Heat Transfer by Conduction
Being this the first mode that traditionally is encountered in the study of heat transfer, with the analysis of conduction the ground will be set for more complicated transfer phenomena. After a brief reference to the basic physical mechanism, as we recognize that heat transport in stationary media is driven by a temperature difference, we start by exploiting first the macroscopic balance for heat conduction. Then, the opportunity is seized to develop proper analytical skills by deriving and integrating the governing differential equations in various cases, following the microscopic balance leading to the distribution of the temperature scalar. With this mechanism, the subject medium participates only through the heat source or sink. Next, some graphical tools will be presented that are of some use for the solution of transient cases, and finally a numerical solution of the governing equations is proposed and initiated, to cast the base for a discussion on more complex transfer phenomena.
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