Enhanced Flow and Temperature Profiles in Ternary Hybrid Nanofluid with Gyrotactic Microorganisms: A Study on Magnetic Field, Brownian Motion, and Thermophoresis Phenomena

Document Type : Research Paper


1 Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig, 44515, Egypt

2 Faculty of engineering, Delta University for Science and Technology, Gamasa, Egypt


This innovative study investigates the flow of ternary hybrid nanofluid containing gyrotactic microorganisms in microchannel. The magnetic field, thermophoresis, and Brownian motion effects are analyzed. The transformation of the PDEs system into ODEs is carried out by using the group transformation method. The innovative findings examine the Newtonian and non-Newtonian models derived from the system of ODEs. Several graphs illustrate how different parameters affect the velocity profile, temperature, concentration, and microorganisms. The power-law index value increases the fluid flow velocity by about 9% at n = 3, 36% at n = 4 relative to the case of n = 2.5 at the center of the boundary layer. Moreover, the ternary hybrid nanofluid exhibits a greater temperature compared to the nanofluid. The current results are compared to the researchers' findings to confirm the validity of the obtained results. When the Prandtl number is between 6 and 10, the Nusselt number reaches 45.49%.


Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Obaideen, K., Nooman AlMallahi, M., Alami, A.H., Ramadan, M., Abdelkareem, M.A., Shehata, N., Olabi, A.G., On the contribution of solar energy to sustainable developments goals: Case study on mohammed bin rashid al maktoum solar park, International Journal of Thermofluids, 12, 2021, 100123.
[2] Farooq, U., Waqas, H., Shah, Z., Kumam, P., Deebani, W., On unsteady 3d bio-convection flow of viscoelastic nanofluid with radiative heat transfer inside a solar collector plate, Scientific Reports, 12, 2022, 2952.
[3] Acharya, N., Das, K., Kundu, P.K., Effects of aggregation kinetics on nanoscale colloidal solution inside a rotating channel, Journal of Thermal Analysis and Calorimetry, 138, 2019, 461-477.
[4] Acharya, N., On the flow patterns and thermal behaviour of hybrid nanofluid flow inside a microchannel in presence of radiative solar energy, Journal of Thermal Analysis and Calorimetry, 141, 2020, 1425-1442.
[5] Fakour, M., Vahabzadeh, A., Ganji, D.D., Scrutiny of mixed convection flow of a nanofluid in a vertical channel, Case Studies in Thermal Engineering, 4, 2014, 15-23.
[6] Acharya, N., Das, K., Kundu, P., Effects of aggregation kinetics on nanoscale colloidal solution inside a rotating channel: A thermal framework, Journal of Thermal Analysis and Calorimetry, 138, 2019, 461-477.
[7] Noreen, S., Farooq, U., Waqas, H., Fatima, N., Alqurashi, M.S., Imran, M., Akgül, A., Bariq, A., Comparative study of ternary hybrid nanofluids with role of thermal radiation and cattaneo-christov heat flux between double rotating disks, Scientific Reports, 13, 2023, 7795.
[8] Khan, S.A., Hayat, T., Alsaedi, A., Thermal conductivity performance for ternary hybrid nanomaterial subject to entropy generation, Energy Reports, 8, 2022, 9997-10005.
[9] Bilal, M., Ullah, I., Alam, M.M., Weera, W., Galal, A.M., Numerical simulations through pcm for the dynamics of thermal enhancement in ternary mhd hybrid nanofluid flow over plane sheet, cone, and wedge, Symmetry, 14, 2022, 2419.
[10] Alqawasmi, K., Alharbi, K.A.M., Farooq, U., Noreen, S., Imran, M., Akgül, A., Kanan, M., Asad, J., Numerical approach toward ternary hybrid nanofluid flow with nonlinear heat source-sink and fourier heat flux model passing through a disk, International Journal of Thermofluids, 18, 2023, 100367.
[11] Mohanty, D., Mahanta, G., Shaw, S., Irreversibility and thermal performance of nonlinear radiative cross-ternary hybrid nanofluid flow about a stretching cylinder with industrial applications, Powder Technology, 433, 2024, 119255.
[12] Waqas, H., Farooq, U., Ibrahim, A., Kamran Alam, M., Shah, Z., Kumam, P., Numerical simulation for bioconvectional flow of burger nanofluid with effects of activation energy and exponential heat source/sink over an inclined wall under the swimming microorganisms, Scientific Reports, 11, 2021, 14305.
[13] Alharbi, F.M., Naeem, M., Zubair, M., Jawad, M., Jan, W.U., Jan, R., Bioconvection due to gyrotactic microorganisms in couple stress hybrid nanofluid laminar mixed convection incompressible flow with magnetic nanoparticles and chemical reaction as carrier for targeted drug delivery through porous stretching sheet, Molecules, 26, 2021, 3954.
[14] Shi, Q.-H., Hamid, A., Khan, M.I., Kumar, R.N., Gowda, R.J.P., Prasannakumara, B.C., Shah, N.A., Khan, S.U., Chung, J.D., Numerical study of bio-convection flow of magneto-cross nanofluid containing gyrotactic microorganisms with activation energy, Scientific Reports, 11, 2021, 16030.
[15] Rashed, A.S., Mahmoud, T.A., Kassem, M.M., Behavior of nanofluid with variable brownian and thermal ‎diffusion coefficients adjacent to a moving vertical plate, Journal of Applied and Computational Mechanics, 7, 2021, 1466-1479.
[16] Rashed, A., Mahmoud, T., Kassem, M., Analysis of homogeneous steady state nanofluid surrounding cylindrical solid pipes, The Egyptian International Journal of Engineering Sciences and Technology, 31, 2020, 71-82.
[17] Mabrouk, S.M., Mahmoud, T.A., Kabeel, A.E., Rashed, A.S., Influence of power-law index and hybrid-nanoparticles concentrations on the behavior of non-newtonian hybrid nanofluid inside water solar collector, Modern Physics Letters B, 38, 2023, 2350226.
[18] Mabrouk, S., Mahmoud, T., Kabeel, A.E., Rashed, A., Essa, F., Thermal and entropy behavior of sustainable solar energy in water solar collector due to non-newtonian power-law hybrid nanofluid, Frontiers in Energy Research, 11, 2023, 1220587.
[19] Abdollahi, S.A., Alizadeh, A.A., Esfahani, I.C., Zarinfar, M., Pasha, P., Investigating heat transfer and fluid flow betwixt parallel surfaces under the influence of hybrid nanofluid suction and injection with numerical analytical technique, Alexandria Engineering Journal, 70, 2023, 423-439.
[20] Waqas, H., Khan, S.A., Khan, S.U., Khan, M.I., Kadry, S., Chu, Y.-M., Falkner-skan time-dependent bioconvrction flow of cross nanofluid with nonlinear thermal radiation, activation energy and melting process, International Communications in Heat and Mass Transfer, 120, 2021, 105028.
[21] Rashed, A.S., Analysis of (3+1)-dimensional unsteady gas flow using optimal system of lie symmetries, Mathematics and Computers in Simulation, 156, 2019, 327-346.
[22] Rashed, A.S., Nasr, E.H., Kassem, M.M., Similarity analysis of mass and heat transfer of fhd steady flow of nanofluid incorporating magnetite nanoparticles (fe3o4), East African Scholars Journal of Engineering and Computer Sciences, 3, 2020, 54-63.
[23] Rashed, A.S., Mabrouk, S.M., Wazwaz, A.-M., Unsteady three-dimensional laminar flow over a submerged plate in electrically conducting fluid with applied magnetic field, Waves in Random and Complex Media, 33, 2023, 505-524.
[24] Rashed, A.S., Mabrouk, S.M., Wazwaz, A.-M., Forward scattering for non-linear wave propagation in (3 + 1)-dimensional jimbo-miwa equation using singular manifold and group transformation methods, Waves in Random and Complex Media, 32, 2022, 663-675.
[25] Saleh, R., Rashed, A.S., Wazwaz, A.-M., Plasma-waves evolution and propagation modeled by sixth order ramani and coupled ramani equations using symmetry methods, Physica Scripta, 96, 2021, 085213.
[26] Sarma, N., Paul, A., Thermophoresis and brownian motion influenced bioconvective cylindrical shaped ag–cuo/h2o ellis hybrid nanofluid flow along a radiative stretched tube with inclined magnetic field, BioNanoScience, 2023, DOI: 10.1007/s12668-023-01280-1.
[27] Paul, A., Sarma, N., Patgiri, B., Mixed convection of shear-thinning hybrid nanofluid flow across a radiative unsteady cone with suction and slip effect, Materials Today Communications, 37, 2023, 107522.
[28] Rafique, K., Mahmood, Z., Khan, U., Eldin, S.M., Oreijah, M., Guedri, K., Khalifa, H.A.E.-W., Investigation of thermal stratification with velocity slip and variable viscosity on mhd flow of al2o3−cu−tio2/h2o nanofluid over disk, Case Studies in Thermal Engineering, 49, 2023, 103292.
[29] Paul, A., Sarma, N., Patgiri, B., Thermal and mass transfer analysis of casson-maxwell hybrid nanofluids through an unsteady horizontal cylinder with variable thermal conductivity and arrhenius activation energy, Numerical Heat Transfer, Part A: Applications, 2023, DOI: 10.1080/10407782.2023.2297000.
[30] Mahmood, Z., Eldin, S.M., Rafique, K., Khan, U., Numerical analysis of mhd tri-hybrid nanofluid over a nonlinear stretching/shrinking sheet with heat generation/absorption and slip conditions, Alexandria Engineering Journal, 76, 2023, 799-819.
[31] Islam, S., Rana, B.M.J., Parvez, M.S., Hossain, M.S., Rahman, M.M., Electroosmotic flow in ternary (tio2-sio2-al2o3) blood-based sutterby nanomaterials with bio-active mixers, International Journal of Thermofluids, 18, 2023, 100363.
[32] Islam, S., Rana, B.M.J., Parvez, M.S., Hossain, M.S., Mazumder, M., Roy, K.C., Rahman, M.M., Dynamics of chemically reactive carreau nanomaterial flow along a stretching riga plate with active bio-mixers and arrhenius catalysts, Heliyon, 9, 2023, e21727.
[33] Rana, B., Arifuzzaman, S.M., Islam, S., Reza-E-Rabbi, S., Hossain, K., Ahmmed, S., Khan, M., Swimming of microbes in entropy optimized nano‚Äźbioconvective flow of prandtl–erying fluid, Heat Transfer, 51, 2022, 5497-5531.
[34] Rana, B.M.J., Arifuzzaman, S.M., Islam, S., Reza-E-Rabbi, S., Al-Mamun, A., Mazumder, M., Roy, K.C., Khan, M.S., Swimming of microbes in blood flow of nano-bioconvective williamson fluid, Thermal Science and Engineering Progress, 25, 2021, 101018.
[35] Islam, M.S., Islam, S., Siddiki, M.N.A.A., Numerical simulation with sensitivity analysis of mhd natural convection using cu-tio2-h2o hybrid nanofluids, International Journal of Thermofluids, 20, 2023, 100509.
[36] Smrity, A.M.A., Yin, P., Design and performance evaluation of pulsating heat pipe using metallic nanoparticles based hybrid nanofluids, International Journal of Heat and Mass Transfer, 218, 2024, 124773.
[37] Jamshed, W., Sirin, C., Selimefendigil, F., Shamshuddin, M.D., Altowairqi, Y., Eid, M.R., Thermal characterization of coolant maxwell type nanofluid flowing in parabolic trough solar collector (ptsc) used inside solar powered ship application, Coatings, 11, 2021, 1552.
[38] Rashed, A.S., Kassem, M.M., Group analysis for natural convection from a vertical plate, Journal of Computational and Applied Mathematics, 222, 2008, 392-403.
[39] Kassem, M., Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux, Journal of Computational and Applied Mathematics, 187, 2006, 72-86.
[40] Sheikholeslami, M., Rokni, H.B., Simulation of nanofluid heat transfer in presence of magnetic field: A review, International Journal of Heat and Mass Transfer, 115, 2017, 1203-1233.
[41] Sojoudi, A., Mazloomi, A., Saha, S.C., Gu, Y.T., Similarity solutions for flow and heat transfer of non-newtonian fluid over a stretching surface, Journal of Applied Mathematics, 2014, 2014, 718319.
[42] Abd-el-Malek, M.B., Helal, M.M., Similarity solutions for magneto-forced-unsteady free convective laminar boundary-layer flow, Journal of Computational and Applied Mathematics, 218, 2008, 202-214.
[43] Moran, M.J., Gaggioli, R.A., A new systematic formalism for similarity analysis, Journal of Engineering Mathematics, 3, 1969, 151-162.
[44] Jamshed, W., Eid, M.R., Azeany Mohd Nasir, N.A., Nisar, K.S., Aziz, A., Shahzad, F., Saleel, C.A., Shukla, A., Thermal examination of renewable solar energy in parabolic trough solar collector utilizing maxwell nanofluid: A noble case study, Case Studies in Thermal Engineering, 27, 2021, 101258.
[45] Jamshed, W., Aziz, A., A comparative entropy based analysis of cu and fe3o4/methanol powell-eyring nanofluid in solar thermal collectors subjected to thermal radiation, variable thermal conductivity and impact of different nanoparticles shape, Results in Physics, 9, 2018, 195-205.
[46] Nezafat, Z., Nasrollahzadeh, M., Biosynthesis of cu/fe3o4 nanoparticles using alhagi camelorum aqueous extract and their catalytic activity in the synthesis of 2-imino-3-aryl-2,3-dihydrobenzo[d]oxazol-5-ol derivatives, Journal of Molecular Structure, 1228, 2021, 129731.
[47] Ghadikolaei, S.S., Hosseinzadeh, K., Ganji, D.D., Jafari, B., Nonlinear thermal radiation effect on magneto casson nanofluid flow with joule heating effect over an inclined porous stretching sheet, Case Studies in Thermal Engineering, 12, 2018, 176-187.
[48] Azam, M., Shakoor, A., Rasool, H.F., Khan, M., Numerical simulation for solar energy aspects on unsteady convective flow of mhd cross nanofluid: A revised approach, International Journal of Heat and Mass Transfer, 131, 2019, 495-505.
[49] Sheikholeslami, M., Ganji, D.D., Numerical investigation for two phase modeling of nanofluid in a rotating system with permeable sheet, Journal of Molecular Liquids, 194, 2014, 13-19.
[50] Sheikholeslami, M., Hatami, M., Ganji, D.D., Nanofluid flow and heat transfer in a rotating system in the presence of a magnetic field, Journal of Molecular Liquids, 190, 2014, 112-120.
[51] Ghobadi, A.H., Hassankolaei, M.G., Numerical treatment of magneto carreau nanofluid over a stretching sheet considering joule heating impact and nonlinear thermal ray, Heat Transfer—Asian Research, 48, 2019, 4133-4151.
[52] Ghasemi, S.E., Hatami, M., Hatami, J., Sahebi, S.A.R., Ganji, D.D., An efficient approach to study the pulsatile blood flow in femoral and coronary arteries by differential quadrature method, Physica A: Statistical Mechanics and its Applications, 443, 2016, 406-414.
[53] Thumma, T., Mishra, S.R., Effect of nonuniform heat source/sink, and viscous and joule dissipation on 3d eyring–powell nanofluid flow over a stretching sheet, Journal of Computational Design and Engineering, 7, 2020, 412-426.