Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/804739
- Effective thermal properties of hollow-sphere structures: a finite element approach
- The University of Newcastle. Faculty of Engineering & Built Environment, School of Engineering
- Scientists and engineers in academia and industry have in recent years become very conversant with numerical techniques of analysis. These techniques are based on the approximate solution of an equation or a set of equations describing a physical problem. From a mathematical point of view, physical problems are described by differential equations or by integral expressions. Thus, the numerical approach seeks to determine the spatial distribution of one or more dependent variables such as temperature, concentration or displacement in a given domain. This chapter aims to give a fundamental introduction into the finite element method for heat conduction problems, i.e. how the method is derived, how elements are formulated and how they work. This theoretical part should impart the basic knowledge on the method which is required for a sensible application of numerical codes. For simplicity of notation, the method is derived for plane two-dimensional geometries. In contrast to simple onedimensional examples, the plane approach comprises many particularities which can be easily transferred to the general three-dimensional case. In the second part of the chapter, the finite element method will be applied to determine the effective thermal conductivity of hollow-sphere structures (HSS).
- Cellular and Porous Materials: Thermal Properties Simulation and Prediction p. 31-71
- Resource Type
- book chapter