Mathematical analysis of a lumped-parameter model for describing the behavior of airborne dust in animal housing
Journal
Applied Mathematical Modelling
Journal Volume
14
Journal Issue
5
Pages
248-257
Date Issued
1990
Author(s)
Feddes J.J.R.
Abstract
Mathematical analysis of a model for describing the dynamic behavior of airborne dust undergoing turbulent diffusive and gravitational deposition in any location of a ventilated airspace is presented from the standpoint of a lumped-parameter approximation. The governing equation can be represented by a first-order vector-matrix differential equation. The key point of the model structure is the transport matrix [B] in terms of transport mechanisms of airborne dust. A matrix [D] is the product of the inverse matrix of [B] and the inverse diagonal matrix of lump volumes. This product can be used to evaluate the local transport phenomena of airborne dust. From the physical and mathematical properties of the model the overall mixing factor of the ventilation system can be estimated. The model is capable of predicting the air exchange rate required to maintain acceptable levels of airborne dust based on dust production rates. An analysis of the stability properties of the system equation is presented. The practical use of the model is also illustrated. © 1990.
SDGs
Type
journal article