Physical insights on bio-convection in prandtl nanofluid over an inclined stretching sheet in non-darcy medium: Numerical simulation

Document Type : Research Article

Authors

1 Department of Mathematics, Mahapurusha Srimanta Sankaradeva Viswavidyalaya, Nagaon, Assam, India.

2 Department of Mathematics, Rajiv Gandhi University, Arunachal Pradesh, India.

Abstract

The innovative aspect of this work is to understand how the intricate interplay between bio-convection, heat transfer, and other behaviours of nanoparticles in a porous zone is affected by Prandtl nanofluid flow across an inclined stretched sheet. The stated equations are transformed into dimensionless form using appropriate similarity transformations, and the resultant set of equations is then numerically solved using MATLAB bvp4c. The acquired results are additionally verified against existing data. The incorporation of special parameters, including the Forchheimer drag (F_r), bio-convection Rayleigh number (R_b), density ratio of motile microorganism (Ω), stretching parameter (ϵ), Prandtl fluid parameter (δ), and elastic parameter (β), adds novelty and complexity to the analysis. The density ratio of motile microorganism plays a crucial role in determining the impact of microorganisms on bio-convection. Depending on whether this parameter is higher or lower than the surrounding fluid, the behaviour of velocity can vary, leading to different fluid flow patterns and dynamics within the system. The higher concentration causes the density of mobile microorganisms to increase, which has a stronger effect on the dynamics of bio-convection. The motile microorganisms considerably contribute to convective heat transmission, and the bacteria's density is extremely excessive compared to the fluid around them.

Keywords

Main Subjects


References:
1. Li, Y.X., Al- Khaled, K., Khan, S.U., et al. “Bio-convective Darcy-Forchheimer periodically accelerated flow of non-Newtonian nanofluid with Cattaneo–Christov and Prandtl effective approach”, Case Studies in Thermal Engineering, 26, 101102 (2021). https://doi.org/10.1016/j.csite.2021.101102
2. Bég, O.A., Prasad, V.R., and Vasu, B. “Numerical study of mixed bioconvection in porous media saturated with nanofluid containing oxytactic microorganisms”, Journal of Mechanics in Medicine and Biology, 13(04), 1350067 (2013). https://doi.org/10.1142/S021951941350067X
3. Waqas, H., Imran, M., Muhammad, T., et al. “On bio-convection thermal radiation in Darcy– Forchheimer flow of nanofluid with gyrotactic motile microorganism under Wu’s slip over stretching cylinder/plate”, International Journal of Numerical Methods for Heat & Fluid Flow, 31(5), pp. 1520-1546 (2021).https://doi.org/10.1108/HFF-05-2020-0313
4. Ahmad, A., Ashraf, M., and Ali, K. “Bioconvection due to gyrotactic microbes in a nanofluid flow through a porous medium”, Haliyon, 6(12), e05832 (2020). https://doi.org/10.1016/j.heliyon.2020.e05832
5. Wang, J., Mustafa, Z., Siddique, I., et al. “Computational analysis for bioconvection of microorganisms in Prandtl nanofluid Darcy–Forchheimer flow across an Inclined Sheet”, Nanomaterials, 12(11), 1791 (2022). https://doi.org/10.3390/nano12111791
6. Yaseen, M., Rawat, S. K., and Kumar, M. “Cattaneo–Christov heat flux model in Darcy–Forchheimer radiative flow of MoS2–SiO2/kerosene oil between two parallel rotating disks”, Journal of Thermal Analysis Calorimetry, 147, pp. 10865–10887 (2022). https://doi.org/10.1007/s10973-022-11248-0
7. Shahid, A., Huang, H., Bhatti, M.M., et al. “Numerical investigation on the swimming of gyrotactic microorganisms in nanofluids through porous medium over a Stretched Surface”, Mathematics, 8(3), 380 (2020). https://doi.org/10.3390/math8030380
8. Alharbi, F.M., Naeem, M., Zubair, M., et al. “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(13), 3954 (2021). https://doi.org/10.3390/molecules26133954
9. Waqas, H., Khan, S.U., Hassan, M., et al. “Analysis on the bioconvection flow of modified second-grade nanofluid containing gyrotactic microorganisms and nanoparticles”, Journal of Molecular Liquids, 291, 111231 (2019). https://doi.org/10.1016/j.molliq.2019.111231
10. Khan, S.U., Waqas, H., Muhammad, T., et. al. “Simultaneous effects of bioconvection and velocity slip in three-dimensional flow of Eyring-Powell nanofluid with Arrhenius activation energy and binary chemical reaction”, Int. Communication of Heat and Mass Transfer, 117, 104738 (2020). https://doi.org/10.1016/j.icheatmasstransfer.2020.104738
11. Muhammad, T., Alamri, S.Z., Waqas, H.D., et al. “Bioconvection flow of magnetized Carreau nanofluid under the influence of slip over a wedge with motile microorganisms”, Journal of Thermal Analysis Calorimetry, 143, pp. 945–957 (2021). https://doi.org/10.1007/s10973-020-09580-4
12. Majeed, A., Golsanami, N., Gong, B., et al. “Analysis of thermal radiation in magneto-hydrodynamic motile gyrotactic micro-organisms flow comprising tiny nanoparticle towards a nonlinear surface with velocity slip”, Alexandria Engineering Journal, 66(1), pp. 543-553 (2023). https://doi.org/10.1016/j.aej.2022.11.012
13. Das, B. and Ahmed, S. “Numerical modeling of bioconvection and heat transfer analysis of Prandtl nanofluid in an inclined stretching sheet: A finite difference scheme”, Numerical Heat Transfer, Part A: Applications, 85(20), pp. 3431–3451 (2023). https://doi.org/10.1080/10407782.2023.2237184
14. Rasheed, H.U., Islam, S., Khan, J., et al. “Numerical solution of chemically reactive and thermally radiative MHD Prandtl nanofluid over a curved surface with convective boundary conditions”, ZAMM‐J. Appl. Math. Mech., e202100125, pp. 1-17 (2021). https://doi.org/10.1002/zamm.202100125
15. Babu, M.J. and Sandeep, N. “Effect of nonlinear thermal radiation on non-aligned bio-convective stagnation point flow of a magnetic-nanofluid over a stretching sheet”, AEJ - Alexandria Engineering Journal, 55(3), pp. 1931–1939 (2016). https://doi.org/10.1016/j.aej.2016.08.001
16. Waqas, H., Farooq, U., Muhammad, T., et al. “Thermal effect on bioconvection flow of Sutterby nanofluid between two rotating disks with motile microorganisms”, Case Studies in Thermal Engineering, 26, 101136 (2021). https://doi.org/10.1016/j.csite.2021.101136
17. Siddiqui, B.K., Batool, S., Malik, M.Y., et al. “Darcy Forchheimer bio-convection flow of Casson nanofluid due to a rotating and stretching disk together with thermal radiation and entropy generation”, Case Studies in Thermal Engineering, 27, 101201 (2021). https://doi.org/10.1016/j.csite.2021.101201.
18. Wang, F., Zhang, J., Algarni, S., et al. “Numerical simulation of hybrid Casson nanofluid flow by the influence of magnetic dipole and gyrotactic microorganism”, Waves in Random and Complex Media, pp. 1–16 (2022). https://doi.org/10.1080/17455030.2022.2032866
19. Wang, F., Asjad, M.I., Rehman, S.U., et al. “MHD Williamson nanofluid flow over a slender elastic sheet of irregular thickness in the presence of Bio-convection”, Nanomaterials, 11, 2297 (2021). https://doi.org/10.3390/nano11092297
20. Wang, F.Z., Asjad, M.I., Zahid, M., et al. “Unsteady thermal transport flow of Casson nanofluids with generalized Mittag-Leffler kernel of Prabhakar’s type”, Journal of Materials Research and Technology, 14, pp. 1292–1300 (2021). https://doi.org/10.1016/j.jmrt.2021.07.029
21. Shampine, L.F., Glandwell, I., and Thomson, S., Solving ODEs with MATLAB, Cambridge, New York, USA: Cambridge University Press, (2003). https://doi.org/10.1017/CBO9780511615542
22. Ahmed, J., Shahzad, A., Farooq, A. et al. “Thermal analysis in swirling flow of titanium dioxide–aluminum oxide water hybrid nanofluid over a rotating cylinder”, J Therm Anal Calorim, 144, pp. 2175–2185 (2021). https://doi.org/10.1007/s10973-020-10190-3
23. Ahmed, A., Khan, M., and Ahmed, J. “Thermal analysis in swirl motion of Maxwell nanofluid over a rotating circular cylinder”, Appl. Math. Mech.-Engl. Ed., 41, pp. 1417–1430 (2020). https://doi.org/10.1007/s10483-020-2643-7
24. Ahmed, J., Shahzad, A., Farooq, A. et al. “Radiative heat transfer in Homann stagnation-point flow of hybrid nanofluid”, Appl Nanosci, 10, pp. 5305–5314 (2020). https://doi.org/10.1007/s13204-020-01464-1
25. Shao, Y., Ahmad, L., Javed, S., et al. “Heat and mass transfer analysis during Homann Visco-elastic slippery motion of nano-materials”, Int. Comm. in Heat and Mass Transfer, 139, 106425 (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106425
26. Khan, M., Ahmed, J., Sultana, F., et al. “Non-axisymmetric Homann MHD stagnation point flow of Al2O3-Cu/water hybrid nanofluid with shape factor impact”, Appl. Math. Mech.-Engl. Ed., 41, pp. 1125–1138 (2020). https://doi.org/10.1007/s10483-020-2638-6
27. Ghoneim, M.E., Ahmed, J., Ali, W., et al. “Carbon nanotubes (CNT) based nanofluid flow due to a rotating cylinder: static and dynamics models”, Microfluid Nanofluid, 26, 83 (2022). https://doi.org/10.1007/s10404-022-02582-8
28. Ahmed, J., Ahmed, A., Sultana, F., et al. “Numerical investigation for non-axisymmetric Homann stagnation point flow of a SWCNT/MWCNT-water nanofluid over a disk”, Waves in Random and Complex Media, 35(1), pp. 162-179 (2025). https://doi.org/10.1080/17455030.2021.2022245
29. Priyadharsini, M., David, M.G.A., Ismail, M.S., et al. “Numerical and sensitivity study on the heat transfer due to bioconvection on unsteady radiative MHD blood flow over a permeable artery with chemical reaction effects”, Int. Comms. in Heat and Mass Transfer, 147, 106981 (2023). https://doi.org/10.1016/j.icheatmasstransfer.2023.106981
30. Priyadharsini, M. and David, M.G.A. “Mathematical modelling and analysis of thermoregulation effects on blood viscosity under magnetic effects and thermal radiation in a permeable stretching capillary”, Journal of Thermal Biology, 111, 103398 (2023). https://doi.org/10.1016/j.jtherbio.2022.103398
31. Priyadharsini, M. “Mathematical analysis of drug-induced chemical reaction on unsteady mhd blood flow with radiation effects through a permeable stretching capillary”, Journal of Porous Media, 26, pp. 63-83 (2023). https://doi.org/10.1615/JPorMedia.2023044167
32. Öztop, H.F., Sakhrieh., A., Abu-Nada, E., et al. “Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure”, Int. Communications in Heat and Mass Transfer, 86, pp. 42-51 (2017). https://doi.org/10.1016/j.icheatmasstransfer.2017.05.011
33. Kolsi, L., Alrashed, A.A.A.A., Al-Salem, K., et al. “Control of natural convection via inclined plate of CNT-water nanofluid in an open sided cubical enclosure under magnetic field”, Int. Journal of Heat and Mass Transfer, 111, pp. 1007-1018 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2017.04.069
34. Selimefendigil, F., Öztop, H.F., and Abu-Hamdeh, N. “Mixed convection due to rotating cylinder in an internally heated and flexible walled cavity filled with SiO2–water nanofluids: effect of nanoparticle shape”, Int. Commun. in Heat and Mass Transfer, 71, pp. 9-19 (2016). https://doi.org/10.1016/j.icheatmasstransfer.2015.12.007
35. Nasir, Md., Waqas, M., Bég, O.A., et al. “Functional magnetic Maxwell viscoelastic nanofluids for tribological coatings- a model for stretching flow using the generalized theory of heat-mass fluxes, Darcy-Forchheimer formulation and dual convection”, Tribology International, 187, 108610 (2023). https://doi.org/10.1016/j.triboint.2023.108610
36. Tabrez, M., Khan, W.A., Taseer, M., et al. “Significance of thermo-dynamical moment of ferromagnetic nanoparticles and bioconvection analysis for magnetized Carreau fluid under the influence of gyrotactic moment of microorganisms”, Tribology International, 186, 108633 (2023). https://doi.org/10.1016/j.triboint.2023.108633
37. Ahmad, A., Anjum, N., Shahid, H., et al. “Impact of Darcy–Forchheimer–Brinkman model on generalized Eyring–Powell liquid subject to Cattaneo–Christov double diffusion aspects”, Int. Journal of Modern Physics, B, 37(18), 2350173 (2023). https://doi.org/10.1142/S0217979223501734
38. Hussain, Z., Khan, W.A., Taseer, M., et al. “Dynamics of gyrotactic microorganisms for chemically reactive magnetized 3D Sutterby nanofluid flow comprising non-uniform heat sink-source aspects”, Journal of Magnetism and Magnetic Materials, 578, 170798 (2023). https://doi.org/10.1016/j.jmmm.2023.170798
39. Anjum, N., Khan, W.A., and Azam, M. “Significance of bioconvection analysis for thermally stratified 3D Cross nanofluid flow with gyrotactic microorganisms and activation energy aspects”, Thermal Science and Engineering Progress, 38, 101596 (2023). https://doi.org/10.1016/j.tsep.2022.101596
40. Nasir, M., Waqas, M., Zamri, N., et al. “Diffusion of dual diffusive chemically reactive Casson nanofluid under Darcy–Forchheimer porosity and Robin conditions from a vertical convective surface: a comparative analysis using HAM and collocation procedures”, Comp. Part. Mech. 10, pp. 1267–1279 (2023). https://doi.org/10.1007/s40571-022-00547-w
41. Waqas, M., Kausar, M. S., and Bég, O. A. “Numerical study of dissipative SW/MWCNT-nanofluid coating flow from a stretching wall to a porous medium with shape factor effects”, Int. Journal of Hydrogen Energy, 48(88), pp. 34536-34550 (2023). https://doi.org/10.1016/j.ijhydene.2023.05.036
42. Hussain, S., Raizah, Z., and Aly, A.M. “Thermal radiation impact on bioconvection flow of nano-enhanced phase change materials and oxytactic microorganisms inside a vertical wavy porous cavity”, Int. Commu. Heat and Mass Transfer, 139, 106454 (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106454
43. Hussain, S., Aly, A.M., and Alsedias, N. “Bioconvection of oxytactic microorganisms with nano-encapsulated phase change materials in an omega-shaped porous enclosure”, Journal of Energy Storage, 56, Part A, 105872 (2022). https://doi.org/10.1016/j.est.2022.105872
44. Hussain, S., Aly, A.M., and Öztop, H.F. “Magneto-bioconvection flow of hybrid nanofluid in the presence of oxytactic bacteria in a lid-driven cavity with a streamlined obstacle”, In. Commu. Heat and Mass Transfer, 134, 106029 (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106029
45. Hussain, S. “Finite element solution for MHD flow of nanofluids with heat and mass transfer through a porous media with thermal radiation, viscous dissipation and chemical reaction effects”, Advances in Applied Mathematics and Mechanics, 9(4), pp. 904-923 (2017). https://doi.org/10.4208/aamm.2014.m793
46. Hussain, S., Jamal, M., Haddad, Z., et al. “Numerical modeling of magnetohydrodynamic thermosolutal free convection of power law fluids in a staggered porous enclosure”, Sustainable Energy Technologies and Assessments, 53, Part A, 102395 (2022). https://doi.org/10.1016/j.seta.2022.102395
47. Li, S., Nasir, M., and Waqas, M., et al. “Bioconvection transport of upper convected Maxwell nano liquid with gyrotactic microorganism, nonlinear thermal radiation, and chemical reaction”, Nanotechnology Reviews, 12, pp. 1-15 (2023). https://doi.org/10.1515/ntrev-2022-0569
48. Elayarani, M., Shanmugapriya, M., and Kumar, P.S. “Intensification of heat and mass transfer process in MHD Carreau nanofluid flow containing gyrotactic microorganisms”, Chem Eng Process – Process Intensif, 160, 108299 (2021).
49. Anjum, N., Khan, W.A., Azam, M., et al. “Significance of bioconvection analysis for thermally stratified 3D cross nanofluid flow with gyrotactic microorganisms and activation energy aspects”, Therm Sci Eng Prog., 38(9), 101596 (2023). https://doi.org/10.1016/j.tsep.2022.101596
50. Khan, A.A., Arshad, A., Ellahi, R., et al. “Heat transmission in Darcy Forchheimer flow of Sutterby nanofluid containing gyrotactic microorganisms”, Int J Numer Methods Heat & Fluid Flow, 33, pp. 135–152 (2023). https://doi.org/10.1108/HFF-03-2022-0194
51. Shahzad, F., Sagheer, M., and Hussain, S. “Transport of MHD nanofluid in a stratified medium containing gyrotactic microorganisms due to a stretching sheet”, Scientia Iranica, F, 28(6), pp. 3786-3805 (2021). https://doi.org/10.24200/SCI.2021.56459.4734
52. Shakiba, A. and Rahimi, A.B. “Reverse flow analysis of hybrid nanofluid MHD mixed convection flow in a vertical cylindrical annulus: An exact solution”, Scientia Iranica, B, 30(5), pp. 1612-1624 (2023). https://doi.org/10.24200/SCI.2023.59823.6446
53. Habibishandiz, M., Saghir, Z., and Zahmatkesh, I. “Thermo-bioconvection performance of nanofluid containing oxytactic microorganisms inside a square porous cavity under constant and periodic temperature boundary conditions”, International Journal of Thermofluids, 17, pp. 1-13 (2023). https://doi.org/10.1016/j.ijft.2022.100269
54. Shamshuddin, M.D., Mabood, F., and Beg, O.A. “Thermomagnetic reactive ethylene glycol-metallic nanofluid transport from a convectively heated porous surface with ohmic dissipation, heat source, thermophoresis and Brownian motion effects”, Int. J. Modell. Simul. 42, pp. 782–796 (2021). https://doi.org/10.1080/02286203.2021.1977531
55. Megahed, A.M. “Improvement of heat transfer mechanism through a Maxwell fluid flow over a stretching sheet embedded in a porous medium and convectively heated”, Math Comput Simul., 187, pp. 97–109 (2022). https://doi.org/10.1016/j.matcom.2021.02.018
56. Khan, M.R., Ahammad, N.A., Alhazmi SE, et al. “En-ergy and mass transport through hybrid nanofluid flow passing over an extended cylinder with the magnetic dipole using a computational approach”, Front. En-ergy Res., 10:980042, pp. 1-14 (2022). https://doi.org/10.3389/fenrg.2022.980042
57. Alqahtani, A.M., Bilal, M., Ali, A., et al. “Numerical solution of an electrically conducting spinning flow of hybrid nanofluid comprised of silver and gold nanoparticles across two parallel surfaces”, Sci Rep 13, 7180, pp. 1-14 (2023). https://doi.org/10.1038/s41598-023-33520-5 
Volume 32, Issue 9
Transactions on Chemical and Geoenergy Engineering
May and June 2025 Article ID:8125
  • Receive Date: 18 August 2023
  • Revise Date: 10 November 2023
  • Accept Date: 04 December 2023