1. Establishing the fundamental laws

The observable macroscopic effect is an equalization of temperatures; however, if certain zones are maintained at constant temperatures by heat input (heat sources) or heat output (heat sinks), there is a continuous diffusion of heat from the hot region to the cold region. Hence the problem: having defined a material system in terms of its geometry and thermophysical characteristics, as well as any heat sources and interactions with the external environment, we now investigate the temperature field and its evolution over time.