Skip to main content
SpringerLink
Log in

Magnetohydrodynamic stagnation point flow of third-grade liquid toward variable sheet thickness

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

Abstract

The current study examines the boundary layer stagnation point flow of third-grade fluid toward a stretching surface with variable thickness. Electrically conducting fluid in the flow is addressed. The resulting equation by suitable transformation yields nonlinear problem which is solved for the convergent solutions. Convergence region is particularly determined for the obtained solutions. Variables highlights for velocity are shown and examined with the help of different graphs. Numerical values of the drag force (skin friction coefficient) are also presented in the tabular form. From given results, it is found that velocity field overshoots for larger values of material parameters of third-grade fluid.

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

Similar content being viewed by others

Abbreviations

u, v :

Fluid velocity component

α :

Wall thickness parameter

α 1, α 2, α 3 :

Material parameters

β 1,  β 2, ɛ 1 :

Material parameters for third-grade fluid

ρ :

Density

σ :

Fluid electrical conductivity

B 0 :

Strength of uniform magnetic field

A 1 :

Thickness control parameter

U e :

Free stream velocity

V:

Velocity field

T :

Cauchy stress tensor

μ :

Dynamics viscosity

U w :

Stretching velocity

ψ :

Stream function

ξ :

Similarity variable

Re :

Reynold number

Ha :

Magnetic parameter

C f :

Skin friction coefficient or drag force

τ w :

Local wall shear stress

Re x :

Local Reynolds number

A :

Ratio parameter

A1 :

Cauchy stress tensor

\(\frac{\text{d}}{{{\text{d}}t}}\) :

Material time derivative

I :

Identity tensor

References

  1. Lin Y, Zheng L, Zhang X, Ma L, Chen G (2015) MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation. Int J Heat Mass Transf 84:903–911

    Article  Google Scholar 

  2. Panigrahi S, Reza M, Mishra AK (2015) Mixed convective flow of a Powell-Eyring fluid over a non-linear stretching surface with thermal diffusion and diffusion thermo. Proc Eng 127:645–651

    Article  Google Scholar 

  3. Zeeshan A, Majeed A (2016) Heat transfer analysis of Jeffery fluid flow over a stretching sheet with suction/injection and magnetic dipole effect. Alex Eng J 55:2171–2181

    Article  Google Scholar 

  4. Javed T, Ali N, Abbas Z, Sajid M (2013) Flow of an Eyring-Powell non-Newtonian fluid over a stretching sheet. Chem Eng Commun 220:327–336

    Article  Google Scholar 

  5. Waqas M, Farooq M, Khan MI, Alsaedi A, Hayat T, Yasmeen T (2016) Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. Int J Heat Mass Transf 102:766–772

    Article  Google Scholar 

  6. Hayat T, Waqas M, Khan MI, Alsaedi A (2016) Impacts of constructive and destructive chemical reactions in magnetohydrodynamic (MHD) flow of Jeffrey liquid due to nonlinear radially stretched surface. J Mol Liq. doi:10.1016/j.molliq.2016.11.023

    Article  Google Scholar 

  7. Mahmood A, Chen B, Ghaffari A (2016) Hydromagnetic Hiemenz flow of micropolar fluid over a nonlinearly stretching/shrinking sheet: dual solutions by using Chebyshev Spectral Newton Iterative Scheme. J Magnet Magnet Mater 416:329–334

    Article  Google Scholar 

  8. Gireesha AJ, Mahanthesh B, Gorla RSR, Krupalakshmi KL (2016) Mixed convection two-phase flow of Maxwell fluid under the influence of non-linear thermal radiation, non-uniform heat source/sink and fluid-particle suspension. Ain Shams Eng J. doi:10.1016/j.asej.2016.04.020

    Article  Google Scholar 

  9. Waqas M, Hayat T, Farooq M, Shehzad SA, Alsaedi A (2016) Cattaneo-Christov heat flux model for flow of variable thermal conductivity generalized Burgers fluid. J Mol Liq 220:642–648

    Article  Google Scholar 

  10. Hayat T, Hussain Z, Alsaedi A (2016) Influence of heterogeneous-homogeneous reactions in thermally stratified stagnation point flow of an Oldroyd-Bfluid. Res Phys 6:1161–1167

    Google Scholar 

  11. Hayat T, Qayyum S, Imtiaz M, Alsaedi A (2016) Impact of Cattaneo-Christov heat flux in Jeffrey fluid flow with homogeneous-heterogeneous reactions. PLOS ONE 11:e0148662

    Article  Google Scholar 

  12. Fosdick RL, Rajagopal KR (1980) Thermodynamics and stability of fluids of third grade. Proc R Soc Lond A 339:351–377

    Article  MathSciNet  Google Scholar 

  13. Makinde OD (2007) Thermal stability of a reactive third grade fluid in a cylindrical pipe: an exploitation of Hermite-Padé approximation technique. Appl Math Comput 189:690–697

    MathSciNet  MATH  Google Scholar 

  14. Baoku G, Olajuwon BI, Mustapha AO (2013) Heat and mass transfer on a MHD third grade fluid with partial slip flow past an infinite vertical insulated porous plate in a porous medium. Int J Heat Fluid Flow 40:81–88

    Article  Google Scholar 

  15. Farooq U, Hayat T, Alsaedi A, Liao S (2014) Heat and mass transfer of two-layer flows of third-grade nano-fluids in a vertical channel. Appl Math Comput 24:528–540

    MathSciNet  MATH  Google Scholar 

  16. Hayat T, Shafiq A, Alsaedi A, Asghar S (2015) Effect of inclined magnetic field in flow of third grade fluid with variable thermal conductivity. AIP Adv 5:087108

    Article  Google Scholar 

  17. Hayat T, Khan MI, Waqas M, Alsaedi A, Yasmeen T (2016) Diffusion of chemically reactive species in third grade flow over an exponentially stretching sheet considering magnetic field effects. Chin J Chem Eng. doi:10.1016/j.cjche.2016.06.008

    Article  Google Scholar 

  18. Rashidi MM, Bagheri S, Momoniat E, Freidoonimehr N (2016) Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. Ain Shams Eng J. doi:10.1016/j.asej.2015.08.012

    Article  Google Scholar 

  19. Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) Chemically reactive flow of third grade fluid by an exponentially convected stretching sheet. J Mol Liq 223:853–860

    Article  Google Scholar 

  20. Sarpkaya T (1961) Flow of non-Newtonian fluids in a magnetic field. AIChE J 7:324–328

    Article  Google Scholar 

  21. Pavlov KB (1974) Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika 10:146–148

    Google Scholar 

  22. Hayat T, Waqas M, Khan MI, Alsaedi A (2016) Analysis of thixotropic nanomaterial in a doubly stratified medium considering magnetic field effects. Int J Heat Mass Transf 102:1123–1129

    Article  Google Scholar 

  23. Hayat T, Khan MI, Waqas M, Alsaedi A (2016) Viscous dissipation effect in flow of magneto–nanofluid with variable properties. J Mol Liq 222:47–54

    Article  Google Scholar 

  24. Hayat T, Farooq S, Alsaedi A, Ahmad B (2017) Numerical study for Soret and Dufour effects on mixed convective peristalsis of Oldroyd 8-constants fluid. Int J Thermal Sci 112:68–81

    Article  Google Scholar 

  25. Khan MI, Kiyani MZ, Malik MY, Yasmeen T, Khan MWA, Abbas T (2016) Numerical investigation of magnetohydrodynamic stagnation point flow with variable properties. Alex Eng J 55:2367–2373

    Article  Google Scholar 

  26. Farooq M, Khan MI, Waqas M, Hayat T, Alsaedi A, Khan MI (2016) MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects. J Mol Liq 220:1097–1103

    Article  Google Scholar 

  27. Turkyilmazoglu M (2016) Equivalences and correspondences between the deforming body induced flow and heat in two-three dimensions. Phys Fluid 28:043102

    Article  Google Scholar 

  28. Yasmeen T, Hayat T, Khan MI, Imtiaz M, Alsaedi A (2016) Ferrofluid flow by a stretched surface in the presence of magnetic dipole and homogeneous-heterogeneous reactions. J Mol Liq 223:1000–1005

    Article  Google Scholar 

  29. Nayak MK, Dash GC, Singh LP (2016) Heat and mass transfer effects on MHD viscoelastic fluid over a stretching sheet through porous medium in presence of chemical reaction. Propuls Power Res 5:70. doi:10.1016/j.jppr.2016.01.006

    Article  Google Scholar 

  30. Abbasbandy S, Hayat T (2009) Solution of the MHD Falkner-Skan flow by homotopy analysis method. Commun Nonlinear Sci Num Simul 14:3591–3598

    Article  MathSciNet  Google Scholar 

  31. Sahoo B, Poncet S (2011) Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition. Int J Heat Mass Transf 54:5010–5019

    Article  Google Scholar 

  32. Liao SJ (2012) Homotopy analysis method in nonlinear differential equations. Springer, Heidelberg

    Book  Google Scholar 

  33. Zheng L, Wang L, Zhang X (2011) Analytic solutions of unsteady boundary flow and heat transfer on a permeable stretching sheet with non-uniform heat source/sink. Commun Nonlinear Sci Num Simul 16:731–740

    Article  Google Scholar 

  34. Abu-Arqub O, El-Ajou A (2013) Solution of the fractional epidemic model by homotopy analysis method. J King Saud Univ Sci 25:73–81

    Article  Google Scholar 

  35. Nayak MK, Dash GC, Singh LP (2014) Steady MHD flow and heat transfer of a third grade fluid in wire coating analysis with temperature dependent viscosity. Int J Heat Mass Transf 79:1087–1095

    Article  Google Scholar 

  36. Wang L, Jian Y, Liu Q, Li F, Chang L (2016) Electromagnetohydrodynamic flow and heat transfer of third grade fluids between two micro-parallel plates. Colloid Surf A 494:87–94

    Article  Google Scholar 

  37. Hayat T, Khan MI, Farooq M, Alsaedi A, Khan MI (2017) Thermally stratified stretching flow with Cattaneo-Christov heat flux International. J Heat Mass Transf 106:289–294

    Article  Google Scholar 

  38. Khan M, Khan WA (2016) Three-dimensional flow and heat transfer to burgers fluid using Cattaneo-Christov heat flux model. J Mol Liq 221:651–657

    Article  Google Scholar 

  39. Hayat T, Khan MI, Farooq M, Alsaedi A, Yasmeen T (2016) Impact of Marangoni convection in the flow of Carbon-water nanofluid with thermal radiation. Int J Heat Mass Transf. doi:10.1016/j.ijheatmasstransfer.2016.08.115

    Article  Google Scholar 

  40. Khan M, Khan WA, Alshomrani AS (2016) Non-linear radiative flow of three-dimensional Burgers nanofluid with new mass flux effect. Int J Heat Mass Transf 101:570–576

    Article  Google Scholar 

  41. Hayat T, Khan MI, Farooq M, Gull N, Alsaedi A (2016) Unsteady three-dimensional mixed convection flow with variable viscosity and thermal conductivity. J Mol Liq 223:297–1310

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    Tasawar Hayat, Muhammad Ijaz Khan & Muhammad Waqas

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah, 21589, Saudi Arabia

    Tasawar Hayat & Ahmed Alsaedi

Authors
  1. Tasawar Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muhammad Ijaz Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Waqas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ahmed Alsaedi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Ijaz Khan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest. This research is a self-funded project.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hayat, T., Khan, M.I., Waqas, M. et al. Magnetohydrodynamic stagnation point flow of third-grade liquid toward variable sheet thickness. Neural Comput & Applic 30, 2417–2423 (2018). https://doi.org/10.1007/s00521-016-2827-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2827-1

Keywords

Search

Navigation