eating)All the heat transfer problems we have examined have been steady state, but there are often circumstances in which thetransient response to heat transfer is critical. An example is the heating up of gas turbine compressors as they are brought up to speed during take-off. The disks that hold the blades are large and take a long time to come to temperature, while the casing is thin and in the path of high velocity compressor flow and thus comes to temperature rapidly. The result is that the case expands away from the blade tips, sometimes enough to cause serious difficulties with aerodynamic performance.
To introduce the topic as well as to increase familiarity with modeling of heat transfer problems, we examine a lumped parameter analysis of an object cooled by a stream. This will allow us to see what the relevant non-dimensional parameters are and, at least in a qualitative fashion, how more complex heat transfer objects will behave. We want to view the object as a ``lump'' described by a single parameter. We need to determine when this type of analysis would be appropriate. To address this, consider the temperature difference between two locations in the object, as shown in Figure 1