Full Project – Mathematical model to determine the level of contaminant in a work space

Full Project – Mathematical model to determine the level of contaminant in a work space

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Mathematical model is a set of mathematical equation representing a process or a system. it is an essential step in the construction of a theory.

The model of a house include a number of factors related to airflow, exhaust fan, forced air, system operation, dust leakage, weather effect as well as factor related to contaminant dispersal including absorption of water vaporand volatile organic compounds. The contaminant studies include carbon monoxide, carbon dioxide, and nitrogen dioxide, fine and coarse. simulation result indicate that the system modification reduced contaminant and concentration  and they lead to large related reduction in the tight room than in the room with typical levels of air tightness, though the typical rooms still has lower post control concentration of a non-delaying contaminant from a constant source.

The types of contaminant within process space differ in relation to the type of concentration.

However, a residential building can be considered as process / work space and common contaminant found there is carbon dioxide. Carbon dioxide is a common contaminant found in a residential or any work space whose concentration build up monitor, it can lead to occupational hazards which is injurious to workers health and may also lead to explosion within the work space.



The context contaminant is defined as airborne materials that are injurious to human health. The materials that may involve in contaminant may be gases; vapor even may be suspension of solid and liquid particles

according to Ejump and Tyler (1991) they “contaminant” as the “presence of one or more particles in the atmosphere which are dangerous to human health plant or animal life, or property which may of which may unreasonable interfere with comfortable enjoyment of life, property or conduct of business”. According to them, contaminant results from two parts phenomenon, a time concentration relationship.

From the above definition, it can then define “pollutant” as the presence of contaminant within the process space under consideration. the types of contaminant within process space differ in relation to the type of process carried out within can be considered as process / work space and the common contaminant found in residential or any work space whose concentration build-up in a space is monitored.



The manual system currently being used has some major problems among these are:-

  1. The time spent in trying to get accurate concentration is much
  2. Waste of human resources.
  • Delay in report presentation.
  1. Time and energy spent in production.
  2. improper record keeping of past concentration



The objectives of this work are:-

  1. To estimate the concentration of contaminant in an enclosure.
  2. Develop a mathematical model for predicting concentration within any given work space.
  • To provide insight into the use to multizone modeling.



All data used in this study are collected from the school of environmental studies, science laboratory technology, engineering department, hospital in Talata Mafara Zamfara State



The scopes of this study are as follows:-

  1. A work space with full-mixed condition (dilution )
  2. A full-mixed condition with any given work space (operation room in the hospital)
  • Work space of constant rate of contaminant generation and ventilation rate over a period of time.
  1. Where the contaminant generation within the work space does not react with each other.

However, it should be noted that the term ventilation does not mean that the concentration of contaminant cannot grow beyond threshold limit value (TLV).



This research work is limited to only science and laboratory technology (SLT) department because of the following reasons:-

  1. Lack of awareness of some part of the institution
  2. Inadequate time.



The importance of this project can be summarize below:-

  1. Used by engineers to design work space and enable them to understand, determine and predict the level of concentration of contaminant.
  2. It enable engineers to design appropriate ventilation system tha will provide full-mixed ventilation within the work space.
  • To select the maximum exposure limit to be used as design criteria and standards to judge the system performance.
  1. To design ‘hood’ and select the volumetric flow rates of exhaust air, recalculated air and make-up air.
  2. To select the most effective gas cleaning to remove contaminant before air is discharged to the outside environment.




Model: a model is a set of instruction for generating behavioral data includes iconic model, analogue model and symbolic model.

-Iconic model: it involves representing object using chart, photograph pictures etc.

– Analogue model: involve using characteristics in one characteristics in another object.

– Symbolic model: which involve the use of symbols, equalities and function to represents an ideal or concept.

Modeling is described as an act of relating real system into model.

Mathematical Model: is defined as an act of relating mathematical model into real process.

Ventilation: the allowing fresh air into the room or a working space.

Work space: this is an area available for use in particular building e.g. office. Or it is a place of minimum amount in a building that is minimum for use e.g. factory, offices, laboratory etc.

Contaminant: These are airborne materials that are injurious and dangerous to human health.

Simulation: this is said to be an experimental process that allow us to understand how the system under study will behave in reality when we limit its behavior in an artificial environment.


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Full Project – Mathematical model to determine the level of contaminant in a work space