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

Document Type : Original Article

Author

Department of Mathematics, 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

References

[1] S. Choi, Enhancing thermal conductivity of fluids with nanoparticles in Developments and Applications of Nonnewtonian Flows; American Society of Mechanical Engineers. New York, USA, 1999, 99-106.
[2] J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Applied Physics Letters, 78(6) 2001, 718-720.
[3] J.N. Halder, M.N. Islam, Water pollution and its impact on the human health, Journal of environment and human, 2(1) 2015, 36-46.
[4] R. Inga and R. Tomas, Mathematical modeling of water quality change in Eastern European River, International journal of science, Environment and Technology, 3(3) 2014, 861-866.
[5] R. Kaushik, Mathematical modelling on water pollution and self-puri cation of river Ganges, Pelagia Res Libr, 6(7) 2015, 57-64.
[6] O.D. Makinde, A.S. Eegunjobi, and M.S. Tshehla, Thermodynamics Analysis of Variable Viscosity HydromagneticCouette Flow in a Rotating System with Hall Effects, Entropy, 17 (11) 2015, 7811-7826.
[7] S. Mirbagheri, M. Abaspour, K. Zamani, Mathematical modeling of water quality in river systems, European Water, 27(28) 2009, 31-41.
[8] M.H Mkwizu, O.D. Makinde and Y. Nkansah-Gyekye, Second Law Analysis of Buoyancy Driven Unsteady Channel Flow of Nanofluids with Convective Cooling, Applied and Computational Mathematics, 4 (3) 2015, 100-115.
[9] M.H Mkwizu, O.D. Makinde and Y. Nkansah-Gyekye, Effects of Navier slip and wall permeability on entropy generation in unsteady generalized Couette flow of nanofluids with convective cooling, UPB Sci. Bull., Ser. D, 77(4) 2015, 201-16.
[10] S. Nazarovs, S. Dejus, and T. Juhna, Modelling water quality in drinking water distribution networks from real-time direction data, Drinking Water Engineering and Science, 5(1) 2012, 39-45.
[11] S. Noorzadeh, F.S. Moghanlou, M. Vajdi, and M. Ataei, Thermal conductivity, viscosity and heat transfer process in nanofluids: A critical review. Journal of Composites and Compounds, 2(5) 2020, 175-192.
[12] M. Panigaj, M.B. Johnson, W. Ke, J. Mcmillan, E.A.Goncharova, M. Chandler and K.A. Afonin, Aptamers as modular components of therapeutic nucleic acid nanotechnology. ACS nano, 13(11) 2019, 12301-12321.
[13] G. Pearce, M. Ramzan Chaudhry, and S. Ghulam. A simple methodology for water quality monitoring, 1998.
[14] W. Rauch, M. Henze, L. Koncsos, P. Reichert, P. Shanahan, L. Somlydy, P. Vanrolleghem, River water quality modelling: I. State of the art, Water Science and Technology, 38(11)1998, 237-44.
[15] P. Reichert and P. Vanrolleghem, Identi ability and uncertainty analysis of the river water quality model no. 1 (RWQM1), Water Science and technology, 43(7) 2001, 329-38.
[16] C.A. Stow, K.H. Reckhow, S.S. Qian, E.C. Lamon III, G.B. Arhonditsis, M.E. Borsuk, and D. Seo, Approaches to Evaluate Water Quality Model Parameter Uncertainty for Adaptive TMDL Implementation 1, JAWRA Journal of the American Water Resources Association, 43(6) 2007, 1499-1507.
[17] T. Spanos, A. Ene, C. Xatzixristou and A. Papaioannou, Assessment of groundwater quality and hydrogeological pro le of Kavala area, Northern Greece. Environmental Physics, 60 2015, 1139-1150.
[18] H. Yarmand, G. Ahmadi, S. Gharehkhani, S.N. Kazi, M.R. Safaei, M.S. Alehashem and A.B. Mahat, Entropy generation during turbulent flow of zirconia-water and other nanofluids in a square cross section tube with a constant heat flux, Entropy, 16(11) 2014, 6116-6132.
Mathematics and Computational Sciences
Volume 2, Issue 3
September 2021
Pages 1-13

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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

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