A Bio-Thermal Convection in a Porous Medium Saturated by Nanofluid Containing Gyrotactic Microorganisms Under an External Magnetic Field
The study of thermal convection in porous media saturated by nanofluid and microorganisms is an important problem for many geophysical and engineering applications. The concept of a mixture of nanofluids and microorganisms has attracted the interest of many researchers due to its ability to improve thermal properties and, as a result, heat transfer rates. This property is actively used both in electronic cooling systems and biological applications. Thus, the purpose of this research is to study biothermal instability in a porous medium saturated by a water-based nanofluid containing gyrotactic microorganisms in the presence of a vertical magnetic field. Given the presence of an external magnetic field in both natural and technological situations, we were motivated to perform this theoretical research. Using the Darcy-Brinkman model, a linear analysis of the convective instability has been considered for both-free boundaries, taking into account the effects of Brownian diffusion and thermophoresis. The Galerkin method was used to perform this analytical study. We have established that heat transfer is accomplished by stationary convection without oscillatory movements. In stationary convection regimes, metal oxide nanofluids (Al2O3), metallic nanofluids (Cu, Ag), and semiconductor nanofluids (TiO2, SiO2) are analyzed. Increasing the Chandrasekhar and Darcy numbers improve system stability significantly, but increasing porosity and modified bioconvection Rayleigh-Darcy number speed up the beginning of instability. To determine the transient behavior of heat and mass transports, a non-linear theory based on the representation of the Fourier series method is applied. In small time intervals, the transitional Nusselt and Sherwood numbers exhibit an oscillatory character. The Sherwood numbers (mass transfer) in the time interval reach stationary values faster than the Nusselt numbers (heat transfer). This research might help with seawater convection in the oceanic crust as well as the construction of biosensors.
D. Ingham and L. Pop, Transport Phenomena in Porous Media (Elsevier, Oxford, 2005).
D. A. Nield and A. Bejan, Convection in porous media (Springer, New York, 2006).
P. Vadasz, '’Instability and convection in rotating porous media: A review,” Fluids, 4, 147-178 (2019), https://doi.org/10.3390/fluids4030147
S. Choi, “Enhancing thermal conductivity of fluids with nanoparticles,” in Development and applications of Non-Newtonian flows, Vol. 66, edited by D. A. Signier and H. P. Wang (ASME, New York, 1995) pp. 99-105.
J. Buongiorno, “Convective Transport in Nanofluids,” J. Heat Trans., 128, 240-250 (2005), https://doi.org/10.1115/1.2150834
D. Tzou, “Thermal instability of nanofluids in natural convection,” Int. J. Heat Mass Transf., 51, 2967-2979 (2008), https://doi.org/10.1016/j.ijheatmasstransfer.2007.09.014
D. A. Nield and A. V. Kuznetsov, “Thermal instability in a porous medium layer saturated by a nanofluid,” Int. J. Heat Mass Transfer, 52, 5796-5801 (2009), https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.023
A. V. Kuznetsov and D. A. Nield, “Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model,” Transp. Porous Media, 81, 409-422 (2010), https://doi.org/10.1007/s11242-009-9413-2
B. S. Bhadauria and S. Agarwal, “Natural convection in a nanofluid saturated rotating porous layer: A nonlinear study,” Transp. Porous Media, 87, 585-602 (2011), https://doi.org/10.1007/s11242-010-9702-9
D. Yadav, G. S. Agrawal, and R. Bhargava, “Thermal instability of rotating nanofluid layer,” Int. J. Eng. Sci., 49, 1171-1184 (2011), https://doi.org/10.1016/j.ijengsci.2011.07.00
G. C. Rana and R. Chand, “On the onset of thermal convection in a rotating nanofluid layer saturating a Darcy-Brinkman porous medium: a more realistic model,” J. Porous Media, 18, 629-635 (2015), https://doi.org/10.1615/JPorMedia.v18.i6.60
U. Gupta, J. Ahuja, and R. K. Wanchoo, “Magneto convection in a nanofluid layer,” Int. J. Heat Mass Transfer, 64, 1163-1171 (2013), https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.035
J. Ahuja, U. Gupta, and R. K. Wanchoo, “Hydromagnetic Stability of Metallic Nanofluids (Cu-Water and Ag-Water) Using Darcy-Brinkman Model,” Int. J. Geophys., 2016, 9 (2016), https://doi.org/10.1155/2016/5864203
J. Sharma, U. Gupta, and R. K. Wanchoo, “Magneto Binary Nanofluid Convection in Porous Medium,” Int. J. Chem. Eng., 2016, 8 (2016), https://doi.org/10.1155/2016/9424036
D. Yadav, R. A. Mohamed, H. H. Cho, and J. Lee, “Effect of Hall Current on the Onset of MHD Convection in a Porous Medium Layer Saturated by a Nanofluid,” J. App. Fluid Mech., 9, 2379-2389 (2016), https://doi.org/10.18869/acadpub.jafm.68.236.25048
J. Ahuja and U. Gupta, “Magneto convection of rotating nanofluids in porous medium: metals and semiconductors as nanoparticles,” Research Journal of Science and Technology, 09, 135-142 (2017), https://doi.org/10.5958/2349-2988.2017.00022.5
A. J. Chamkha, S. K. Jena, and S. K. Mahapatra, “MHD convection of nanofluids: A review,” J. Nanofluids, 4, 271-292 (2015), https://doi.org/10.1166/jon.2015.1166
J. Ahuja and J. Sharma, “Rayleigh-benard instability in nanofluids: a comprehensive review,” Micro and Nano Syst. Lett., 8, 21 (2020), https://doi.org/10.1186/s40486-020-00123-y
T. J. Pedley, N. A. Hill, and J. O. Kessler, “The growth of bioconvection patterns in a uniform suspension of gyrotactic microorganisms,” J. Fluid Mech., 195, 223-338 (1988)
N. A. Hill, T. J. Pedley, and J. O. Kessler, “Growth of bioconvection patterns in a suspension of gyrotactic microorganisms in a layer of finite depth,” J. Fluid Mech., 208, 509-543 (1989), https://doi.org/10.1017/s0022112088002393
T. J. Pedley and J. O. Kessler, “Hydrodynamic phenomena in suspensions of swimming microorganisms,” Ann. Rev. Fluid Mech., 24, 313-358 (1992), https://doi.org/10.1146/ANNUREV.FL.24.010192.001525
A. A. Avramenko, “Model of Lorenz instability for bioconvection,” Dopov. Nac. akad. nauk Ukr. 10, 68-76 (2010).
E. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci., 20, 130-141 (1963), https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
A. V. Kuznetsov, “The onset of nanofluid bioconvection in a suspension containing both nanoparticles and gyrotactic microorganisms,” Int. Commun. Heat Mass Transfer, 37, 1421-1425 (2010), https://doi.org/10.1016/j.icheatmasstransfer.2010.08.015
A. V. Kuznetsov, “Non-oscillatory and oscillatory nanofluid bio-thermal convection in a horizontal layer of finite depth,” Eur. J. Mech. B. Fluids, 30, 156-165 (2011), https://doi.org/10.1016/j.euromechflu.2010.10.007
S. Saini and Y. D. Sharma, “A Bio-Thermal Convection in WaterBased Nanofluid Containing Gyrotactic Microorganisms: Effect of Vertical Throughflow,” J. Appl. Fluid Mech., 11, 895-903 (2018), https://doi.org/10.29252/jafm.11.04.28062
N. Faiza, A. Shafiq, L. Zhao, and A. Naseem, “MHD biconvective flow of Powell Eyring nanofluid over stretched surface,” Aip Advances, 7, 065013 (2017), https://doi.org/10.1063/1.4983014
S. Zuhra, N. S. Khan, Z. Shah, and S. Islam, “Simulation of bioconvection in the suspension of second grade nanofluid containing nanoparticles and gyrotactic microorganisms,” Aip Advances, 8, 105210 (2018), https://doi.org/10.1063/1.5054679
S. M. Atif, S. Hussain, and M. Sagheer, “Magnetohydrodynamic stratified bioconvective flow of micropolar nanofluid due to gyrotactic microorganisms,” Aip Advances, 9, 025208 (2019), https://doi.org/10.1063/1.5085742
A. A. M. Arafa, Z. Z. Rashed, and S. E. Ahmed, “Radiative MHD bioconvective nanofluid flow due to gyrotactic microorganisms using AtanganaBaleanu Caputo fractional derivative,” Phys. Scr., 96, 055211 (2021),
M. I. Asjad, N. Sarwar, B. Ali, S. Hussain, T. Sitthiwirattha, and J. Reunsumrit, “Impact of Bioconvection and Chemical Reaction on MHD Nanofluid Flow Due to Exponential Stretching Sheet,” Symmetry, 13, 2334 (2021), https://doi.org/10.3390/sym13122334
A. V. Kuznetsov and A. A. Avramenko, “Stability Analysis of Bioconvection of Gyrotactic Motile Microorganisms in a Fluid Saturated Porous Medium,” Transp. Porous Media, 53, 95-104 (2003), https://doi.org/10.1023/A:1023582001592
D. A. Nield, A. V. Kuznetsov, and A. A. Avramenko, “The onset of bioconvection in a horizontal porous-medium layer,” Transp. Porous Media, 54, 335-344 (2004), https://doi.org/10.1023/B:TIPM.0000003662.31212.5b
A. A. Avramenko and A. V. Kuznetsov, “The Onset of Convection in a Suspension of Gyrotactic Microorganisms in Superimposed Fluid and Porous Layers: Effect of Vertical Throughflow,” Transp. Porous Media, 65, 159-176 (2006),
A. V. Kuznetsov, “The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms,” Eur. J. Mech. B/Fluids, 25, 223-233 (2006), https://doi.org/10.1016/j.euromechflu.2005.06.003
D. A. Nield and A. V. Kuznetsov, “The cheng-minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid: A revised model,” Int. J. Heat Mass Transfer, 65, 682-685 (2013), https://doi.org/10.1016/j.ijheatmasstransfer.2013.06.054
M. Zhao, S. Wang, H. Wang, and U. S. Mahabaleshwar, “Darcy-Brinkman bio-thermal convection in a suspension of gyrotactic microorganisms in a porous medium,” Neural Comput. Appl, 31, 1061-1067 (2019), https://doi.org/10.1007/s00521-017-3137-y
A. Mahdy, “Gyrotactic Microorganisms Mixed Convection Nanofluid Flow along an Isothermal Vertical Wedge in Porous Media,” Int. J. Aerosp. Mech. Eng., 11, 840-850 (2017), https://doi.org/10.5281/zenodo.1130959
A. Alsenafi and M. Ferdow, “Dual solution for double-diffusive mixed convection opposing flow through a vertical cylinder saturated in a darcy porous media containing gyrotactic microorganisms,” Sci. Rep., 11, 19918 (2021), https://doi.org/10.1038/s41598-021-99277-x
H. A. Nabwey, S.M.M. EL-Kabeir, A. Rashad, and M. Abdou, “Gyrotactic microorganisms mixed convection flow of nanofluid over a vertically surfaced saturated porous media,” Alex. Eng. J., 61, 1804-1822 (2022), https://doi.org/10.1016/j.aej.2021.06.080
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1981).
Y. Yang, Z. G. Zhang, E. A. Grulke, W. B. Anderson, and G. Wu, “Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow,” Int. J. Heat Mass Transfer, 48, 1107-1116 (2005), https://doi.org/10.1016/j.ijheatmasstransfer.2004.09.038
J. C. Umavathi, D. Yadav, and M. B. Mohite, “Linear and nonlinear stability analyses of double-diffusive convection in a porous medium layer saturated in a maxwell nanofluid with variable viscosity and conductivity,” Elixir Mech. Engg., 79, 30407-30426 (2015)
S. Agarwal, N. Sacheti, P. Chandran, B. S. Bhadauria, and A. K. Singh, “Non-linear Convective Transport in a Binary Nanofluid Saturated Porous Layer,” Transp. Porous Med., 93, 29-49 (2012), https://doi.org/10.1007/s11242-012-9942-y
M. Zhao, S. Wang, S. Li, Q. Zhang, and U. Mahabaleshwar, “Chaotic Darcy-Brinkman convection in a fluid saturated porous layer subjected to gravity modulation,” Results Phys., 9, 1468-1480 (2018), https://doi.org/10.1016/j.rinp.2018.04.047
Copyright (c) 2022 Michael I. Kopp, Volodymyr V. Yanovsky, Ulavathi S. Mahabaleshwar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).