Abstract
The focus of this research is the exploration of bio-convection in micropolar nanoparticles. This exploration is influenced by a stretching surface. Micropolar nanofluids are distinguished by their unique rheological properties. Recently, they have gained significant attention due to their potential applications. These applications span across various domains. They include tissue engineering, solar collector efficiency, biotechnology, nano-medicine drug delivery, and biomaterial synthesis. In addition, this study incorporates the characteristics of the heat transfer rate and velocity slip parameter and its relevance to various particle applications, such as heat transfer, fluid concentration, and material processing. In the present study, the nanoliquid flow, velocity slip parameter, and heat and mass transfer over a horizontal stretching sheet under the impact of motile microorganisms are investigated, numerically. These characteristics are under the influence of micro-inertia, micro-rotation, and slip. A numerical technique is used to solve these equations. The solutions are for certain values of the parameters involved. One such parameter is the velocity slip parameter. The classical Navier–Stokes equations of motion are transformed into a simpler form. This transformation is achieved by employing a similarity approach. The resulting system of non-linear equations is solved numerically. This solution is achieved with the aid of a finite difference method. This method is embedded with an iterative successive over the relaxation approach. The impact of relevant flow parameters is elaborated. These parameters include bioconvection, stretching, and nanoparticle concentration. Their impact on temperature and velocity fields is detailed through graphs and tables. The findings reveal that the temperature experiences fluctuations. These fluctuations occur as the microrotation velocity of liquid particles and biological convection increase. There is a notable temperature drop followed by a subsequent rise. This happens when the microorganism concentration limit (omega) is reached. The conclusions of this study are to illuminate how the magnetic field as well as thermal radiation and velocity slip parameters affect the flow pattern, fluid concentration, temperature distributions, and heat transfer rate in the biological fluids near the stretching surface. The calculated results from this study are compared with data available in the literature.
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References
Abdelmalek, Z., Tayebi, T., Dogonchi, A. S., Chamkha, A. J., Ganji, D. D., & Tlili, I. (2020). Role of various configurations of a wavy circular heater on convective heat transfer within an enclosure filled with nanofluid. International Communications in Heat and Mass Transfer, 113, 104525.
Ali, B., Siddique, I., Ahmadian, A., Senu, N., Ali, L., & Haider, A. (2022). Significance of Lorentz and Coriolis forces on dynamics of water based silver tiny particles via finite element simulation. Ain Shams Engineering Journal, 13(2), 101572.
Ahmed, Z., Nadeem, S., Saleem, S., & Ellahi, R. (2019). Numerical study of unsteady flow and heat transfer CNT-based MHD nanofluid with variable viscosity over a permeable shrinking surface. International Journal of Numerical Methods for Heat & Fluid Flow, 29(12), 4607–4623.
Ali, M. E. (1995). On thermal boundary layer on a power-law stretched surface with suction or injection. International Journal of Heat and Fluid Flow, 16(4), 280–290.
Ali, B., Siddique, I., Khan, I., Masood, B., & Hussain, S. (2021). Magnetic dipole and thermal radiation effects on hybrid base micropolar CNTs flow over a stretching sheet: Finite element method approach. Results in Physics, 25, 104145.
Ali, B., Raju, C. S. K., Ali, L., Hussain, S., & Kamran, T. (2021). G-Jitter impact on magnetohydrodynamic non-Newtonian fluid over an inclined surface: Finite element simulation. Chinese Journal of Physics, 71, 479–491.
Ali, B., Shafiq, A., Siddique, I., Al-Mdallal, Q., & Jarad, F. (2021). Significance of suction/injection, gravity modulation, thermal radiation, and magnetohydrodynamic on dynamics of micropolar fluid subject to an inclined sheet via finite element approach. Case Studies in Thermal Engineering, 28, 101537.
Boujelbene, M., Majeed, A., Baazaoui, N., Barghout, K., Ijaz, N., Abu-Libdeh, N., & Ali, M. R. (2023). Effect of electrostatic force and thermal radiation of viscoelastic nanofluid flow with motile microorganisms surrounded by PST and PHF: Bacillus anthracis in biological applications. Case Studies in Thermal Engineering, 52, 103691.
Bagh, A., Naqvi, R. A., Hussain, D., Aldossary, O. M., & Hussain, S. (2020). Magnetic rotating flow of a hybrid nano-materials Ag-MoS2 and Go-MoS2 in C2H6O2-H2O hybrid base fluid over an extending surface involving activation energy: FE simulation. Mathematics, 8(10), 1730.
Dogonchi, A. S., Asghar, Z., & Waqas, M. (2020). CVFEM simulation for Fe3O4-H2O nanofluid in an annulus between two triangular enclosures subjected to magnetic field and thermal radiation. International Communications in Heat and Mass Transfer, 112, 104449.
Dogonchi, A. S., Nayak, M. K., Karimi, N., Chamkha, A. J., & Ganji, D. D. (2020). Numerical simulation of hydrothermal features of Cu–H 2 O nanofluid natural convection within a porous annulus considering diverse configurations of heater. Journal of Thermal Analysis and Calorimetry, 141, 2109–2125.
Dogonchi, A. S., Tayebi, T., Chamkha, A. J., & Ganji, D. D. (2020). Natural convection analysis in a square enclosure with a wavy circular heater under magnetic field and nanoparticles. Journal of Thermal Analysis and Calorimetry, 139, 661–671.
Dogonchi, A. S., Waqas, M., Gulzar, M. M., Hashemi-Tilehnoee, M., Seyyedi, S. M., & Ganji, D. D. (2019). Simulation of Fe3O4-H2O nanoliquid in a triangular enclosure subjected to Cattaneo-Christov theory of heat conduction. International Journal of Numerical Methods for Heat & Fluid Flow, 29(11), 4430–4444.
Dogonchi, A. S., Waqas, M., Seyyedi, S. M., Hashemi-Tilehnoee, M., & Ganji, D. D. (2020). A modified Fourier approach for analysis of nanofluid heat generation within a semi-circular enclosure subjected to MFD viscosity. International Communications in Heat and Mass Transfer, 111, 104430.
Ellahi, R., Sait, S. M., Shehzad, N., & Ayaz, Z. (2020). A hybrid investigation on numerical and analytical solutions of electro-magnetohydrodynamics flow of nanofluid through porous media with entropy generation. International Journal of Numerical Methods for Heat & Fluid Flow, 30(2), 834–854.
Eringen, A. C. (1964). Simple micro fluids. International Journal of Engineering Science, 2(2), 205–217.
Eringen, A. C. (1966). Theory of micropolar fluids. Journal of Mathematics and Mechanics, 16, 1–18. https://doi.org/10.1512/iumj.1967.16.16001
Eringen, A. C., & Chang, T. S. (1970). Micropolar description of hydrodynamic turbulence. Recent Advances in Engineering, Science, 5, 1–8.
Fuzhang, W., Akhtar, S., Nadeem, S., & El-Shafay, A. S. (2022). Mathematical computations for the physiological flow of Casson fluid in a vertical elliptic duct with ciliated heated wavy walls. Waves in Random and Complex Media, 1–14. https://doi.org/10.1080/17455030.2022.2072973
Faiz, M., Tayebi, T., Ali, K., Malekshah, E. H., & Ahmad, S. (2023). Interaction of nanoparticles with motile gyrotactic microorganisms in a Darcy-Forchheimer magnetohydrodynamic flow-A numerical study. Heliyon, 9(7), 1–12. https://doi.org/10.1016/j.heliyon.2023.e17840
Ghadikolaei, S. S., Hosseinzadeh, K., Yassari, M., Sadeghi, H., & Ganji, D. D. (2018). Analytical and numerical solution of non-Newtonian second-grade fluid flow on a stretching sheet. Thermal Science and Engineering Progress, 5, 309–316.
Ghalambaz, M., Groşan, T., & Pop, I. (2019). Mixed convection boundary layer flow and heat transfer over a vertical plate embedded in a porous medium filled with a suspension of nano-encapsulated phase change materials. Journal of Molecular Liquids, 293, 111432.
Ghalambaz, M., Izadpanahi, E., Noghrehabadi, A., & Chamkha, A. (2015). Study of the boundary layer heat transfer of nanofluids over a stretching sheet: Passive control of nanoparticles at the surface. Canadian Journal of Physics, 93(7), 725–733.
Hashemi-Tilehnoee, M., Dogonchi, A. S., Seyyedi, S. M., Chamkha, A. J., & Ganji, D. D. (2020). Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block. Journal of Thermal Analysis and Calorimetry, 141(5), 2033–2045.
Hassanien, I. A., Abdullah, A. A., & Gorla, R. S. R. (1998). Flow and heat transfer in a power-law fluid over a nonisothermal stretching sheet. Mathematical and Computer Modelling, 28(9), 105–116.
Hayat, T., Abbas, Z., & Javed, T. (2008). Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet. Physics Letters A, 372(5), 637–647.
Hill, N. A., & Pedley, T. J. (2005). Bioconvection. Fluid Dynamics Research, 37(1–2), 1.
Hoseinpour, V., & Ghaemi, N. (2018). Green synthesis of manganese nanoparticles: Applications and future perspective–A review. Journal of Photochemistry and Photobiology B: Biology, 189, 234–243.
Izadi, M., Behzadmehr, A., & Shahmardan, M. M. (2015). Effects of inclination angle on mixed convection heat transfer of a nanofluid in a square cavity. International Journal for Computational Methods in Engineering Science and Mechanics, 16(1), 11–21.
Izadi, M., Javanahram, M., Zadeh, S. M. H., & Jing, D. (2020). Hydrodynamic and heat transfer properties of magnetic fluid in porous medium considering nanoparticle shapes and magnetic field-dependent viscosity. Chinese Journal of Chemical Engineering, 28(2), 329–339.
Izadi, M., Mohebbi, R., Chamkha, A., & Pop, I. (2018). Effects of cavity and heat source aspect ratios on natural convection of a nanofluid in a C-shaped cavity using Lattice Boltzmann method. International Journal of Numerical Methods for Heat & Fluid Flow, 28(8), 1930–1955.
Izadi, M., Shahmardan, M. M., Norouzi, M., Rashidi, A. M., & Behzadmehr, A. (2014). Cooling performance of a nanofluid flow in a heat sink microchannel with axial conduction effect. Applied Physics A, 117, 1821–1833.
Izadi, M., Sinaei, S., Mehryan, S. A. M., Oztop, H. F., & Abu-Hamdeh, N. (2018). Natural convection of a nanofluid between two eccentric cylinders saturated by porous material: Buongiorno’s two phase model. International Journal of Heat and Mass Transfer, 127, 67–75.
Kiwan, S., & Ali, M. E. (2008). Near-slit effects on the flow and heat transfer from a stretching plate in a porous medium. Numerical Heat Transfer, Part A: Applications, 54(1), 93–108.
Khadimallah, M. A., Harbaoui, I., Helaili, S., Benslimane, A., Sharif, H., Hussain, M., & Tounsi, A. (2023). Response of rotational parameter in the stagnation point with motile microorganism: Unsteady nanofluid. Advances in Concrete Construction, 15(4), 241–249.
Kumar, V., Tiwari, A. K., & Ghosh, S. K. (2015). Application of nanofluids in plate heat exchanger: A review. Energy Conversion and Management, 105, 1017–1036.
Lukaszewicz, G. (2012). Micropolar fluids: Theory and applications. Springer Science & Business Media. https://doi.org/10.1007/978-1-4612-0641-5
M. Mehryan, S. A., MoradiKashkooli, F., Soltani, M., & Raahemifar, K. (2016). Fluid flow and heat transfer analysis of a nanofluid containing motile gyrotactic micro-organisms passing a nonlinear stretching vertical sheet in the presence of a non-uniform magnetic field; numerical approach. PLoS One, 11(6), e0157598.
Mabood, F., Khan, W. A., & Ismail, A. M. (2015). MHD boundary layer flow and heat transfer of nanofluids over a nonlinear stretching sheet: A numerical study. Journal of Magnetism and Magnetic Materials, 374, 569–576.
Majeed, A., Zeeshan, A., Bhatti, M. M., & Ellahi, R. (2020). Heat transfer in magnetite (Fe3O4) nanoparticles suspended in conventional fluids: Refrigerant-134a (C2H2F4), kerosene (C10H22), and water (H2O) under the impact of dipole. Heat Transfer Research, 51(3), 217–232. https://doi.org/10.1615/HeatTransRes.2019029919
Makinde, O. D., & Aziz, A. (2011). Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. International Journal of Thermal Sciences, 50(7), 1326–1332.
Mehryan, S. A. M., Izadi, M., & Sheremet, M. A. (2018). Analysis of conjugate natural convection within a porous square enclosure occupied with micropolar nanofluid using local thermal non-equilibrium model. Journal of Molecular Liquids, 250, 353–368.
Mehryan, S. A. M., Kashkooli, F. M., Soltani, M., & Raahemifar, K. (2016). Fluid flow and heat transfer analysis of a nanofluid containing motile microorganisms passing a nonlinear stretching vertical sheet in the presence of a non-uniform magnetic field; numerical approach. PLoS ONE, 11(6), 1–32.
Mishra, S. R., Pattnaik, P. K., & Dash, G. C. (2015). Effect of heat source and double stratification on MHD free convection in a micropolar fluid. Alexandria Engineering Journal, 54(3), 681–689.
Noghrehabadi, A., Pourrajab, R., & Ghalambaz, M. (2012). Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature. International Journal of Thermal Sciences, 54, 253–261.
Platt, J. R. (1961). “Bioconvection patterns” in cultures of free-swimming organisms. Science, 133(3466), 1766–1767.
Ramezanizadeh, M., Nazari, M. A., Ahmadi, M. H., & Açıkkalp, E. (2018). Application of nanofluids in thermosyphons: A review. Journal of Molecular Liquids, 272, 395–402.
Salleh, M. Z., Nazar, R., & Pop, I. (2010). Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating. Journal of the Taiwan Institute of Chemical Engineers, 41(6), 651–655.
Sarafraz, M. M., Pourmehran, O., Yang, B., Arjomandi, M., & Ellahi, R. (2020). Pool boiling heat transfer characteristics of iron oxide nano-suspension under constant magnetic field. International Journal of Thermal Sciences, 147, 106131.
Sheikholeslami, M., & Ganji, D. D. (2017). Applications of nanofluid for heat transfer enhancement. William Andrew.
Tawfik, M. M. (2017). Experimental studies of nanofluid thermal conductivity enhancement and applications: A review. Renewable and Sustainable Energy Reviews, 75, 1239–1253.
Wang, F., Jamshed, W., Ibrahim, R. W., Abdalla, N. S. E., Abd-Elmonem, A., & Hussain, S. M. (2023). Solar radiative and chemical reactive influences on electromagnetic Maxwell nanofluid flow in Buongiorno model. Journal of Magnetism and Magnetic Materials, 576, 170748.
Wang, F., Ahmed, A., Khan, M. N., Ahammad, N. A., Alqahtani, A. M., Eldin, S. M., & Abdelmohimen, M. A. (2023). Natural convection in nanofluid flow with chemotaxis process over a vertically inclined heated surface. Arabian Journal of Chemistry, 16(4), 104599.
Xu, H., & Pop, I. (2014). Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms. International Journal of Heat and Mass Transfer, 75, 610–623.
Zadeh, S. M. H., Mehryan, S. A. M., Sheremet, M. A., Izadi, M., & Ghodrat, M. (2020). Numerical study of mixed bio-convection associated with a micropolar fluid. Thermal Science and Engineering Progress, 18, 100539.
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Conceptualization: A. Majeed; methodology, N. Ijaz; software: A. Majeed and F. Muhammad; validation: A. Majeed and F. Muhammad; writing—original draft preparation: A. Majeed; writing—review and editing: N. Ijaz, K. Barghout, and N. Abu-Libdeh; supervision: N. Ijaz, A. Majeed, and F. Muhammad; project administration: A. Majeed. All authors have read and agreed to the published version of the manuscript.
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Muhammad, F., Majeed, A., Ijaz, N. et al. Exploration of Heat Transfer Rate and Chemically Reactive Bio-convection Flow of Micropolar Nanofluid with Gyrotactic Microorganisms. BioNanoSci. (2024). https://doi.org/10.1007/s12668-024-01425-w
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DOI: https://doi.org/10.1007/s12668-024-01425-w