Skip to main content
SpringerLink
Log in

Impact of inclined Lorentz forces on tangent hyperbolic nanofluid flow with zero normal flux of nanoparticles at the stretching sheet

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This framework is devoted to analyze the tangent hyperbolic fluid in the presence of nanoparticles. In order to disperse the nanoparticle from the surface of sheet, condition of zero normal flux of nanoparticles is introduced at the surface. Inclined magnetic field is applied with an aligned angle \(\gamma\) at the surface of the sheet. Moreover, consideration of nanoparticles which are passively controlled at the surface is physically more realistic condition. The system of partial differential equations generated for tangent hyperbolic nanofluid are modeled and then converted into the system of nonlinear ordinary differential equations by employing suitable similarity transformations. Obtained systems of ordinary differential equations along with the condition of zero normal flux are successfully solved numerically by Runge–Kutta fourth-order method with shooting technique. The effects of various emerging parameters on velocity, temperature and concentration profiles are discussed in detail and presented graphically. Variation of skin friction coefficient and local Nusselt number are also oriented to analyze the variation of nanofluid at the surface. Considerable effects are found on velocity, temperature and concentration with the variable values of Weissenberg number \(We\) and inclination of angle \(\gamma\). It is finally concluded that increase in the Weissenberg number and power law index reduce the velocity profile; however, thermophoresis parameter shows the dominant effects on temperature and concentration profile. Significant effects on velocity, temperature and concentration profiles are also determined for both suction and injection cases.

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
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Pop I, Ingham DB (2001) Convective heat transfer: mathematical and computational modelling of viscous fluids and porous media. Pergamon, Amsterdam

    Google Scholar 

  2. Nadeem S, Akram S (2009) Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel. ZNA 64a:559–567

    Google Scholar 

  3. Friedman AJ, Dyke SJ, Phillips BM (2013) Over-driven control for large-scale MR dampers. Smart Mater Struct 22(045001):15

    Google Scholar 

  4. Nadeem S, Maraj EN (2013) The mathematical analysis for peristaltic flow of hyperbolic tangent hyperbolic fluid in a curved channel. Commun Theor Phys 59:729–736

    Article  MathSciNet  Google Scholar 

  5. Akbar NS, Nadeem S, Haq RU, Khan ZH (2013) Numerical solutions of Magneto-hydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet. Indian J Phys 87:1121–1124

    Article  Google Scholar 

  6. Naseer M, Malik MY, Nadeem S, Rehman A (2014) The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder. Alex Eng J 53:747–750

    Article  Google Scholar 

  7. Akbar NS (2014) Peristaltic flow of Tangent Hyperbolic fluid with convective boundary condition. Eur Phys J Plus 129:214

    Article  Google Scholar 

  8. Akram S, Nadeem S (2014) Consequence of nanofluid on peristaltic transport of a hyperbolic tangent fluid model in the occurrence of apt (tending) magnetic field. J Magn Magn Mater 358:183–191

    Article  Google Scholar 

  9. Shahzad A, Ali R (2012) Approximate analytic solution for magneto-hydrodynamic flow of a non-Newtonian fluid over a vertical stretching sheet. Can J Appl Sci 2:202–215

    Google Scholar 

  10. Ahmed J, Shahzad A, Khan M, Ali R (2015) A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet. AIP Adv 5:117117

    Article  Google Scholar 

  11. Shahzad A, Ali R (2013) MHD flow of a non-Newtonian Power law fluid over a vertical stretching sheet with the convective boundary condition. Walailak J Sci Technol (WJST) 10:43–56

    Google Scholar 

  12. Choi S (1995) Enhancing thermal conductivity of fluids with nanoparticle, development and applications of non-Newtonian flow. ASME FED-231/MD6699–105

  13. Buongionro J (2006) Convective transport in nanofluids. J Heat Transf ASME 128:240–250

    Article  Google Scholar 

  14. Huang X, Teng X, Chen D, Tang F, He J (2010) The effect of the shape of mesoporous silica nanoparticles on cellular uptake and cell function. Biomaterials 31:438–448

    Article  Google Scholar 

  15. Ferrouillat S, Bontemps A, Poncelet O, Soriano O, Gruss JA (2011) Influence of nanoparticle shape factor on convective heat transfer of water-based ZnO nanofluids. Performance evaluation criterion. Int J Mech Ind Eng 1:1–13

    Google Scholar 

  16. Albanese A, Tang PS, Chan WC (2012) The effect of nanoparticle size, shape, and surface chemistry on biological systems. Annu Rev Biomed Eng 14:1–16

    Article  Google Scholar 

  17. Khan WA, Khan ZH, Haq RU (2015) Flow and heat transfer of ferrofluids over a flat plate with uniform heat flux. Eur Phys Plus 130:86

    Article  Google Scholar 

  18. Haq RU, Nadeem S, Khan ZH, Noor NFM (2015) MHD squeezed flow of water functionalized metallic nanoparticles over a sensor surface. Phys E 73:45–53

    Article  Google Scholar 

  19. Hussain ST, Haq RU, Khan ZH, Nadeem S (2016) Water driven flow of carbon nanofluid nanotubes in a rotating channel. J Mol Liquid 214:136–144

    Article  Google Scholar 

  20. Rehaman S, Ul Haq R, Khan ZH, Lee C (2016) Entropy generation analysis of non-Newtonian nanofluid with zero normal flux of nanoparticles at the stretching surface. J Taiwan Inst Chem Eng 63:226–235

    Article  Google Scholar 

  21. Kuznetsov AV, Nield DA (2010) Natural convective boundary layer flow of a nanofluid past a vertical plate. Int J Therm Sci 49:243–247

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  23. Bachok N, Ishak A, Pop I (2010) Boundary layer flow of nanofluids over a moving surface in a flowing fluid. Int J Therm Sci 49:1663–1668

    Article  Google Scholar 

  24. Makinde OD, Aziz A (2011) Boundary layer flow of a nanofluid past a stretching sheet with convective boundary condition. Int J Therm Sci 50:1326–1332

    Article  Google Scholar 

  25. Ibrahim W, Shanker B (2012) Boundary layer flow and heat transfer of nanofluid over a vertical plate with convective surface boundary condition. J Fluids Eng 134:081203

    Article  Google Scholar 

  26. Ibrahim W, Shankar B, Nandeppanavar MM (2013) MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet. Int J Heat and Mass Transfer 56(1–2):1–9. doi:10.1016/j.ijheatmasstransfer.2012.08.034

    Article  Google Scholar 

  27. Ibrahim W, Ul Haq R (2015) Magnetohydrodynamic (MHD) stagnation point flow of nanofluid past a stretching sheet with convective boundary condition. J Braz Soc Mech Sci Eng. doi:10.1007/s40430-015-0347-z

    Google Scholar 

  28. Akbar NS, Nadeem S, Haq RU, Khan ZH (2013) Radiation effects on MHD stagnation point flow of nanofluid towards a stretching surface with convective boundary condition. Chin J Aeronaut 26:1389–1397

    Article  Google Scholar 

  29. Nadeem S, Haq R (2013) Effect of thermal radiation for magneto hydrodynamic boundary layer flow of a nanofluid past a stretching sheet with convective boundary conditions. J Comput Theor Nanosci 11:32–40

    Article  Google Scholar 

  30. Ul Haq R, Noor NFM, Khan ZH (2016) Numerical simulation of water base magnetite nanoparticles between two parallel disks. Adv Powder Technol 27(4):1568–1575. doi:10.1016/j.apt.2016.05.020

    Article  Google Scholar 

  31. Kuznetsov AV, Nield DA (2014) Natural convective boundary layer flow of a nanofluid past a vertical plate: a revised model. Int J Therm Sci 77:126–129

    Article  Google Scholar 

  32. Khan ZH, Khan WA, Pop I (2013) Triple diffusive free convection along a horizontal Plate in porous media saturated by nanofluid with convective boundary condition. Int J Heat Mass Transf 66:603–612

    Article  Google Scholar 

  33. Ibrahim W, Haq RU (2015) Magneto hydrodynamic (MHD) stagnation point flow of nanofluid past a stretching sheet with convective boundary condition. J Braz Soc Mech Sci Eng 38:1155–1164

    Article  Google Scholar 

  34. Haq RU, Nadeem S, Khan ZH, Akbar NS (2015) Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet. Phys E 65:17–23

    Article  Google Scholar 

  35. Fathizadeh M, Madani M, Khan Y, Faraz N, Yildirım A, Tutkun S (2013) J King Saud Univ Sci. doi:10.1016/j.jksus.2011.08.003

    Google Scholar 

  36. Haq RU, Nadeem S, Khan ZH, Akabr NS (2014) Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet. Phys E 65:17–23

    Article  Google Scholar 

  37. Haq RU, Nadeem S, Akbar NS, Khan ZH (2015) Buoyancy and radiation effect on stagnation point flow of micropolar nanofluid along a vertically convective stretching surface. IEEE Trans Nanotechnol 14(1):42–50

    Article  Google Scholar 

  38. Nadeem S, Haq RU, Akbar NS, Lee C, Khan ZH (2013) Numerical study of boundary layer flow and heat transfer of Oldroyd-B nanofluid towards a stretching sheet. PLoS ONE 8(8):e69811

    Article  Google Scholar 

  39. Saleem S, Nadeem S, Haq RU (2014) Buoyancy and metallic particle effects on an unsteady water-based fluid flow along a vertically rotating cone. Eur Phys J Plus 129:213

    Article  Google Scholar 

  40. Haq RU, Nadeem S, Khan ZH, Noor NFM (2015) Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes. Phys B 457(15):40–47

    Article  Google Scholar 

Download references

Acknowledgments

The first author is very thankful to University Grants Commission, India, for providing the opportunity to do this research work under UGC - Faculty Development Program (FDP), India.

Author information

Authors and Affiliations

  1. Department of Mathematics, Govt. Degree College, Peddapalli, Karimnagar, Telangana, India

    Besthapu Prabhakar

  2. Department of Mathematics, Osmania University, Hyderabad, Telangana, India

    Besthapu Prabhakar & Shankar Bandari

  3. Department of Electrical Engineering, Bahria University, Islamabad Campus, Islamabad, 44000, Pakistan

    Rizwan Ul Haq

Authors
  1. Besthapu Prabhakar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shankar Bandari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rizwan Ul Haq
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rizwan Ul Haq.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prabhakar, B., Bandari, S. & Ul Haq, R. Impact of inclined Lorentz forces on tangent hyperbolic nanofluid flow with zero normal flux of nanoparticles at the stretching sheet. Neural Comput & Applic 29, 805–814 (2018). https://doi.org/10.1007/s00521-016-2601-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2601-4

Keywords

Search

Navigation