[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Bioconvection in Porous Square Cavity Containing Oxytactic Microorganisms in the Presence of Viscous Dissipation

Discontinuity, Nonlinearity, and Complexity 11(2) (2022) 301--313 | DOI:10.5890/DNC.2022.06.009

Ramesh Alluguvelli$^{1}$, Chandra Shekar Balla$^{2 }$, Kishan Naikoti$^{3}$

$^{1}$ Department of Mathematics, Geethanjali College of Engineering and Technology, Cheeryal, Telangana,

501301, India

$^{2}$ Department of Mathematics, Chaitanya Bharathi Institute of Technology, Gandipet, Hyderabad, Telangana,

500075, India

$^{3}$ Department of Mathematics, Osmania University, Hyderabad, Telangana 500007, India

Download Full Text PDF

 

Abstract

This is paper reports an investigation of oxytacic-bioconvective flow in a porous square cavity under the influence of viscous dissipation. Darcy model of Boussinesq approximation is employed to formulate the bioconvective flow in the porous medium. The governing nonlinear partial differential equations are nondimensionalised using suitable dimensionless parameters then solved by Galerkin finite element method. The computational numerical results are described by the surface plots of stream function, temperature, concentrations of oxygen and microorganisms, average Nusselt number, average Sherwood numbers of concentrations of oxygen and microorganisms. The effects of key parameters such as Peclet number (Pe), Rayleigh number of bioconvection (Rb), Eckert number (Ec), Lewis number (Le) and Rayleigh number (Ra) are presented and inspected. Eckert number (Ec) and Peclet number (Pe) improve the bioconvection flow and rate of heat transfer. It is also observed that the isoconcentration patterns of oxygen and microorganism density are controlled by Ec and Pe.

References

  1. [1]  Nield, D.A. and Simmons, C.T. (2019), A Brief introduction to convection in porous media, Transport in Porous Media, 130(1), 237-250.
  2. [2]  Vafai, K. (2005), Hand Book of Porous Media. 2nd edn New York.
  3. [3]  Pop, I. and Ingham, D.B. (2001), Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media, Elsevier.
  4. [4]  Rahman, M.M., Pop, I., and Saghir, M.Z. (2019), Steady free convection flow within a titled nanofluid saturated porous cavity in the presence of a sloping magnetic field energized by an exothermic chemical reaction administered by Arrhenius kinetics, International Journal of Heat and Mass Transfer, 129, 198-211.
  5. [5]  Chandra Sekhar, B., Kishan, N., and Haritha, C. (2017), Convection in nanofluid-filled porous cavity with heat absorption/generation and radiation, Journal of Thermophysics and Heat Transfer, 31(3), 549-562.
  6. [6]  Balla, C.S., Kishan, N., Gorla, R.S., and Gireesha, B.J. (2017), MHD boundary layer flow and heat transfer in an inclined porous square cavity filled with nanofluids, Ain Shams Engineering Journal, 8(2), 237-254.
  7. [7]  Chandra Shekar, B., Haritha, C., and Kishan, N. (2019), Magnetohydrodynamic convection in a porous square cavity filled by a nanofluid with viscous dissipation effects, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 233(3), 474-488.
  8. [8]  Childress, S., Levandowsky, M., and Spiegel, E.A. (1975), Pattern formation in a suspension of swimming microorganisms: equations and stability theory, Journal of Fluid Mechanics, 69(3), 591-613.
  9. [9]  Pedley, T.J., Hill, N.A., and Kessler, J.O. (1988), The growth of bioconvection patterns in a uniform suspension of gyrotactic micro-organisms, Journal of Fluid Mechanics, 195, 223-237.
  10. [10]  Hill, N.A., Pedley, T.J., and Kessler, J.O. (1989), Growth of bioconvection patterns in a suspension of gyrotactic micro-organisms in a layer of finite depth, Journal of Fluid Mechanics, 208, 509-543.
  11. [11]  Hillesdon, A.J., Pedley, T.J., and Kessler, J.O. (1995), The development of concentration gradients in a suspension of chemotactic bacteria, Bulletin of mathematical biology, 57(2), 299-344.
  12. [12]  Hillesdon, A.J. and Pedley, T.J. (1996), Bioconvection in suspensions of oxytactic bacteria: linear theory, Journal of Fluid Mechanics, 324, 223-259.
  13. [13]  Becker, S.M., Kuznetsov, A.V., and Avramenko, A.A. (2004), Numerical modeling of a falling bioconvection plume in a porous medium, Fluid Dynamics Research, 35(5), 323.
  14. [14]  Kuznetsov, A.V. (2005), Thermo-bioconvection in a suspension of oxytactic bacteria, International communications in heat and mass transfer, 32(8), 991-999.
  15. [15]  Kuznetsov, A.V. (2005), Investigation of the onset of thermo-bioconvection in a suspension of oxytactic microorganisms in a shallow fluid layer heated from below, Theoretical and Computational Fluid Dynamics, 19(4), 287-299.
  16. [16]  Sheremet, M.A. and Pop, I. (2014), Thermo-bioconvection in a square porous cavity filled by oxytactic microorganisms, Transport in Porous Media, 103(2), 191-205.
  17. [17]  Kuznetsov, A.V. (2006), The onset of thermo-bioconvection in a shallow fluid saturated porous layer heated from below in a suspension of oxytactic microorganisms, European Journal of Mechanics-B/Fluids, 25(2), 223-233.
  18. [18]  Ahmed, S.E., Oztop, H.F., Mansour, M.A., and Abu-Hamdeh, N. (2018), Magnetohydrodynamic mixed thermo-bioconvection in porous cavity filled by oxytactic microorganisms, Thermal Science, 22(6 Part B), 2711-2721.
  19. [19]  Raz, O. and Avron, J.E. (2007), Swimming, pumping and gliding at low Reynolds numbers, New Journal of Physics, 9(12), 437.
  20. [20]  Weibel, D.B., Garstecki, P., Ryan, D., DiLuzio, W.R., Mayer, M., Seto, J.E., and Whitesides, G.M. (2005), Microoxen: Microorganisms to move microscale loads, Proceedings of the National Academy of Sciences, 102(34), 11963-11967.
  21. [21]  Desouky, S.M., Abdel-Daim, M.M., Sayyouh, M.H., and Dahab, A.S. (1996), Modelling and laboratory investigation of microbial enhanced oil recovery, Journal of Petroleum Science and Engineering, 15(2-4), 309-320.
  22. [22]  Saranya, S. and Radha, K.V. (2014), Review of nanobiopolymers for controlled drug delivery, Polymer-Plastics Technology and Engineering, 53(15), 1636-1646.
  23. [23]  Balla, C.S., Alluguvelli, R., Naikoti, K., and Makinde, O.D. (2020), Effect of chemical reaction on bioconvective flow in oxytactic microorganisms suspended porous cavity, Journal of Applied and Computational Mechanics, 6(3), 653-664.
  24. [24]  Balla, C.S., Haritha, C., Naikoti, K., and Rashad, A.M. (2019), Bioconvection in nanofluid-saturated porous square cavity containing oxytactic microorganisms, International Journal of Numerical Methods for Heat {$\&$ Fluid Flow}.
  25. [25]  Balla, C.S. and Naikoti, K. (2019), Numerical Solution of MHD Bioconvection in a Porous Square Cavity due to Oxytactic Microorganisms, Applications and Applied Mathematics, Special Issue 4, 69-81.
  26. [26]  Balla, C.S., Ramesh, A., Kishan, N., Rashad, A.M., and Abdelrahman, Z.M.A. (2019), Bioconvection in oxytactic microorganism-saturated porous square enclosure with thermal radiation impact, Journal of Thermal Analysis and Calorimetry, 1-9.
  27. [27]  Chamkha, A.J., Rashad, A.M., Kameswaran, P.K., and Abdou, M.M.M. (2017), Radiation effects on natural bioconvection flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with streamwise temperature variation, Journal of Nanofluids, 6(3), 587-595.
  28. [28]  Khan, W.A., Rashad, A.M., Abdou, M.M.M., and Tlili, I. (2019), Natural bioconvection flow of a nanofluid containing gyrotactic microorganisms about a truncated cone. European Journal of Mechanics-B/Fluids, 75, 133-142.
  29. [29]  Rashad, A.M. and Nabwey, H.A. (2019), Gyrotactic mixed bioconvection flow of a nanofluid past a circular cylinder with convective boundary condition, Journal of the Taiwan Institute of Chemical Engineers, 99, 9-17.
  30. [30]  Mansour, M.A., Rashad, A.M., Mallikarjuna, B., Hussein, A.K., Aichouni, M., and Kolsi, L. (2019), MHD mixed bioconvection in a square porous cavity filled by gyrotactic microorganisms, Int J Heat Technol, 37(2), 433-445.
  31. [31]  Ferdows, M., Zaimi, K., Rashad, A.M., and Nabwey, H.A. (2020), MHD Bioconvection Flow and Heat Transfer of Nanofluid through an Exponentially Stretchable Sheet, Symmetry, 12(5), 692.
  32. [32]  Alluguvelli, R., Balla, C.S., Bandari, L., and Naikoti, K. (2020, October), Investigation on natural convective flow of ethylene glycol nanofluid containing nanoparticles Fe3O4 in a porous cavity with radiation. In AIP Conference Proceedings, 2269(1), p. 060004, AIP Publishing LLC.
  33. [33]  Gebhart, B. (1962), Effects of viscous dissipation in natural convection. Journal of fluid Mechanics, 14(2), 225-232.
  34. [34]  Mahajan, R.L. (1989), Viscous dissipation effects in buoyancy induced flows. International journal of heat and mass transfer, 32(7), 1380-1382.
  35. [35]  Mallesh, M.P., Rajesh, V., Kavitha, M., and Chamkha, A.J. (2020, July), Study of time dependent free convective kerosene-nanofluid flow with viscous dissipation past a porous plate, In AIP Conference Proceedings, 2246(1), p. 020009, AIP Publishing LLC.
  36. [36]  Haritha, C., Shekar, B.C., and Kishan, N. (2018), MHD Natural Convection Heat Transfer in a Porous Square Cavity Filled by Nanofluids with Viscous Dissipation, J. Nanofluids, $7$, 928-938.
  37. [37]  Gireesha, B.J., Kumar, K.G., Rudraswamy, N.G., and Manjunatha, S. (2018), Effect of viscous dissipation on three dimensional flow of a nanofluid by considering a gyrotactic microorganism in the presence of convective condition, In Defect and Diffusion Forum 388, pp. 114-123, Trans Tech Publications Ltd.
  38. [38]  Uddin, M.J., Khan, W.A., and Ismail, A.I. (2013), Effect of dissipation on free convective flow of a non-Newtonian nanofluid in a porous medium with gyrotactic microorganisms, Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 227(1), 11-18.
  39. [39]  Khan, U., Ahmed, N., and Mohyud-Din, S.T. (2016), Influence of viscous dissipation and Joule heating on MHD bio-convection flow over a porous wedge in the presence of nanoparticles and gyrotactic microorganisms, SpringerPlus, 5(1), 2043.
  40. [40]  Reddy, J.N. (2004), An introduction to the finite element method, 1221, New York: McGraw-Hill.
  41. [41]  Kishan, N. and Shekar, B.C. (2015), Finite element analysis of fully developed unsteady MHD convection flow in a vertical rectangular duct with viscous dissipation and heat source/sink, Journal of Applied Science and Engineering, 18(2), 143-152.
  42. [42]  Manole, D.M. (1992), Numerical benchmark results for natural convection in a porous medium cavity. In Heat and Mass Transfer in Porous Media, ASME Conference 1992, 216, pp. 55-60.
  43. [43]  Baytas, A.C. and Pop, I. (1999), Free convection in oblique enclosures filled with a porous medium, International Journal of Heat and Mass Transfer, 42(6), 1047-1057.
  44. [44]  Revnic, C., Grosan, T., Pop, I., and Ingham, D.B. (2009), Free convection in a square cavity filled with a bidisperse porous medium, International Journal of Thermal Sciences, 48(10), 1876-1883.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates