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Estimation of Thermal Pollution Using Numerical Simulation of Energy Equation Coupled with Viscous Burgers’ Equation
Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
- 1 Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
- 2 Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
- 3 Department of Mathematics, Jahangirnagar University, Dhaka, Bangladesh
American Journal of Computational Mathematics·Volume 12 (2022)·Pages 306–313·Published 20 July 2022·DOI10.4236/ajcm.2022.123020
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Abstract
In this paper, we implement energy equation coupled with viscous Burgers’ equation as a mathematical model for the estimation of thermal pollution of river water. The model is a nonlinear system of partial differential equations (PDEs) that read as an initial and boundary value problem (IBVP). For the numerical solution of the IBVP, we investigate an explicit second-order Lax- Wendroff type scheme for nonlinear parabolic PDEs. We present the numerical solutions graphically as a temperature profile , which shows good qualitative agreement with natural phenomena of heat transfer. We estimate the thermal pollution of water caused by industrialization on the bank of a river .
KeywordsViscous Burgers’ EquationEnergy EquationHeat TransferLax-Wendroff Type SchemeThermal Pollution
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