ABSTRACT
This chapter aims to assemble and understand the equations required for the construction of the numerical method and the associated computer program. The application of the First Law of Thermodynamics to an infinitesimal control volume in a solid or a stationary medium leads to the well-known heat conduction equation. The heat conduction equation is a direct result of the gradient-driven flux law and of the conservation principle implied by the First Law of Thermodynamics. There are many other physical processes in which the relevant flux is also governed by a gradient law and for which a conservation principle exists. Then it follows that these processes will be governed by differential equations that have the same appearance. A given physical problem can have more than one variable governed by the general differential equation. For example, in a mixture of many chemical species, the dependent variables are the concentrations of individual species.
