Heat Transfer in Composite Materials

Seiichi Nomura, Dr. Eng. and A. Haji-Sheikh, Ph.D., The University of Texas at Arlington

978-1-60595-459-2, November 2017, 215 pages, 6×9, Hardcover book

• New methods for determining temperature distributions in heterogeneous media, including composite materials
• Offers unique tools to predict temperatures in steady-state and transient-state conditions
• Connects analytical solutions for temperature distribution with thermal stress analysis


This book provides analytical methods for predicting temperature distribution in isotropic and anisotropic composite media for both steady and transient states, with a focus on how temperature differences affect the properties of composite materials. In so doing, the text offers original equations for the behavior of heat conduction.

To begin, steady-state heat conduction in fiber-reinforced and particulate composites is described from a micromechanics point of view. Analytical solutions are furnished for steady-state and transient heat conduction in laminated composites, with a focus on the special equations for the transient conditions. Next, a theoretical overview is given of rapid energy transport in heterogeneous composites under a local thermal non-equilibrium condition. This is followed by a discussion of the effective thermal conductivity of unbounded composites using models such as those of Hashin/Shtrikman, Maxwell-Garnett effective medium theory, Mori-Tanaka, and self-consistent approximation. The final part investigates thermal stresses caused by a mismatch of the thermal expansion coefficients at the interface of matrix and fibers due to non-uniform temperature distribution. In this way, connections with engineering implications are drawn between thermal stress analysis and the unique methods and results for investigating heat conduction presented in the initial chapters of the book.

Preface

Chapter 1. Basic Equations for Heat Transfer
1.1. Fourier’s Law
1.2. Equation of Energy
1.3. Examples of Temperature Distribution in Homogeneous Materials
1.4. References

Chapter 2. Heat Conduction in Matrix-Inclusion/Fiber Composites
2.1. Introduction
2.2. Spherical/Cylindrical Inclusion Problems in an Unbounded Medium
2.3. Spheroidal Inclusion Problems in an Unbounded Medium
2.4. Circular Inclusion Problems in a Bounded Medium
2.5. References

Chapter 3. Steady State Heat Conduction in Multi-Layer Composite Materials
3.1. Introduction
3.2. Steady State Energy Equation
3.3. Non-Homogeneous Condition over y = 0 Surface
3.4. Non-Homogeneous Condition over x = a Surface
3.5. Volumetric Heat Source with Homogeneous Boundary Conditions
3.6. A Solution Technique using the Galerkin Method
3.7. Comments and Discussions
3.8. References
3.9. Appendix A: Orthogonality Conditions

Chapter 4. Transient Heat Conduction in Multi-Layer Composite Materials
4.1. Introduction
4.2. Mathematical Relations
4.3. Method of Computing the Eigenvalues
4.4. Governing Equations for Heat Conduction in Cylinders
4.5. Governing Equations for Heat Conduction in Spheres
4.6. Modified Galerkin Method
4.7. References

Chapter 5. Heat Conduction in Composites with Phase Delay
5.1. Introduction
5.2. Dual-Phase-Lag Energy Transport Relations
5.3. Temperature Solution in Finite Regular Bodies
5.4. Temperature Solution in Semi-Infinite Bodies
5.5. Plane Source in an Infinite Domain
5.6. References

Chapter 6. Effective Thermal Conductivities
6.1. Introduction
6.2. Rule of Mixtures Model
6.3. Maxwell’s Effective Medium Theory
6.4. Mori-Tanaka Model
6.5. Upper and Lower Bounds of Hashin and Shtrikman
6.6. Self-Consistent Model
6.7. References

Chapter 7. Thermal Stresses in Composites by Heat Flow
7.1. Introduction
7.2. Review of Thermal Stresses
7.3. Thermal Stress Field
7.4. Results
7.5. References

Index

978-1-60595-459-2, November 2017, 215 pages, 6×9, Hardcover book

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USD Price: $134.50

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