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On solving the chlorine transport model via Laplace transform.
A F Aljohani1, A Ebaid2, E A Algehyne1
1Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, 71491, Saudi Arabia.
Scientific Reports
|July 15, 2022
Summary
This study presents an effective method for solving a two-dimensional chlorine transport model in pipes. The approach successfully derives an exact solution using the method of residues, yielding Bessel functions.
Area of Science:
- Fluid dynamics
- Mathematical modeling
- Chemical engineering
Background:
- Accurate modeling of contaminant transport in pipe systems is crucial for water quality management.
- Existing analytical methods face challenges with complex boundary conditions in two-dimensional models.
- Chlorine transport in pipes is a key concern for maintaining disinfectant residual levels.
Purpose of the Study:
- To develop and validate an effective analytical method for solving a two-dimensional chlorine transport model in pipes.
- To obtain an exact solution for the concentration distribution under specific boundary conditions.
- To derive an expression for the dimensionless cup-mixing average concentration.
Main Methods:
- The study employs a second-order partial differential equation to represent the chlorine transport model.
- The Laplace transform is utilized, with challenges overcome by implementing the method of residues.
- The exact solution is derived in terms of Bessel functions.
Main Results:
- An exact analytical solution for the two-dimensional chlorine transport model is successfully obtained.
- The solution is expressed using Bessel functions, providing a precise mathematical description.
- A dimensionless cup-mixing average concentration is analytically derived.
Conclusions:
- The method of residues provides an effective and straightforward approach to solve complex transport models.
- The derived analytical solution offers valuable insights into chlorine distribution in pipes.
- The methodology can be extended to similar models with varying boundary conditions.
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