Numerical Investigation of MHD Carreau Hybrid Nanofluid Flow over a Stretching Sheet in a Porous Medium with Viscosity Variations and Heat Transport

Document Type : Research Paper


Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan.


This article delves into the interpretation of the Lorentz force's impact when employing the Carreau hybrid nanofluid model with infinite shear rate viscosity over a stretching sheet, which incorporates porous medium. This model is highly effective in elucidating various non-Newtonian fluid behaviors, encompassing shear thinning and thickening properties. The governing equations consist of coupled nonlinear PDEs, which are transformed into a set of coupled nonlinear ODEs using similarity transformations. These equations are then numerically solved using a MATLAB built-in solver (bvp4c). Different characteristics of the considered flow of various parameters, such as the magnetic parameter, porous media parameter, Weissenberg number, stretching parameter, ratio parameter, coefficients space, and heat source/sinks, on temperature and velocity profiles, which are presented graphically. Additionally, the impacts of these parameters on the skin-friction coefficient and Nusselt number are tabulated. The Key findings suggest that, the higher values of the porous media parameter, magnetic parameter, Weissenberg number, and stretching parameter led to a decrease in velocity by 67.12% and 75.49% on average. Moreover, the velocity profile, Nusselt number, and skin friction coefficient are higher for the Al2O3/KO-based nanofluid compared to the Al2O3+MoS2/KO-based hybrid nanofluid. Also, the boundary layer of the hybrid nanofluid is observed to be hotter than that of the single nanoparticle nanofluid.


Main Subjects

[1].         Choi, SU,JA Eastman. Enhancing thermal conductivity of fluids with nanoparticles. Argonne National Lab.(ANL), Argonne, IL (United States), 1995.
[2].         Lee, S, S-S Choi, S Li, and,J Eastman, Measuring thermal conductivity of fluids containing oxide nanoparticles, 1999.
[3].         Buongiorno, J, Convective transport in nanofluids, Journal of Heat Transfer. Vol 128, pp 240-250, 2006.
[4].         Kuznetsov, A,D Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, Vol. 49, No. 2, pp. 243-7, 2010.
[5].         Khan, W,I Pop, Boundary-layer flow of a nanofluid past a stretching sheet, International journal of heat and mass transfer, Vol. 53, No. 11-12, pp. 2477-2483, 2010.
[6].         Makinde, OD,A Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, International Journal of Thermal Sciences, Vol. 50, No. 7, pp. 1326-1332, 2011.
[7].         Alwawi, FA, HT Alkasasbeh, A Rashad,R Idris, MHD natural convection of Sodium Alginate Casson nanofluid over a solid sphere, Results in physics, Vol. 16, pp. 102818, 2020.
[8].         Swalmeh, MZ, HT Alkasasbeh, A Hussanan,M Mamat, Heat transfer flow of Cu-water and Al2O3-water micropolar nanofluids about a solid sphere in the presence of natural convection using Keller-box method, Results in Physics, Vol. 9, pp. 717-724, 2018.
[9].         Alkasasbeh, H, M Swalmeh, H Bani Saeed, F Al Faqih,A Talafha, Investigation on CNTs-water and human blood based Casson nanofluid flow over a stretching sheet under impact of magnetic field, Frontiers in Heat and Mass Transfer (FHMT), Vol. 14, pp. 1-10, 2020.
[10].       Alkasasbeh, HT, MZ Swalmeh, A Hussanan,M Mamat, Numerical solution of heat transfer flow in micropolar nanofluids with oxide nanoparticles in water and kerosene oil about a horizontal circular cylinder, IAENG International Journal of Applied Mathematics, Vol. 49, No. 3, pp. 1-8, 2019.
[11].       Alkasasbeh, HT, MZ Swalmeh, A Hussanan,M Mamat, Effects of mixed convection on methanol and kerosene oil based micropolar nanofluid containing oxide nanoparticles, CFD Letters, Vol. 11, No. 1, pp. 55-68, 2019.
[12].       Sen, S, M Das, M Nayak,O Makinde, Natural convection and heat transfer of micropolar hybrid nanofluid over horizontal, inclined and vertical thin needle with power-law varying boundary heating conditions, Physica Scripta, Vol. 98, No. 1, pp. 015206, 2022.
[13].       Hosseinzadeh, K, M Mardani, M Paikar, A Hasibi, T Tavangar, M Nimafar, D Ganji,MB Shafii, Investigation of second grade viscoelastic non-Newtonian nanofluid flow on the curve stretching surface in presence of MHD, Results in Engineering, Vol. 17, pp. 100838, 2023.
[14].       Lee, C, K Choi, R Leavitt,L Eastman, Infrared hot‐electron transistor with a narrow bandpass filter for high temperature operation, Applied physics letters, Vol. 66, No. 1, pp. 90-102, 1995.
[15].       Sundar, LS, KV Sharma, MK Singh,A Sousa, Hybrid nanofluids preparation, thermal properties, heat transfer and friction factor–a review, Renewable and Sustainable Energy Reviews, Vol. 68, pp. 185-198, 2017.
[16].       Waini, I, A Ishak,I Pop, Unsteady flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid, International journal of heat and mass transfer, Vol. 136, pp. 288-297, 2019.
[17].       Sreedevi, P, P Sudarsana Reddy,A Chamkha, Heat and mass transfer analysis of unsteady hybrid nanofluid flow over a stretching sheet with thermal radiation, SN Applied Sciences, Vol. 2, No. 7, pp. 1222-1234, 2020.
[18].       Yashkun, U, K Zaimi, NAA Bakar, A Ishak,I Pop, MHD hybrid nanofluid flow over a permeable stretching/shrinking sheet with thermal radiation effect, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31, No. 3, pp. 1014-1031, 2020.
[19].       Rajesh, V, MA Sheremet,HF Öztop, Impact of hybrid nanofluids on MHD flow and heat transfer near a vertical plate with ramped wall temperature, Case Studies in Thermal Engineering, Vol. 28, pp. 101557, 2021.
[20].       Alkasasbeh, H, Numerical solution of heat transfer flow of casson hybrid nanofluid over vertical stretching sheet with magnetic field effect, CFD Letters, Vol. 14, No. 3, pp. 39-52, 2022.
[21].       Shaw, S, S Samantaray, A Misra, M Nayak,O Makinde, Hydromagnetic flow and thermal interpretations of Cross hybrid nanofluid influenced by linear, nonlinear and quadratic thermal radiations for any Prandtl number, International Communications in Heat and Mass Transfer, Vol. 130, pp. 105816, 2022.
[22].       Talebi Rostami, H, M Fallah Najafabadi, K Hosseinzadeh,D Ganji, Investigation of mixture-based dusty hybrid nanofluid flow in porous media affected by magnetic field using RBF method, International Journal of Ambient Energy, Vol. 43, No. 1, pp. 6425-6435, 2022.
[23].       Swalmeh, MZ, HT Alkasasbeh, A Hussanan, T Nguyen Thoi,M Mamat, Microstructure and inertial effects on natural convection micropolar nanofluid flow about a solid sphere, International Journal of Ambient Energy, Vol. 43, No. 1, pp. 666-677, 2022.
[24].       Alkasasbeh, H, Mathematical modeling of MHD flow of hybrid micropolar ferrofluids about a solid sphere, Frontiers in Heat and Mass Transfer (FHMT), Vol. 18, pp. 1-10, 2022.
[25].       Alkasasbeh, HT, FM Al Faqih, Aa Alizadeh, MA Fazilati, H Zekri, D Toghraie, A Mourad, K Guedri,O Younis, Computational modeling of hybrid micropolar nanofluid flow over a solid sphere, Journal of Magnetism and Magnetic Materials, pp. 170444, 2023.
[26].       Upreti, H, AK Pandey, N Joshi,O Makinde, Thermodynamics and heat transfer analysis of magnetized Casson hybrid nanofluid flow via a Riga plate with thermal radiation, Journal of Computational Biophysics and Chemistry, Vol. 22, No. 03, pp. 321-334, 2023.
[27].       Alipour, N, B Jafari,K Hosseinzadeh, Optimization of wavy trapezoidal porous cavity containing mixture hybrid nanofluid (water/ethylene glycol Go–Al2O3) by response surface method, Scientific Reports, Vol. 13, No. 1, pp. 1635-1646, 2023.
[28].       Zangooee, M, K Hosseinzadeh,D Ganji, Hydrothermal analysis of hybrid nanofluid flow on a vertical plate by considering slip condition, Theoretical and Applied Mechanics Letters, Vol. 12, No. 5, pp. 100357, 2022.
[29].       Carreau, PJ, Rheological equations from molecular network theories, Transactions of the Society of Rheology, Vol. 16, No. 1, pp. 99-127, 1972.
[30].       Khan, M, H Sardar, MM Gulzar,AS Alshomrani, On multiple solutions of non-Newtonian Carreau fluid flow over an inclined shrinking sheet, Results in physics, Vol. 8, pp. 926-932, 2018.
[31].       Crane, LJ, Flow past a stretching plate, Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 21, pp. 645-657, 1970.
[32].       Zyphur, MJ, PD Allison, L Tay, MC Voelkle, KJ Preacher, Z Zhang, EL Hamaker, A Shamsollahi, DC Pierides,P Koval, From data to causes I: Building a general cross-lagged panel model (GCLM), Organizational Research Methods, Vol. 23, No. 4, pp. 651-687, 2020.
[33].       Ullah, H, MI Khan,T Hayat, Modeling and analysis of megneto-Carreau fluid with radiative heat flux: Dual solutions about critical point, Advances in Mechanical Engineering, Vol. 12, No. 8, pp. 1687814020945477, 2020.
[34].       Salahuddin, T, Carreau fluid model towards a stretching cylinder: Using Keller box and shooting method, Ain Shams Engineering Journal, Vol. 11, No. 2, pp. 495-500, 2020.
[35].       Ayub, A, Z Sabir, SZH Shah, S Mahmoud, A Algarni, R Sadat,MR Ali, Aspects of infinite shear rate viscosity and heat transport of magnetized Carreau nanofluid, The European Physical Journal Plus, Vol. 137, No. 2, pp. 247-259, 2022.
[36].       Hamad, M,M Ferdows, Similarity solutions to viscous flow and heat transfer of nanofluid over nonlinearly stretching sheet, Applied Mathematics and Mechanics, Vol. 33, pp. 923-930, 2012.
[37].       Khan, M,Hashim, Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet, AIP Advances, Vol. 5, No. 10, pp. 107203, 2015.
Volume 54, Issue 3
September 2023
Pages 410-424
  • Receive Date: 23 August 2023
  • Revise Date: 06 September 2023
  • Accept Date: 10 September 2023