ABSTRACT
The first three sections introduce diffusion of heat in one direction. This is an example of model evolution with the simplest model being for the temperature of a well-stirred liquid where the temperature does not vary with space. The model is then enhanced by allowing the mass to have different temperatures in different locations. Because heat flows from hot to cold regions, the subsequent model will be more complicated. In Section 1.4 a similar model is considered, and the application will be to the prediction of the pollutant concentration in a stream resulting from a source of pollution up stream. Both of these models are discrete versions of the continuous model that are partial differential equations. Section 1.5 indicates how these models can be extended to heat and mass transfer in two directions, which is discussed in more detail in Chapters 3 and 4. In the last section variations of the mean value theorem are used to estimate the errors made by replacing the continuous model by a discrete model. Additional introductory materials can be found in G. D. Smith [23], and in R. L. Burden and J. D. Faires [4].
