This booklet is a continuation of the ‘How & Why…’ set of booklets published by NAFEMS, designed to guide both new and experienced analysts in a range of problem types. The booklets are written to introduce various analysis methodologies to both engineering managers and engineers in a straightforward and informed manner.

It has been assumed, however, that the principle users’ of this booklet will have at least one year’s experience of using the Finite Element project in heat transfer. However, a structural engineering background is not essential to understand the booklet. It is only assumed that the reader understands a little basic Finite Element jargon, including the terms such as node, element etc. If required this information can be obtained from other NAFEMS publications in this series such as ‘How to Understand Finite Element Jargon’.

The text begins by defining three modes of heat transfer viz. conduction, convection and radiation and then introduces the objectives of undertaking a thermal analysis. Some real life examples, which require temperature calculations, have been highlighted. The introduction concludes with a simple flow chart to classify linear, non-linear, steady-state and transient problems.

The second chapter describes the mathematics of the Finite Element method in layman’s language. The chapter provides an insight of the physics of heat conduction with the associated technical jargon such as internal heat generation, boundary value problem, boundary conditions and material properties. The Finite Element formulation has been detailed for a simple steady-state heat conduction problem. Governing equations, material property requirements/characteristics together with prescription of all relevant boundary conditions have been explained for different types of thermal problems and tabulated at the end of the chapter for quick reference. Schemes for time stepping methods and solution strategies for non-linear problems have been introduced with minimal mathematical rigour.

Contents

Introduction

Finite Element Formulation for Heat Transfer

Finite Element Formulation

• Classification of Heat Conduction Problems
• Linear Steady State Analysis
• Linear Transient Analysis
• Non-Linear Steady State Analysis
• Non-Linear Transient Analysis

Steps Involved in Undertaking a Thermal Analysis

• Geometry
• Material properties
• Mesh Generation
• Loading and Boundary Conditions
• Selection of parameters Specific to Numerical Computation

A Case Study

Other Analysis Schemes

• Finite Difference Schemes
• Boundary Element Method

Nomenclature and Units

Glossary

References

Appendix 1: Analogy between Elasticity and Thermal Analysis