ABSTRACT
We now model the problem of Fig. 10-11 using lumped techniques. Here the rod is divided into segments, each segment exhibiting only energy storage (no thermal resistance) and having a uniform temperature throughout the segment at any instant of time. Between these segments we place localized thermal resistances. As in any lumped model, there is always the question of how to define the lumped elements and also how many lumps to choose. No hard-and-fast rules are available and past experience is often the best guide. By doing lumped analyses of problems for which the "exact" (distributed-parameter) models can be solved, we have a standard against which to compare and can thus get some feeling for the nature and degree of approximation caused by the lumping. Let us do this for the aluminum rod with response as in Fig. 10-13.
