16 - Three-Dimensional Problems

Abstract

This chapter deals with the three-dimensional heat transfer problems. The axisymmetric problems are the types of three-dimensional problems. These problems are modeled and solved by using ring elements. The chapter presents the solution of axisymmetric problems using triangular ring elements and tetrahedron elements. The linear interpolation functions in terms of natural conditions are used for simplicity. The finite element solution of axisymmetric problem involves five steps. The first step is to replace the solid body of revolution by an assembly of triangular ring elements. The second step is to assume linear variation of temperature inside an element by using a natural coordinate system. Third step involves the derivation of element matrices and vectors. Once the element matrices and vectors are available, the overall or system equations are derived in the fourth step. Finally, the equations are solved after incorporation of the known boundary conditions. The chapter also presents a computer program called HEATAX for the solution of axisymmetric heat transfer problems.