ABSTRACT
This chapter introduces 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 chapter is considered with a similar model, and the application will be to the prediction of the pollutant concentration in a stream resulting from a source of pollution upstream. It shows how these models can be extended to heat and mass transfer in two directions. Variations of the mean value theorem are used to estimate the errors made by replacing the continuous model by a discrete model. The chapter discusses newton cooling models with theorems, application and examples. It explains heat diffusion in a wire with its applications and examples and also discusses flow and decay of a pollutant in a stream.
