Skip to main content
SpringerLink
Log in

Internal heat generation on bioconvection of an MHD nanofluid flow due to gyrotactic microorganisms

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The principal aim of this paper is to analyse the two-dimensional magnetohydrodynamic flow and heat and mass transfer phenomena of water-based nanofluid containing gyrotactic microorganisms over a vertical plate by means of heat generation or absorption. Set of nonlinear ordinary differential equations are derived from the governing partial differential equations of the two-dimensional flow of MHD nanofluid and nanoparticles by utilizing appropriate similarity transformations. The numerical results are obtained with the proposed novel spectral relaxation method. The results revealed that in the heat and mass transfer, the motile microorganism flux rates as well as the velocity profiles are decreased throughout the fluid medium with the impact of magnetic field strength. Moreover, the drag stress rate and motile microorganism profiles are increased with the enhancement of magnetic field. Even though the problem of nanofluid has been broadly investigated, limited discoveries can be found through a gyrotactic microorganisms. Indeed, this paper managed to obtain the numerical analysis is performed. Furthermore, the authors also considered the MHD phenomena, heat generation or absorption effects. Very few studies in the fluid with gyrotactic microorganisms embedded in this parameter in their problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. A.I. Alsabery, I. Hashim, A. Hajjar, M. Ghalambaz, S. Nadeem, M. Saffari Pour, Entropy generation and natural convection flow of hybrid nanofluids in a partially divided wavy cavity including solid blocks. Energies 13, 2942 (2020)

    Google Scholar 

  2. A. Aziz, W.A. Khan, I. Pop, Free convection boundary layer flow past a horizontal flat plate embedded in porous medium filled by nanofluid containing gyrotactic microorganisms. Int. J. Therm. Sci. 56, 48–57 (2012)

    Google Scholar 

  3. A. Bejan, Convection Heat Transfer, 2nd edn. (Wiley, New York, 1995)

    MATH  Google Scholar 

  4. J. Buongiorno, Convective transport in nanofluids. ASME J. Heat Transf. 128, 240–250 (2006)

    Google Scholar 

  5. J. Buongiorno, W. Hu, Nanofluid coolants for advanced nuclear power plants. Paper No. 5705, Proceedings of ICAPP’05, Seoul, May 15–19 (2005)

  6. C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics (Springer, Berlin, 1988)

    MATH  Google Scholar 

  7. T. Chakraborty, K. Das, K. Prabir Kumar, Framing the impact of external magnetic field on bioconvection of a nanofluid flow containing gyrotactic microorganisms with convective boundary conditions. Alex. Eng. J. 57, 61–71 (2018)

    Google Scholar 

  8. H. Chen, J. Chen, Y. Geng, K. Chen, K. Chen, Three-dimensional boundary layer flow over a rotating disk with power law stretching in a nanofluid containing gyrotactic microorganisms. Heat Transf. Asian Res. 47(3), 569–582 (2018)

    MathSciNet  Google Scholar 

  9. W. Duangthongsuk, S. Wongwises, Effect of thermophysical properties models on the predicting of the convective heat transfer coefficient for low concentration nanofluid. Int. Commun. Heat Mass Transf. 35(10), 1320–1326 (2008)

    Google Scholar 

  10. K. Ganesh Kumar, B.J. Gireesha, S. Manjunatha, N.G. Rudraswamy, “Effect of nonlinear thermal radiation on double-diffusive mixed convection boundary layer flow of viscoelastic nanofluid over a stretching sheet. Int. J. Mech. Mater. Eng. 12, 18 (2017)

    Google Scholar 

  11. K. Gangadhar, T. Kannan, P. Jayalakshmi, Magnetohydrodynamic micropolar nanofluid past a permeable stretching/shrinking sheet with Newtonian heating. J. Braz. Soc. Mech. Sci. Eng. 39, 4379–4391 (2017)

    Google Scholar 

  12. K. Gangadhar, T. Kannan, G. Sakthivel, K. Dasaradha Ramaiah, Unsteady free convective boundary layer flow of a nanofluid past a stretching surface using a spectral relaxation method. Int. J. Ambient Energy 41(6), 609–616 (2020)

    Google Scholar 

  13. K. Gangadhar, K. Keziya, S.M. Ibrahim, Effect of thermal radiation on engine oil nanofluid flow over a permeable wedge under convective heating: Keller box method. Multidiscip. Model. Mater. Struct. 15(1), 187–205 (2019)

    Google Scholar 

  14. K. Gangadhar, N.S.L.V. Narasimharao, B. Satyanarayana, Thermal diffusion and viscous dissipation effects on heat and mass filled with TiO2 and Al2O3 water based nanofluids. Comput. Therm. Sci. 11(6), 523–539 (2019)

    Google Scholar 

  15. P. Geng, A.V. Kuznetsov, Introducing the concept of effective diffusivity to evaluate the effect of bioconvection on small solid particles. Int. J. Transp. Phenom. 7, 321–338 (2005)

    Google Scholar 

  16. M. Ghalambaz, T. Grosan, I. Pop, 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. J. Mol. Liq. 293, 111432 (2019)

    Google Scholar 

  17. S. Ghorai, N.A. Hill, Development and stability of gyrotactic plumes in bioconvection. J. Fluid Mech. 400, 1–31 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  18. A. Hajjar, S.A.M. Mehryan, M. Ghalambaz, Time periodic natural convection heat transfer in a nano-encapsulated phase—change suspension. Int. J. Mech. Sci. 166, 105243 (2020)

    Google Scholar 

  19. N.A. Hill, T.J. Pedley, 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)

    ADS  MathSciNet  MATH  Google Scholar 

  20. T. Ishikawa, Suspension biomechanics of swimming microbes. J. R. Soc. Interface 6(39), 815–834 (2009)

    Google Scholar 

  21. W.A. Khan, O.D. Makinde, MHD nanofluid bioconvection due to gyrotactic microorganisms over a convectively heat stretching sheet. Int. J. Therm. Sci. 81, 118–124 (2014)

    Google Scholar 

  22. W.A. Khan, I. Pop, Boundary-layer flow of a nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53, 2477–2483 (2010)

    MATH  Google Scholar 

  23. W.A. Khan, O.D. Makinde, Z.H. Khan, MHD boundary layer flow of a nanofluid containing gyrotactic microorganisms past a vertical plate with Navier slip. Int. J. Heat Mass Transf. 74, 285–291 (2014)

    Google Scholar 

  24. A.V. Kuznetsov, Bio-thermal convection induced by two different species of microorganisms. Int. Commun. Heat Mass Transf. 38, 548–553 (2011)

    Google Scholar 

  25. A.V. Kuznetsov, Nanofluid bioconvection in water-based suspensions containing nanoparticles oxytactic microorganisms: oscillatory instability. Nanoscale Res. Lett. 6, 1–13 (2011)

    Google Scholar 

  26. A.V. Kuznetsov, D.A. Nield, 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 Transf. 65, 682–685 (2013)

    Google Scholar 

  27. A. Mahdy, Natural convection boundary layer flow due to gyrotactic microorganisms about a vertical cone in porous media saturated by a nanofluid. J. Braz. Soc. Mech. Sci. Eng. 38, 67–76 (2016)

    Google Scholar 

  28. A. Malvandi, F. Hedayati, D.D. Ganji, Nanofluid flow on the stagnation point of a permeable non-linearly stretching/shrinking sheet. Alex. Eng. J. 57, 2199–2208 (2018)

    Google Scholar 

  29. M.F.M. Basir, Rakesh Kumar, A.I.M. Ismail, G. Sarojamma, P.V. Satya Narayana, J. Raza, A. Mahmood, Exploration of thermal-diffusion and diffusion-thermal effects on the motion of temperature-dependent viscous fluid conveying microorganism. Arab. J. Sci. Eng. 44, 8023–8033 (2019)

    Google Scholar 

  30. A.M. Megahed, MHD viscous Casson fluid flow and heat transfer with second-order slip velocity and thermal slip over a permeable stretching sheet in the presence of internal heat generation/absorption and thermal radiation. Eur. Phys. J. Plus 130, 81 (2015)

    Google Scholar 

  31. S.S. Motsa, A new spectral relaxation method for similarity variable nonlinear boundary layer flow systems. Chem. Eng. Commun. 201(2), 241–256 (2014)

    Google Scholar 

  32. T.J. Pedley, N.A. Hill, J.O. Kessler, The growth of bioconvection patterns in a uniform suspension of gyrotactic microorganisms. J. Fluid Mech. 195, 223–237 (1988)

    ADS  MathSciNet  MATH  Google Scholar 

  33. A. Raees, M. Raees-ul-Haq, H. Xu, Q. Sun, Three-dimensional stagnation flow of a nanofluid containing both nanoparticles and microorganisms on a moving surface with anisotropic slip. Appl. Math. Model. 40(5-6), 4136–4150 (2016)

    MathSciNet  MATH  Google Scholar 

  34. P. Rana, R. Bhargava, Numerical study of heat transfer enhancement in mixed convection flow along a vertical plate with heat source/sink utilizing nanofluids. Commun. Nonlinear Sci. Numer. Simul. 16(11), 4318–4334 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  35. S. Reddy, A.J. Chamkha, Soret and Dufour effects on MHD convective flow of Al2O3-water and TiO2-water nanofluids past a stretching sheet in porous media with heat generation/absorption. Adv. Powder Technol. 27, 1207–1218 (2016)

    Google Scholar 

  36. J. Reza, F. Mebarek-Oudina, O.D. Makinde, MHD slip flow of Cu-Kerosene nanofluid in a channel with stretching walls using 3-stage LobattoIiia formula. Defect Diffus. Forum 387, 51–62 (2018)

    Google Scholar 

  37. A.V. Rosca, MdJ Uddin, I. Pop, Boundary layer flow over a moving vertical flat plate with convective thermal boundary condition. Bull. Malays. Math. Sci. Soc. 39, 1287–1306 (2016)

    MathSciNet  MATH  Google Scholar 

  38. H. Sardar, L. Ahmad, M. Khan, Investigation of mixed convection flow of Carreau nanofluid over a wedge in the presence of Soret and Dufour effects. Int. J. Heat Mass Transf. 137, 809–822 (2019)

    Google Scholar 

  39. M. Sheikholeslami, D.D. Ganji, M.Y. Javed, R. Ellahi, Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two-phase model. J. Magn. Magn. Mater. 374, 36–43 (2015)

    ADS  Google Scholar 

  40. S. Siddiqa, H. Gul-E, N. Begum, S. Saleem, M.A. Hossain, R.S. Reddy Gorla, Numerical solutions of nanofluid bioconvection due to gyrotactic microorganisms along a vertical wavy cone. Int. J. Heat Mass Transf. 101, 608–613 (2016)

    Google Scholar 

  41. P.R. Sobhana Babu, M. Venkata Subba Rao, K. Gangadhar, Boundary layer flow of radioactive non-Newtonian nanofluid embedded in a porous medium over a stretched sheet using the spectral relaxation method. Mater. Today: Proc. 19(6), 2672–2680 (2019)

    Google Scholar 

  42. M.D. Tausif, K. Das, P.K. Kundu, Multiple slip effects on bioconvection of nanofluid flow containing gyrotactic microorganisms and nanoparticles. J. Mol. Liq. 220, 518–526 (2016)

    Google Scholar 

  43. L.N. Trefethen, Spectral Methods in MATLAB (SIAM, Philadelphia, 2000)

    MATH  Google Scholar 

  44. M. Venkata Subba Rao, K. Gangadhar, P.L.N. Varma, A spectral relaxation method for three-dimensional MHD flow of nanofluid flow over an exponentially stretching sheet due to convective heating: an application to solar energy. Indian J. Phys. 92(12), 1577–1588 (2018)

    ADS  Google Scholar 

  45. H. Xu, I. Pop, Mixed convection flow of a nanofluid over a stretching surface with uniform free stream in the presence of both nanoparticles and gyrotactic microorganisms. Int. J. Heat Mass Transf. 75, 610–623 (2014)

    Google Scholar 

  46. H. Xu, T. Fan, I. Pop, Analysis of mixed convection flow of a nanofluid in a vertical channel with the Buongiorno mathematical model. Int. Commun. Heat Mass Transf. 44, 15–22 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Acharya Nagarjuna University Campus, Ongole, Andhra Pradesh, 523001, India

    Gangadhar Kotha & Surekha Penki

  2. Department of Mathematics, Vignan’s Lara Institute of Technology and Science, Vadlamudi, Guntur, Andhra Pradesh, 522213, India

    Venkata Ramana Kolipaula

  3. Division of Mathematics, Department of Sciences and Humanities, Vignan’s Foundation for Science, Technology and Research, Vadlamudi, Andhra Pradesh, 522 213, India

    Munagala Venkata Subba Rao

  4. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Ali J. Chamkha

  5. Institute of Theoretical and Applied Research (ITAR), Duy Tan University, Hanoi, 100000, Vietnam

    Ali J. Chamkha

Authors
  1. Gangadhar Kotha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Venkata Ramana Kolipaula
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Munagala Venkata Subba Rao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Surekha Penki
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ali J. Chamkha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali J. Chamkha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kotha, G., Kolipaula, V.R., Venkata Subba Rao, M. et al. Internal heat generation on bioconvection of an MHD nanofluid flow due to gyrotactic microorganisms. Eur. Phys. J. Plus 135, 600 (2020). https://doi.org/10.1140/epjp/s13360-020-00606-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00606-2

Search

Navigation