10.57647/j.ijnd.2025.1603.18

Energy transition in bioconvective darcy-forchheimer nanofluid flow: A numerical study

  1. Mechanical Engineering Department, Hamedan University of Technology, Hamedan, Iran
Energy Transition in Bioconvective Darcy-Forchheimer Nanofluid Flow over a Permeable Vertical Plate: A Numerical Study

Received: 2024-03-28

Revised: 2024-12-08

Accepted: 2024-12-14

Published in Issue 2025-06-01

How to Cite

Hajialigol, N. (2025). Energy transition in bioconvective darcy-forchheimer nanofluid flow: A numerical study. International Journal of Nano Dimension, 16(3 (July 2025). https://doi.org/10.57647/j.ijnd.2025.1603.18

PDF views: 279

Abstract

Darcy-Forchheimer nanofluids (NF) can be utilized to develop oil recovery efficiency from oil reservoirs. Nanoparticles in the NF can aid in increasing rock permeability, reducing oil viscosity, and facilitating oil flow to wells. Unsteady Darcy-Forschheimer NF bioconvective flow with activation energy and Arrhenius chemical reaction on a permeable tensile surface was investigated. The flow equations are partial differential equations that are translated into ordinary differential equations (ODE) using suitable similarity transformations. Runge–Kutta integration with the shooting method of modified Newton–Raphson methods was used to resolve these ODEs numerically. Several graphs and tables were utilized to display how changes in the evolving parameters influence the flow fields. The result demonstrated that the unsteadiness parameter, porous medium permeability, Hartmann number, porosity parameter, and Grashof parameter increased the velocity profile, while the buoyancy ratio decreased it. Unsteadiness parameter, Hartmann number, buoyancy ratio, bioconvective Rayleigh number, Prandtl number, Eckert number, and internal heat generation raised the temperature profile. The porosity parameter, Grashof number, and radiation parameter led to a decrease in temperature profile. The unsteadiness parameter, Hartmann number, buoyancy ratio, thermophoresis, Prandtl number, and Eckert number reduced the concentration profile. The growth of the parameter of internal heat generation had almost no effect on the concentration profile. The radiation parameter and Brownian motion enhanced the concentration profile.

Keywords

  • Activation energy,
  • Magnetohydrodynamics,
  • Porous medium,
  • Darcy-Forchheimer,
  • Nanofluid

References

  1. Goldstein R. E., (2015), Green algae as model organisms for biological fluid dynamics. Annual Review of Fluid Mechanics, 47, 343–375. https://doi.org/10.1146/annurev-fluid-010313-141426
  2. Cussler E. L., (2009), Bioconvection. Annual Review of Fluid Mechanics, 41: 87–110. https://journals.scholarsportal.info/browse/00664189.
  3. Patten, J. (2016). Bioconvection: A new approach to drug delivery. Trends in Biotechnology, 34(11), 878–887.
  4. Friedrichs M., Holzner M., (2009), Pattern formation in bioconvection triggered by the gradient of light. Experiments in Fluids, 47(5): 753–761. 10.1007/978-1-0716-0421-2_214
  5. Elgeti J., Gompper G. (2013), Emergence of metachronal waves in cilia arrays. Proceedings of the National Academy of Sciences, 110(12): 4470–4475. https://doi.org/10.1073/pnas.1218869110
  6. Zhang L., Wang P., (2016). Enhanced biofuel production through bioconvection. Bioresource Technology, 218: 581–588. https://doi.org/10.1016/j.wasman.2007.10.009
  7. Shafiq A., Sindhu T. N. (2017), Statistical study of hydromagnetic boundary layer flow of Williamson fluid regarding a radiative surface. Results in Physics, 7: 3059-3067. DOI: https://doi.org/10.1016/j.rinp.2017.07.077
  8. Choi U. S., (1995), Enhancing Thermal Conductivity of Fluids with Nanoparticles, in Developments and Applications of non-Newtonian Flows. vol. 231, Amer. Soc.Mech. Eng., New York pp. 99–105. https://www.researchgate.net/publication/236353373_Enhancing_thermal_conductivity_of_fluids_with_nanoparticles
  9. Shafiq A., Sindhu T. N., Al-Mdallal Q. M. (2021), A sensitivity study on carbon nanotubes significance in Darcy–Forchheimer flow towards a rotating disk by response surface methodology. Scientific Reports, 11: 8812. DOI: https://doi.org/10.1038/s41598-021-87956-8
  10. Shafiq A., Çolak A. B., Sindhu T. N. (2023), Construction of neural network based intelligent computing for treatment of Darcy-Forchheimer sisko nanofluid flow with Rosseland's radiative process. Heat Transfer Research, 54(9): 77-98. DOI: 10.1615/HeatTransRes.2023046617.
  11. Shafiq A., Çolak A. B., Sindhu T. N. (2024), Comparative analysis to study the Darcy–Forchheimer Tangent hyperbolic flow towards cylindrical surface using artificial neural network: An application to Parabolic Trough Solar Collector. 216: 213-230. DOI: https://doi.org/10.1016/j.matcom.2023.09.014
  12. Shafiq A., Çolak A. B., Sindhu T. N., Muhammad T. (2022), Optimization of Darcy-Forchheimer squeezing flow in nonlinear stratified fluid under convective conditions with artificial neural network. Heat Transfer Research, 53(3): 67-89. DOI: 10.1615/HeatTransRes.2021041018
  13. Çolak A. B., Shafiq A., Sindhu T. N. (2022), Modeling of Darcy–Forchheimer bioconvective Powell Eyring nanofluid with artificial neural network. Chinese Journal of Physics, 77: 2435-2453. DOI: https://doi.org/10.1016/j.cjph.2022.04.004
  14. Shafiq A., Çolak A. B., Sindhu T. N. (2023), Optimization of the numerical treatment of the Darcy–Forchheimer flow of Ree–Eyring fluid with chemical reaction by using artificial neural networks. International Journal for Numerical Methods in Fluids, 95910: 176-192. DOI: https://doi.org/10.1002/fld.5147
  15. Shafiq A., Çolak A. B., Sindhu T. N. (2023), Modeling of Darcy‐Forchheimer magnetohydrodynamic Williamson nanofluid flow towards nonlinear radiative stretching surface using artificial neural network. International Journal for Numerical Methods in Fluids, 95(9): 1502-1520. DOI: https://doi.org/10.1002/fld.5216
  16. Shafiq A., Çolak A. B., Sindhu T. N. (2021), Designing an artificial neural network of nanoparticle diameter and solid-fluid interfacial layer on single-walled carbon nanotubes/ethylene glycol nanofluid flow on thin slendering needles. International Journal for Numerical Methods in Fluids, 93(12): 3384-3404. DOI: https://doi.org/10.1002/fld.5038
  17. Shafiq A., Çolak A. B., Sindhu T. N. (2023), Modeling of Soret and Dufour's convective heat transfer in nanofluid flow through a moving needle with artificial neural network. Arabian Journal for Science and Engineering, 48: 2807–2820. DOI: https://doi.org/10.1007/s13369-022-06945-9
  18. Jawad M., Mebarek-Oudina F., Vaidya H., Prashar P. (2022), Influence of bioconvection and thermal radiation on MHD Williamson non-Casson fluid flow with the swimming of gyrotactic microorganisms due to porous stretching sheet. J. Nanofluids, 11(4): 500-509. DOI: https://doi.org/10.1166/jon.2022.1863
  19. Sharma B. K., Gandhi R. (2022), Combined effects of joule heating and non-uniform heat source/sink on unsteady MHD mixed convective flow over a vertical stretching surface embedded in a darcy-forchheimer porous medium. Propulsion and power research (2): 276-292. https://doi.org/10.1016/j.jppr.2022.06.001
  20. Shafiq A., Lone S. A., Sindhu T. N., Nonlaopon K. (2022), Statistical modelling for the Darcy–Forchheimer flow of Casson cobalt ferrite-water/ethylene glycol nanofluid under nonlinear radiation. Symmetry, 14(8): 1717. https://doi.org/10.3390/sym14081717
  21. Shafiq A., Mebarek-Oudina F., Sindhu T. N., Rasool G. (2022), Sensitivity analysis for Walters-B nanoliquid flow over a radiative Riga surface by RSM. Scientia Iranica, 29(3): 1236-1249. DOI: 10.24200/SCI.2021.58293.5662
  22. Tadesse F. B., Makinde O. D., Enyadene L. G., (2021). Hydromagnetic stagnation point flow of a magnetic ferrofluid past a convectively heated permeable stretching/shrinking sheet in a darcy-forchheimer porous medium. International Research Journal Pharm. vol 7: 107-115. https://doi.org/10.1007/s12046-021-01643-y
  23. Vedavathi N., Dharmaiah G., Venkatadri K., Gaffar, S. A. (2021), Numerical study of radiative non-Darcy nanofluid flow over a stretching sheet with convective Nield conditions and energy activation. Nonlinear Engineering, 10(1): 159-176. 10.1515/nleng-2021-0012
  24. Shafiq A., Çolak A. B., Sindhu T. N. (2023), Analyzing activation energy and binary chemical reaction effects with artificial intelligence approach in axisymmetric flow of third grade nanofluid subject to Soret and Dufour effects. Heat Transfer Research, 54(3): 75-94. DOI: 10.1615/HeatTransRes.2022045008
  25. Zhang L., Bhatti M. M., Shahid A., Ellahi R., Bég O. A., Sait S. M. (2021), Nonlinear nanofluid fluid flow under the consequences of Lorentz forces and Arrhenius kinetics through a permeable surface: A robust spectral approach. Journal of the Taiwan Institute of Chemical Engineers, 124: 98-105. www.elsevier.com/locate/jtice
  26. Khan A., Saeed A., Tassaddiq A., Gul T., Mukhtar S., Kumam P., & Kumam W. (2021), Bio-convective micropolar nanofluid flow over thin moving needle subject to Arrhenius activation energy, viscous dissipation and binary chemical reaction. Case Studies in Thermal Engineering, 25: 100-989. https://doi.org/10.1016/j.csite.2021.100989.
  27. Shafiq A., Sindhu T. N., Khalique C. M. (2020), Numerical investigation and sensitivity analysis on bioconvective tangent hyperbolic nanofluid flow towards stretching surface by response surface methodology. Alexandria Engineering Journal, 59(6): 4533-4548. DOI: https://doi.org/10.1016/j.aej.2020.08.007
  28. Bhatti M. M., Al-Khaled K., Khan S. U., Chammam W., & Awais M. (2023), Darcy–Forchheimer higher-order slip flow of Eyring–Powell nanofluid with nonlinear thermal radiation and bioconvection phenomenon. Journal of Dispersion Science and Technology, 44(2): 225-235. DOI:10.1080/01932691.2021.1942035
  29. Habib U., Abdal S., Siddique I., & Ali R. (2021), A comparative study on micropolar, Williamson, Maxwell nanofluids flow due to a stretching surface in the presence of bioconvection, double diffusion and activation energy. International Communications in Heat and Mass Transfer, 127: 105-551. DOI:10.1016/j.icheatmasstransfer.2021.105551
  30. Rahman M., Haq F., Darab P. C., Sallah M., Abdelmohsen S. A., Fadhl B. M., Makhdoum, B. M. (2023), Mixed convection and activation energy impacts on MHD bioconvective flow of nanofluid with irreversibility assessment. Heliyon, 9(6). DOI:10.1016/j.heliyon.2023.e16490
  31. Jawad M., Saeed A., Gul T., & Bariq A. (2021), MHD Darcy-Forchheimer flow of Casson nanofluid due to a rotating disk with thermal radiation and Arrhenius activation energy. Journal of Physics Communications, 5(2): 025008.
  32. Tamilzharasan B. M., Karthikeyan S., Kaabar M. K., Yavuz M., Özköse F. (2022), Magneto mixed convection of Williamson nanofluid flow through a double stratified porous medium in attendance of activation energy. Mathematical and Computational Applications, 27(3): 46. DOI 10.1088/2399-6528/abe4e0
  33. Rashid S., Khan M. I., Hayat T., Ayub M., Alsaedi A. (2020), Darcy–Forchheimer flow of Maxwell fluid with activation energy and thermal radiation over an exponential surface. Appl. Nanosci, 10: 2965–2975. DOI:10.1007/s13204-019-01008-2
  34. Shafiq A., Rasool G., & Khalique C. M. (2020), Significance of thermal slip and convective boundary conditions in three-dimensional rotating darcy-forchheimer nanofluid flow. Symmetry 12: 741. DOI:10.3390/sym12050741
  35. Hayat T., Aziz A., Muhammad T., & Alsaedi A. (2017), Darcy–Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface. Commun. Theor. Phys. 68: 387–394. 10.1088/0253-6102/68/3/387
  36. Bestman A.R. (1990), Natural convection boundary layer with suction mass transfer in a porous medium. Int. J. Energy Res. 14: 389–396. https://doi.org/10.1002/er.4440140403
  37. Dawar A., Shah Z., Islam S. (2021), Mathematical modelling and study of MHD flow of Williamson nanofluid over a nonlinear stretching plate with activation energy. Heat Transfer, 50: 2558–2570. https://doi.org/10.1002/htj.21992
  38. Alsaadi F. E., Hayat T., Khan M.I., & Alsaadi F.E. (2020), Heat transport and entropy optimization inflow of magneto-Williamson nanomaterial with Arrhenius activation energy. Comput. Methods Programs Biomed. 183, 105051. DOI: 10.1016/j.cmpb.2019.105051
  39. Muhammad R., Khan, M.I., Jameel, M., Khan N.B. (2020), Fully developed Darcy-Forchheimer mixed convective flow over a curved surface with activation energy and entropy generation. Comput. Methods Programs Biomed. 188, 105298. DOI: 10.1016/j.cmpb.2019.105298
  40. Danook S.H., Jasim, Q.K., Hussein A.M. (2020), Nanofluid Convective Heat Transfer Enhancement Elliptical Tube inside Circular Tube under Turbulent Flow. Math. Comput. Appl. 23, 78. https://doi.org/10.3390/mca23040078
  41. Jamshed W., Goodarzi M., Prakash M., Nisar K.S., Zakarya M., Abdel-Aty A.H. (2021), Evaluating the unsteady Casson nanofluid over a stretching sheet with solar thermal radiation: An optimal case study. Case Stud. Therm. Eng. 26: 101- 160. https://doi.org/10.1016/j.csite.2021.101160
  42. Alghamdi M., Wakif A., Thumma T., Khan U. (2021), Case Studies in Thermal Engineering Significance of variability in magnetic field strength and heat source on the radiative-convective motion of sodium alginate-based nanofluid within a Darcy-Brinkman porous structure bounded vertically by an irregular slender surface. Case Stud. Therm. Eng. 28, 101428. https://doi.org/10.1016/j.csite.2021.101428
  43. Arain M. B., Bhatti M. M., Zeeshan A., Saeed T., & Hobiny A. (2020), Analysis of Arrhenius kinetics on multiphase flow between a pair of rotating circular plates. Mathematical Problems in Engineering, 1-17. DOI:10.1155/2020/2749105
  44. Algehyne E.A., El-Zahar E.R., Elhag S.H., (2022), Investigation of thermal performance of Maxwell hybrid nanofluid boundary value problem in vertical porous surface via finite element approach. Sci Rep 12: 2335. DOI:10.1038/s41598-022-06213-8
  45. Shafiq A., Mebarek-Oudina F., Sindhu T. N., Abidi A. (2021), A study of dual stratification on stagnation point Walters' B nanofluid flow via radiative Riga plate: a statistical approach. The European Physical Journal Plus, 136: 407. DOI: https://doi.org/10.1140/epjp/s13360-021-01394-z