In this Worked Problem we look at heating ducts in automobiles. This problem consists of a transient (time dependent) heat transfer application made up of a duct, in which the air at a fixed temperature in the inlet is flowing in contact with a plastic insulated wall. The problem is parametrized: the Peclet number as a measure of axial transport velocity field (modeling the physics of the problem) and the thickness of the plastic wall (modeling the geometry).
This Worked Problem is described by the coupling of unsteady heat transfer by conductivity into a plastic material (representing the thickness of the duct) and by convection inside the duct where the air is flowing. There is a coupling between diffusion (conduction) and convection-diffusion phenomena.