ABSTRACT
There are so many fruitful applications of tensor calculus. Even this is only a brief introduction to some of the most basic equations of engineering and physics. To model reality accurately, it may be necessary to account for more effects by adding more terms to the equations herein, making the equations more complex and coupled together. Moreover, there is a vast literature developing analytical and numerical techniques for solving these equations. A gradient in the temperature field of a solid or fluid at rest will result in the transfer of heat energy by conduction. A general boundary condition is to prescribe the heat transferred from the surface of a conductor to an adjacent medium such as a fluid. The heat transfer coefficient depends upon the surface geometry, properties of the adjacent medium, flow of adjacent fluid, and so on. The linear field equations for an isotropic elastic solid consist of the strain-displacement relations, the equilibrium equations, and the stress-strain relations.
