### Engineering Motivation

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).

### Physical Principles

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.