Heat conduction applied in ‘River Pollutant Diffusion’

Qihao Chen, Ruiqi Hu and Youwei Wang
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Qihao Chen: BSC Mathematics with Finance , Liverpool , University of Liverpool
Ruiqi Hu: Department of Mathematics, College of Literature, Science and the Arts, University of Michigan, Ann Arbor, MI, USA
Youwei Wang: College of Liberal Arts, University of Minnesota , Twins city, MN, USA

Technium Sustainability, 2024, vol. 8, 54-61

Abstract: Environment problems are a highly valued topic in today’s society, where water pollution issue is one of the most significant that could threaten human’s safety. Sources such as industrial wastewater and agricultural runoff are affecting the water quality. Rivers around the world suffer from varying degrees of pollution. In this paper, we investigate river heat pollution and employ a numerical model to investigate its evolution and impacts downstream by adapting the heat advection-diffusion equation. We explore the stability of our numerical solutions using von Neumann stability analysis of the forward and backward differencing method of discretization of the analytical equations. We further consider a setting where there are multiple sources of pollutant in the river to explore interaction of the two pollution sources. We use python to develop the model and plot temperature diffusion in the river as a function of time and location. Our model reflects the relationship between the speed of diffusion and thermal diffusivity, and how advection enhances pollutant. Our results show that heat pollution is very quickly transported to other locations and can affect water and food quality in many locations along the river. Additionally, pollution in rivers with fast currents will be more readily transported downstream, therefore both proximity to cities and speed of river water needs to be taken into account when addressing the problem of heat pollution in rivers near cities.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:tec:sustai:ojs:12029

DOI: 10.47577/sustainability.v8i.12029

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