FDM Simulation of Cu–Al₂O₃/Water Casson Hybrid Nanofluid Flow and Thermal Transport in a Couette System

  • Khasim Ali Department of Mathematics, Nawab Shah Alam Khan College of Engineering and Technology, Hyderabad, Telangana, India https://orcid.org/0000-0001-8449-7090
  • Ramesh Alluguvelli Department of Mathematics, Geethanjali College of Engineering and Technology, Keesara, Hyderabad, Telangana, India https://orcid.org/0000-0002-5075-4375
  • Swatmaram Department of Mathematics, Chaitanya Bharathi Institute of Technology, Hyderabad, Telangana, India
  • Chandra Shekar Balla Government Junior College, Amangal, Ranga Reddy, Telangana, India https://orcid.org/0000-0002-1919-1367
  • K. Praveen Kumar Department of Humanities and Science, Government Polytechnic, Hyderabad, Telangana, India
  • E. Jagathprabhav Department of Humanities and Science, Government Polytechnic, Shadnagar, Telangana, India
Keywords: Couette flow, Variable viscosity, Al2O3-H2O nanofluid, Biot number, Stretching parameter

Abstract

This paper numerically inspects the unsteady Couette Casson hybrid nanofluid (HNF) containing copper (Cu) and aluminum oxide (Al₂O₃) nanoparticles dissolved in water. The upper wall is set in uniform motion, and the lower wall is taken as stationary and stretchable. Finite difference method (FDM) is used to integrate the governed nonlinear partial differential equations. The results are explored through streamlines, isotherms, Nusselt number and skin friction. The impact of key dimensionless numbers such as Grashof number, Biot number, stretching parameter, Casson parameter, and Eckert number on Cu-Al₂O₃-water HNF is discussed. The results disclose that the flow and heat transfer(HT) can be controlled considerably by the key parameters.

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References

N. Casson, “A flow equation for the PIGMENT-oil suspensions of the printing ink type,” in: Rheology of Disperse Systems, edited by C.C. Mill, (Pergamon, 1959), pp. 84–102.

Mukhopadhyay, S., “Casson fluid flow and heat transfer over a nonlinearly stretching surface,” Chinese Physics B, 22(7), 074701 (2013). https://doi.org/10.1088/1674-1056/22/7/074701

M. Abd El-Aziz, and A.A. Afify, “MHD Casson fluid flow over a stretching sheet with entropy generation analysis and Hall influence,” Entropy, 21(6), 592 (2019). https://doi.org/10.3390/e21060592

K. Gangadhar, D.N. Bhargavi, and V.S.R. Munagala, “Steady Boundary Layer Flow of Casson Fluid over a Nonlinear Stretched Sheet in Presence of Viscous Dissipation Using the Spectral Relaxation Method,” Mathematical Modelling of Engineering Problems, 7(3), 351-358 (2020). https://doi.org/10.18280/mmep.070304

I.A. Tantry, S. Wani, and B. Agrawal, “Study of MHD boundary layer flow of a casson fluid due to an exponentially stretching sheet with radiation effect,” Int. J. Stat. Appl. Math, 6, 138-144 (2021). https://doi.org/10.13140/RG.2.2.33054.41286

M.M. Nandeppanavar, “Flow and Heat Transfer Analysis of Casson Fluid due to a stretching sheet: An Analytical Solution,” Advances in Physics theories and Applications, 50, 2224-2225 (2015).

M.B. Ashraf, T. Hayat, and A. Alsaedi, “Mixed convection flow of Casson fluid over a stretching sheet with convective boundary conditions and Hall effect,” Boundary Value Problems, 2017(1), 137 (2017). https://doi.org/10.1186/s13661-017-0869-7

J. Qing, M.M. Bhatti, M.A. Abbas, M.M. Rashidi, and M.E.S. Ali, “Entropy generation on MHD Casson nanofluid flow over a porous stretching/shrinking surface,” Entropy, 18(4), 123 (2016). https://doi.org/10.3390/e18040123

Walawender, W.P., Chen, T.Y. and Cala, D.F., “An approximate Casson fluid model for tube flow of blood,” Biorheology, 12(2), 111-119 (1975). https://doi.org/10.3233/bir-1975-12202

Batra, R.L. and Jena, B., “Flow of a Casson fluid in a slightly curved tube,” International journal of engineering science, 29(10), 1245-1258 (1991). https://doi.org/10.1016/0020-7225(91)90028-2

Pramanik, S., “Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation,” Ain shams engineering journal, 5(1), 205-212 (2014). https://doi.org/10.1016/j.asej.2013.05.003

Mustafa, M., Hayat, T., Pop, I. and Aziz, A., “Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate, “Heat Transfer—Asian Research, 40(6), 563-576 (2011). https://doi.org/10.1002/htj.20358

Shashikumar, N.S., Kumara, B.P., Gireesha, B.J. and Makinde, O.D., “Thermodynamics analysis of MHD Casson fluid slip flow in a porous microchannel with thermal radiation,” Diffusion foundations, 16, 120-139 (2018). https://doi.org/10.4028/www.scientific.net/df.16.120

Choi, S.U.S. “Enhancing thermal conductivity of fluids with nanoparticles,” in: Development and Applications of Non-Newtonian Flows, edited by D. Singer, and H. Wang, (American Society of Mechanical Engineers, New York, 1995), pp. 99-106.

Tiwari, R.K. and Das, M.K., “Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids,” International Journal of heat and Mass transfer, 50(9-10), 2002-2018 (2007). https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.034

Khan, U., Zaib, A., Pop, I., Waini, I. and Ishak, A., “MHD flow of a nanofluid due to a nonlinear stretching/shrinking sheet with a convective boundary condition: Tiwari–Das nanofluid model,” International Journal of Numerical Methods for Heat & Fluid Flow, 32(10), 3233-3258 (2022). https://doi.org/10.1108/hff-11-2021-0730

Kumar, M., Reddy, G.J., Kumar, N.N. and Bég, O.A., “Computational study of unsteady couple stress magnetic nanofluid flow from a stretching sheet with Ohmic dissipation,” Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 233(2-4), 49-63 (2019). https://doi.org/10.1177/2397791419843730

Bao, H.X., Arain, M.B., Shaheen, S., Khan, H.I., Inc, M. and Yao, S.W., “Boundary-layer flow of heat and mass for Tiwari-Das nanofluid model over a flat plate with variable wall temperature,” Thermal Science, 26(Spec. issue 1), 39-47 (2022). https://doi.org/10.2298/tsci22s1039b

Mustafa, M., Khan, J.A., Hayat, T. and Alsaedi, A., “Numerical solutions for radiative heat transfer in ferrofluid flow due to a rotating disk: Tiwari and Das model,” International Journal of Nonlinear Sciences and Numerical Simulation, 19(1), 1-10 (2018). https://doi.org/10.1515/ijnsns-2015-0196

Shekar, B. C., & Kishan, N. “Finite element analysis of natural convective heat transfer in a porous square cavity filled with nanofluids in the presence of thermal radiation,” Journal of Physics: Conference Series, 662(1), 012017 (2015). https://doi.org/10.1088/1742-6596/662/1/012017

Suresh, S., Venkitaraj, K.P., Selvakumar, P. and Chandrasekar, M., “Effect of Al2O3–Cu/water hybrid nanofluid in heat transfer,” Experimental Thermal and Fluid Science, 38, 54-60 (2012). https://doi.org/10.1016/j.expthermflusci.2011.11.007

Waqas, H., Farooq, U., Liu, D., Abid, M., Imran, M. and Muhammad, T., “Heat transfer analysis of hybrid nanofluid flow with thermal radiation through a stretching sheet: A comparative study,” International Communications in Heat and Mass Transfer, 138, 106303 (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106303

Muneeshwaran, M., Srinivasan, G., Muthukumar, P. and Wang, C.C., “Role of hybrid-nanofluid in heat transfer enhancement–A review,” International Communications in Heat and Mass Transfer, 125, 105341 (2021). https://doi.org/10.1016/j.icheatmasstransfer.2021.105341; Jha, B. K. “Natural convection in unsteady MHD Couette flow,” Heat and mass transfer, 37(4), 329-331(2001). https://doi.org/10.1007/pl00013295

Rajesh, V. and Öztop, H.F., “Conjugate MHD natural convection in a chamber filled by ternary hybrid nanofluid with entropy generation,” Numerical Heat Transfer, Part A: Applications, 86(19), 6671-6692 (2025). https://doi.org/10.1080/10407782.2024.2344201

Hansda, S., Chattopadhyay, A., Goswami, K.D., Pandit, S.K., Öztop, H.F. and Sheremet, M.A., “Optimizing entropy production in bi-diffusive convection within trapezoidal porous enclosure using radiative trihybrid nanofluids and T-shaped baffle,” European Journal of Mechanics-B/Fluids, 113, 204268 (2025). https://doi.org/10.1016/j.euromechflu.2025.204268

Attia, H. A. “Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity,” International Journal of Non-Linear Mechanics, 43(8), 707-715 (2008). https://doi.org/10.1016/j.ijnonlinmec.2008.03.007

Ghara, N., Maji, S. L., Das, S., Jana, R., & Ghosh, S. K. “Effects of Hall current and ion-slip on unsteady MHD Couette flow,” Open Journal of Fluid Dynamics, 2(01), 1 (2012). https://doi.org/10.4236/ojfd.2012.21001

K. Jha, B., & A. Apere, C. “Combined effect of hall and ion-slip currents on unsteady mhd couette flows in a rotating system,” Journal of the Physical Society of Japan, 79(10), 104401 (2010). https://doi.org/10.1143/jpsj.79.104401

Guria M, Jana RN, Ghosh SK, “Unsteady Couette flow in a rotating system,” Int. J. Non-Linear Mech. 41, 838–843 (2006). https://doi.org/10.1016/j.ijnonlinmec.2006.04.010

Ali, A. O., & Makinde, O. D. “Modelling the Effect of Variable Viscosity on Unsteady Couette Flow of Nanofluids with Convective Cooling,” Journal of Applied Fluid Mechanics, 8(4), 793-802 (2015). https://doi.org/10.18869/acadpub.jafm.67.223.22967

Karim, M. E., Samad, M. A., & Ferdows, M. “Numerical study of the effect of variable viscosity on unsteady pulsatile nanofluid flow through a Couette channel of stretching wall with convective heat transfer,” AIP Conference Proceedings, 2121(1), 070005 (2019). https://doi.org/10.1063/1.5115912

Hajmohammadi, M. R. “Cylindrical Couette flow and heat transfer properties of nanofluids; single-phase and two-phase analyses,” Journal of Molecular Liquids, 240, 45-55 (2017). https://doi.org/10.1016/j.molliq.2017.05.043

Wakif, A., Boulahia, Z., Ali, F., Eid, M. R., & Sehaqui, R. “Numerical analysis of the unsteady natural convection MHD Couette-nanofluid flow in the presence of thermal radiation using single and two-phase nanofluid models for Cu-water nanofluids,” International Journal of Applied and Computational Mathematics, 4(3), 1-27 (2018). https://doi.org/10.1007/s40819-018-0513-y

Zeeshan, A., Khan, M.I., Ellahi, R. and Marin, M., “Computational intelligence approach for optimising MHD Casson ternary hybrid nanofluid over the shrinking sheet with the effects of radiation,” Applied Sciences, 13(17), 9510 (2023). https://doi.org/10.3390/app13179510

Akbar, N.S., Hussain, M.F., Alghamdi, M. and Muhammad, T., “Thermal characteristics of magnetized hybrid Casson nanofluid flow in a converging–diverging channel with radiative heat transfer: A computational analysis,” Scientific Reports, 13(1), 21891 (2023). https://doi.org/10.1038/s41598-023-49397-3

Das, S., Ali, A. and Jana, R.N., “Insight into the dynamics of magneto-casson hybrid nanoliquid caused by a plate rotation,” World Journal of Engineering, 18(1), 66-84 (2021). https://doi.org/10.1108/wje-07-2020-0261

Krishna, M.V., “Hall and ion slip effects on the MHD flow of Casson hybrid nanofluid past an infinite exponentially accelerated vertical porous surface,” Waves in Random and Complex Media, 34(5), 4658-4687 (2024). https://doi.org/10.1080/17455030.2021.1998727

Mishra, S.R., Mathur, P. and Pattnaik, P.K., “Hybrid nanofluid flow of non-Newtonian Casson fluid for the analysis of Entropy through a permeable medium,” Journal of Nanofluids, 11(3), 328-339 (2022). https://doi.org/10.1166/jon.2022.1846

Rehman, A., Khan, D., Mahariq, I., Elkotb, M.A., and Elnaqeeb, T., “Viscous dissipation effects on time-dependent MHD Casson nanofluid over stretching surface: A hybrid nanofluid study,” Journal of Molecular Liquids, 408, 125370 (2024). https://doi.org/10.1016/j.molliq.2024.125370

Varatharaj, K., Tamizharasi, R., Sivaraj, R. and Vajravelu, K., “Simulation of MHD-Casson hybrid nanofluid dynamics over a permeable stretching sheet: effects of heat transfer and thermal radiation,” Journal of Thermal Analysis and Calorimetry, 149(15), 8693-8711 (2024). https://doi.org/10.1007/s10973-024-13347-6

Balla, C.S., Ali, K. and Rajashekhar Reddy, Y., “Effectiveness of silver-magnesium oxide-water hybrid nanofluid in Couette channel,” Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 239(1-2), 3-10 (2025). https://doi.org/10.1177/23977914231196379

Ali, K., Reddy, Y.R. and Shekar, B.C., “Thermo-fluidic transport process in magnetohydrodynamic Couette channel containing hybrid nanofluid,” Partial Differential Equations in Applied Mathematics, 7, 100468 (2023). https://doi.org/10.1016/j.padiff.2022.100468

Raza, A., Almusawa, M.Y., Ali, Q., Haq, A.U., Al-Khaled, K. and Sarris, I.E., “Solution of water and sodium alginate-based casson type hybrid nanofluid with slip and sinusoidal heat conditions: A prabhakar fractional derivative approach,” Symmetry, 14(12), 2658 (2022). https://doi.org/10.3390/sym14122658

Paul, A., Sarma, N. and Patgiri, B., “MHD Al2O3/Cu-water Casson hybrid nanofluid flow across a porous exponentially stretching sheet,” Latin American Applied Research-An international journal, 54(4), 467-476 (2024). https://doi.org/10.52292/j.laar.2024.3282

Reddy, V.S., Kandasamy, J. and Sivanandam, S., “Impacts of casson model on hybrid nanofluid flow over a moving thin needle with dufour and soret and thermal radiation effects,” Mathematical and Computational Applications, 28(1), 2 (2022).

Sarkar, A., Mondal, H. and Nandkeolyar, R., “Mixed convective hydromagnetic unsteady Casson hybrid nanofluid flow analysis and entropy optimization over an inclined surface with viscous dissipation,” Discover Molecules, 2(1), 10 (2025).

Ishaq, M., Khan, S.U., Garalleh, H.A., Sowayan, A.S. and Tlili, I., “Thermal performance of casson hybrid nanofluid with radiative effects and convective conditions: applications to energy systems and industrial heat transfer,” Multiscale and Multidisciplinary Modeling, Experiments and Design, 8(2), 141 (2025). https://doi.org/10.1007/s41939-024-00720-z

Published
2026-03-14
Cited
How to Cite
Ali, K., Alluguvelli, R., Swatmaram, Balla, C. S., Kumar, K. P., & Jagathprabhav, E. (2026). FDM Simulation of Cu–Al₂O₃/Water Casson Hybrid Nanofluid Flow and Thermal Transport in a Couette System. East European Journal of Physics, (1), 473-483. https://doi.org/10.26565/2312-4334-2026-1-54