Skip to main content
SpringerLink
Log in

Impact of Stefan blowing on thermal radiation and Cattaneo–Christov characteristics for nanofluid flow containing microorganisms with ablation/accretion of leading edge: FEM approach

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

Abstract

The impacts of Stefan blowing on Cattaneo–Christov characteristics and bioconvection of self-motive microorganisms mixed in water-based nanofluids with a ablation/accretion of leading edge are examined in the present investigation. Governing partial differential formulation is transmuted into ordinary differential form via similarity functions. The finite element method is harnessed to yield solution of numerical for the resulting set of nonlinear coupled equations with coding implementation in MATLAB. It is noteworthy that the reliability and validity of the current numerical solution are an excellent agreement with existing specific solutions in the literature. The interest in computational effort centered about the formation of boundary layer patterns for microorganism distribution, fluid temperature, volume fraction of nanoinclusions and fluid velocity when influential parameters are varied. The most important results of the current examination are that upgrade in Stefan blowing parameter undermines the fluid velocity while an increment in ablation/accretion impact at leading edge shows in a deceleration in flow velocity. Another significant result is that an increment in ablation/accretion at leading edge upsurges the fluid temperature and concentrations.

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
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. I. Abbas, Natural frequencies of a poroelastic hollow cylinder. Acta Mech. 186(1–4), 229–237 (2006)

    MATH  Google Scholar 

  2. I.A. Abbas, H.M. Youssef, A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method. Int. J. Thermophys. 33(7), 1302–1313 (2012)

    ADS  Google Scholar 

  3. F. Abbasi, M. Mustafa, S. Shehzad, M. Alhuthali, T. Hayat, Analytical study of cattaneo-christov heat flux model for a boundary layer flow of oldroyd-b fluid. Chin. Phys. B 25(1), 014701 (2015)

    Google Scholar 

  4. F.M. Abbasi, S.A. Shehzad, T. Hayat, A. Alsaedi, A. Hegazy, Influence of cattaneo-christov heat flux in flow of an oldroyd-b fluid with variable thermal conductivity. Int. J. Numer. Methods Heat Fluid Flow 11, 0148662 (2016)

    Google Scholar 

  5. K. Al-Khaled, S.U. Khan, I. Khan, Chemically reactive bioconvection flow of tangent hyperbolic nanoliquid with gyrotactic microorganisms and nonlinear thermal radiation. Heliyon 6(1), e03117 (2020)

    Google Scholar 

  6. B. Ali, R.A. Naqvi, Y. Nie, S.A. Khan, M.T. Sadiq, A.U. Rehman, S. Abdal, Variable viscosity effects on unsteady mhd an axisymmetric nanofluid flow over a stretching surface with thermo-diffusion: Fem approach. Symmetry 12(2), 234 (2020)

    Google Scholar 

  7. B. Ali, Y. Nie, S.A. Khan, M.T. Sadiq, M. Tariq, Finite element simulation of multiple slip effects on mhd unsteady maxwell nanofluid flow over a permeable stretching sheet with radiation and thermo-diffusion in the presence of chemical reaction. Processes 7(9), 628 (2019)

    Google Scholar 

  8. B. Ali, X. Yu, M.T. Sadiq, A.U. Rehman, L. Ali, A finite element simulation of the active and passive controls of the mhd effect on an axisymmetric nanofluid flow with thermo-diffusion over a radially stretched sheet. Processes 8(2), 207 (2020)

    Google Scholar 

  9. L. Ali, X. Liu, B. Ali, Finite element analysis of variable viscosity impact on mhd flow and heat transfer of nanofluid using the cattaneo-christov model. Coatings 10(4), 395 (2020)

    Google Scholar 

  10. L. Ali, X. Liu, B. Ali, S. Mujeed, S. Abdal, Finite element analysis of thermo-diffusion and multi-slip effects on mhd unsteady flow of casson nano-fluid over a shrinking/stretching sheet with radiation and heat source. Appl. Sci. 9(23), 5217 (2019)

    Google Scholar 

  11. L. Ali, X. Liu, B. Ali, S. Mujeed, S. Abdal, Finite element simulation of multi-slip effects on unsteady mhd bioconvective micropolar nanofluid flow over a sheet with solutal and thermal convective boundary conditions. Coatings 9(12), 842 (2019)

    Google Scholar 

  12. F. Alzahrani, I.A. Abbas, Generalized thermoelastic interactions in a poroelastic material without energy dissipations. Int. J. Thermophys. 41, 7 (2020)

    Google Scholar 

  13. A. Bejan, Convection Heat Transfer (Wiley, London, 2013)

    MATH  Google Scholar 

  14. J. Buongiorno, Convective transport in nanofluids. J. Heat Transf. 128(3), 240–250 (2006)

    Google Scholar 

  15. C. Cattaneo, Sulla conduzione del calore. Atti. Sem. Mat. Fis. Univ. Modena 3, 83–101 (1948)

    MathSciNet  MATH  Google Scholar 

  16. C. Christov, On frame indifferent formulation of the maxwell-cattaneo model of finite-speed heat conduction. Mech. Res. Commun. 36(4), 481–486 (2009)

    MathSciNet  MATH  Google Scholar 

  17. A. El-Naggar, Z. Kishka, A. Abd-Alla, I. Abbas, S. Abo-Dahab, M. Elsagheer, On the initial stress, magnetic field, voids and rotation effects on plane waves in generalized thermoelasticity. J. Comput. Theor. Nanosci. 10(6), 1408–1417 (2013)

    Google Scholar 

  18. T. Fang, A note on the unsteady boundary layers over a flat plate. Int. J. Non-Linear Mech. 43(9), 1007–1011 (2008)

    ADS  Google Scholar 

  19. T. Fang, W. Jing, Flow, heat, and species transfer over a stretching plate considering coupled stefan blowing effects from species transfer. Commun. Nonlinear Sci. Numer. Simul. 19(9), 3086–3097 (2014)

    ADS  MathSciNet  MATH  Google Scholar 

  20. J.B.J. Fourier, Théorie analytique de la chaleur, paris. Académie des Sciences p. 3 (1822)

  21. R.A. Hamid, R. Nazar, I. Pop, Stagnation point flow, heat transfer and species transfer over a shrinking sheet with coupled stefan blowing effects from species transfer. In: AIP Conference Proceedings, vol. 1784, p. 050005. AIP Publishing LLC (2016)

  22. S. Han, L. Zheng, C. Li, X. Zhang, Coupled flow and heat transfer in viscoelastic fluid with cattaneo-christov heat flux model. Appl. Math. Lett. 38, 87–93 (2014)

    MathSciNet  MATH  Google Scholar 

  23. T. Hayat, M.I. Khan, M. Farooq, T. Yasmeen, A. Alsaedi, Stagnation point flow with cattaneo-christov heat flux and homogeneous-heterogeneous reactions. J. Mol. Liquids 220, 49–55 (2016)

    Google Scholar 

  24. T. Hayat, Z. Nisar, H. Yasmin, A. Alsaedi, Peristaltic transport of nanofluid in a compliant wall channel with convective conditions and thermal radiation. J. Mol. Liq. 220, 448–453 (2016)

    Google Scholar 

  25. F. He, Z. Wang, L. Wang, J. Li, J. Wang, Effects of surfactant on capillary evaporation process with thick films. Int. J. Heat Mass Transfer 88, 406–410 (2015)

    Google Scholar 

  26. M.R. Ilias, N.A. Rawi, N. Raji, S. Shafie, Unsteady aligned mhd boundary layer flow and heat transfer of magnetic nanofluid past a vertical flat plate with leading-edge accretion (2006)

  27. K. Jyothi, P.S. Reddy, M.S. Reddy, Carreau nanofluid heat and mass transfer flow through wedge with slip conditions and nonlinear thermal radiation. J. Braz. Soc. Mech. Sci. Eng. 41(10), 415 (2019)

    Google Scholar 

  28. S.A. Khan, Y. Nie, B. Ali, Multiple slip effects on magnetohydrodynamic axisymmetric buoyant nanofluid flow above a stretching sheet with radiation and chemical reaction. Symmetry 11(9), 1171 (2019)

    Google Scholar 

  29. S.A. Khan, Y. Nie, B. Ali, Multiple slip effects on mhd unsteady viscoelastic nano-fluid flow over a permeable stretching sheet with radiation using the finite element method. SN Appl. Sci. 2(1), 66 (2020)

    Google Scholar 

  30. R. Kumar, I.A. Abbas, Deformation due to thermal source in micropolar thermoelastic media with thermal and conductive temperatures. J. Comput. Theor. Nanosci. 10(9), 2241–2247 (2013)

    Google Scholar 

  31. A. Kuznetsov, Bio-thermal convection induced by two different species of microorganisms. Int. Commun. Heat Mass Transfer 38(5), 548–553 (2011)

    Google Scholar 

  32. F. Mabood, W.A. Khan, A computational study of unsteady radiative magnetohydrodynamic blasius and sakiadis flow with leading-edge accretion (ablation). Heat Transfer 49(3), 1355–1373 (2020)

    Google Scholar 

  33. M. Mustafa, Cattaneo-christov heat flux model for rotating flow and heat transfer of upper-convected maxwell fluid. Aip Adv. 5(4), 047109 (2015)

    ADS  Google Scholar 

  34. M. Nayak, J. Prakash, D. Tripathi, V. Pandey, S. Shaw, O. Makinde, 3d bioconvective multiple slip flow of chemically reactive casson nanofluid with gyrotactic micro-organisms. Heat Transfer Asian Res. 49(1), 135–153 (2020)

    Google Scholar 

  35. G. Nellis, S. Klein, Internal forced convection. In: Heat transfer, pp. 634–712. Cambridge University Press (2008)

  36. G. Palani, I. Abbas, Free convection mhd flow with thermal radiation from an impulsively started vertical plate. Nonlinear Anal. Model. Control 14(1), 73–84 (2009)

    MATH  Google Scholar 

  37. C. RamReddy, P. Murthy, A.J. Chamkha, A. Rashad, Soret effect on mixed convection flow in a nanofluid under convective boundary condition. Int. J. Heat Mass Transfer 64, 384–392 (2013)

    Google Scholar 

  38. J.N. Reddy, Solutions Manual for an Introduction to the Finite Element Method (McGraw-Hill, New York, 1993)

    Google Scholar 

  39. N.C. Roşca, I. Pop, Unsteady boundary layer flow of a nanofluid past a moving surface in an external uniform free stream using buongiorno’s model. Comput. Fluids 95, 49–55 (2014)

    MathSciNet  MATH  Google Scholar 

  40. S. Choi, Enhancing thermal conductivity of fluids with nanoparticle in development and applications of non-Newtonian flow. ASME Fluids Eng. Div. 231, 99–105 (1995)

    Google Scholar 

  41. T. Saeed, I. Abbas, M. Marin, A gl model on thermo-elastic interaction in a poroelastic material using finite element method. Symmetry 12(3), 488 (2020)

    Google Scholar 

  42. S. Shehzad, F. Abbasi, T. Hayat, B. Ahmad, Cattaneo-christov heat flux model for third-grade fluid flow towards exponentially stretching sheet. Appl. Math. Mech. 37(6), 761–768 (2016)

    MathSciNet  Google Scholar 

  43. M. Sheikholeslami, A.J. Chamkha, Influence of lorentz forces on nanofluid forced convection considering marangoni convection. J. Mol. Liq. 225, 750–757 (2017)

    Google Scholar 

  44. M. Siavashi, H.R.T. Bahrami, H. Saffari, Numerical investigation of flow characteristics, heat transfer and entropy generation of nanofluid flow inside an annular pipe partially or completely filled with porous media using two-phase mixture model. Energy 93, 2451–2466 (2015)

    Google Scholar 

  45. G. Swapna, L. Kumar, P. Rana, B. Singh, Finite element modeling of a double-diffusive mixed convection flow of a chemically-reacting magneto-micropolar fluid with convective boundary condition. J. Taiwan Inst. Chem. Eng. 47, 18–27 (2015)

    Google Scholar 

  46. L. Todd, A family of laminar boundary layers along a semi-infinite flat plate. Fluid Dyn. Res. 19(4), 235–249 (1997)

    ADS  MathSciNet  MATH  Google Scholar 

  47. M.J. Uddin, M. Kabir, O.A. Bég, Computational investigation of stefan blowing and multiple-slip effects on buoyancy-driven bioconvection nanofluid flow with microorganisms. Int. J. Heat Mass Transfer 95, 116–130 (2016)

    Google Scholar 

  48. H. Waqas, S.U. Khan, M. Bhatti, M. Imran, Significance of bioconvection in chemical reactive flow of magnetized carreau-yasuda nanofluid with thermal radiation and second-order slip. J. Therm. Anal. Calorim. 2012, 1–14 (2020)

    Google Scholar 

  49. M. Waqas, T. Hayat, M. Farooq, S. Shehzad, A. Alsaedi, Cattaneo-christov heat flux model for flow of variable thermal conductivity generalized burgers fluid. J. Mol. Liq. 220, 642–648 (2016)

    Google Scholar 

  50. D. Wen, Y. Ding, Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. Int. J. Heat Mass Transfer 47(24), 5181–5188 (2004)

    Google Scholar 

  51. S. Xun, J. Zhao, L. Zheng, X. Zhang, Bioconvection in rotating system immersed in nanofluid with temperature dependent viscosity and thermal conductivity. Int. J. Heat Mass Transfer 111, 1001–1006 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, 127 West Youyi Road, Xian, 710072, China

    Bagh Ali

  2. School of Aerospace and Mechanical Engineering, Nanyang Technological University, Singapore, Singapore

    Sajjad Hussain

  3. School of Mathematics, Northwest University, No. 229 North Taibai Avenue, Xi’an, 7100069, China

    Sohaib Abdal

  4. Department of applied physics, Northwestern Polytechnical University, 127 West Youyi Road, Xian, 710072, China

    Muhammad Muntazir Mehdi

Authors
  1. Bagh Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sajjad Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sohaib Abdal
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Muntazir Mehdi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sajjad Hussain.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ali, B., Hussain, S., Abdal, S. et al. Impact of Stefan blowing on thermal radiation and Cattaneo–Christov characteristics for nanofluid flow containing microorganisms with ablation/accretion of leading edge: FEM approach. Eur. Phys. J. Plus 135, 821 (2020). https://doi.org/10.1140/epjp/s13360-020-00711-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00711-2

Search

Navigation