patch modeling, in contrast to defining it on the nodes as followed in the regular BEM solutions. The temperature distribution from the surface of the hot surface of the cube and sphere is plotted. Also the convergence study is conducted to get the solution convergence towards the exact solution for the case of a sphere and comparison of these two objects for thermal distribution is done.