A Mathematical Description of Water Vapor Mass Transfer for a Vented Automotive Lamp

Plastic automotive lamp assemblies are vented by a variety of methods to reduce the likelihood of condensation forming in the lamp and to prevent water ingress lamp warranty returns. Previously, it has been shown that the humidity in a vented automotive lamp can be described empirically by a decreasing exponential (i.e. decay). It was also shown that this formula by applying Fick’s Law of Diffusion, particularly the exponential constant (k), can be related to basic physical properties of the lamp system. Specifically, the exponential constant is a ratio of the product of a characteristic cross-section area of the vent and the permeability of water vapor over the product of the lamp volume and a characteristic length of the vent. This description was shown to be less accurate at time t greater than 30 minutes and additional details of the vented lamp system were proposed for better fit to the experimental data. This investigation proposes that the additional description for the vented lamp system is better associated with the absorption and desorption of water from the plastic parts of the lamp assembly. The water release from the plastic in the lamp can be described by an additional term supplying water vapor content to the lamp volume. Further, an investigation of the ratio of parameters defining the exponential constant of the water release from the lamp plastic components is addressed and compared to experiment. A discussion of this description’s limitations and use as an engineering design tool is included.