# Mathematical modeling of the impacts of the nanoparticle in River-Aquatic system with convective cooling

Document Type : Original Article

Author

Department of Mathematics, Faculty of Science, Muslim University of Morogoro, Morogoro, Tanzania

Abstract

In this study, a mathematical model to examine the combined effects of nanoparticles of Copper (Cu) and Alumina ( Al 2 O 3) in unsteady channel flow of water (river) based nanofluids was established. Both first and second laws of thermodynamics were employed to analyze the model. Using the discretization finite difference method together with the Runge-Kutta integration scheme, the governing partial differential equations were solved numerically. Numerical simulations on the effects of parameter variation on concentration and temperature were graphically presented and quantitatively discussed. Results show that the nanofluid concentration increases with an increase in thermophoresis parameter (Nt) and nanoparticle volume fraction (η ) and decreases with the increase in the Biot number (Bi). While nanofluid temperature increases with Biot number (Bi), Schmidt number (Sc) and the Brownian motion parameter (Nb), and decreases with an increased nanoparticle volume fraction (η ). From the study, it was recommended that in cooling systems and industrial processes nanofluids were found significant to be used for the effective operation of machines and cooling systems. Using the same geometry of the channel flow and the same problem, the Brownian motion in any fluid system has a great impact also.

Keywords

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### History

• Receive Date: 22 June 2021
• Revise Date: 22 July 2021
• Accept Date: 03 August 2021
• First Publish Date: 03 August 2021