Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Vectors and Tensors
- 3 Kinematics of a Continuum
- 4 Stress Vector and Stress Tensor
- 5 Conservation of Mass, Momentum, and Energy
- 6 Constitutive Equations
- 7 Applications in Heat Transfer, Fluid Mechanics, and Solid Mechanics
- Answers to Selected Problems
- References and Additional Readings
- Subject Index
7 - Applications in Heat Transfer, Fluid Mechanics, and Solid Mechanics
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Vectors and Tensors
- 3 Kinematics of a Continuum
- 4 Stress Vector and Stress Tensor
- 5 Conservation of Mass, Momentum, and Energy
- 6 Constitutive Equations
- 7 Applications in Heat Transfer, Fluid Mechanics, and Solid Mechanics
- Answers to Selected Problems
- References and Additional Readings
- Subject Index
Summary
It is really quite amazing by what margins competent but conservative scientists and engineers can miss the mark, when they start with the preconceived idea that what they are investigating is impossible. When this happens, the most wellinformed men become blinded by their prejudices and are unable to see what lies directly ahead of them.
Arthur C. ClarkeIntroduction
This chapter is dedicated to the application of the conservation principles to the solution of some simple problems of solid mechanics, fluid mechanics, and heat transfer. In the solid mechanics applications, we assume that stresses and strains are small so that linear strain-displacement relations and Hooke's law are valid, and we use appropriate governing equations derived in the previous chapters. In fluid mechanics applications, finding exact solutions of the Navier–Stokes equations is an impossible task. The principal reason is the nonlinearity of the equations, and consequently, the principle of superposition is not valid. We shall find exact solutions for certain flow problems for which the convective terms (i.e., v · ∇v) vanish and problems become linear. Of course, even for linear problems flow geometry must be simple to be able to determine the exact solution. The solution of problems of heat transfer in solid bodies is largely an exercise of solving Poisson's equation in one, two, and three dimensions.
- Type
- Chapter
- Information
- Principles of Continuum MechanicsA Study of Conservation Principles with Applications, pp. 162 - 214Publisher: Cambridge University PressPrint publication year: 2010