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Neural Computing and Applications

, Volume 31, Supplement 2, pp 857–864 | Cite as

Darcy–Forchheimer stretched flow of MHD Maxwell material with heterogeneous and homogeneous reactions

  • M. Adil SadiqEmail author
  • T. Hayat
Original Article

Abstract

The intention here is to explore the effectiveness of magnetic field and heterogeneous–homogeneous reactions in flow induced by heated sheet moving with nonlinear velocity. Constitutive expression for an incompressible Maxwell material is taken into account. Consideration of Darcy–Forchheimer relation characterizes the porous medium effect. Developed nonlinear problems are calculated for meaningful expression of velocity, temperature and concentration. Characteristics for the significant variables on the physical quantities are graphically addressed. Our analysis indicates that impacts of larger Deborah number and inertia coefficient on velocity distribution are qualitatively similar. It is also observed that concentration has reverse behavior for strength of homogeneous and heterogeneous reaction parameters.

Keywords

Maxwell liquid MHD Darcy–Forchheimer stretched flow Newtonian heating Heterogeneous and homogeneous reactions 

Notes

Acknowledgements

Useful comments of reviewer are appreciated. Also we thank for financial support of this research King Fahd University of petroleum and Minerals through project Code. IN 151027.

Compliance with ethical standards

Conflict of interest

It is declared that we have no conflict of interest.

References

  1. 1.
    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 Therm Sci 112:68–81CrossRefGoogle Scholar
  2. 2.
    Khan WA, Khan M, Alshomrani AS (2016) Impact of chemical processes on 3D Burgers fluid utilizing Cattaneo–Christov double-diffusion: applications of non-Fourier’s heat and non-Fick’s mass flux models. J Mol Liq 223:1039–1147CrossRefGoogle Scholar
  3. 3.
    Waqas M, Hayat T, Farooq M, Shehzad SA, Alsaedi A (2016) Cattaneo–Christov heatflux model for flow of variable thermal conductivity generalized Burgers fluid. J Mol Liq 220:642–648CrossRefGoogle Scholar
  4. 4.
    Das K, Sharma RP, Sarkar A (2016) Heat and mass transfer of a second grade magnetohydrodynamic fluid over a convectively heated stretching sheet. J Comput Des Eng 3:330–336Google Scholar
  5. 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 102:766–772CrossRefGoogle Scholar
  6. 6.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid. J Mol Liq 215:704–710CrossRefGoogle Scholar
  7. 7.
    Hayat T, Bashir G, Waqas M, Alsaedi A (2016) MHD flow of Jeffrey liquid due to a nonlinear radially stretched sheet in presence of Newtonian heating. Res Phys 6:817–823Google Scholar
  8. 8.
    Hayat T, Farooq S, Alsaedi A, Ahmad B (2016) Hall and radial magnetic field effects on radiative peristaltic flow of Carreau–Yasuda fluid in a channel with convective heat and mass transfer. J Mag Mag Mater 412:207–216CrossRefGoogle Scholar
  9. 9.
    Khan MI, Waqas M, Hayat T, Alsaedi A (2017) A comparative study of Casson fluid with homogeneous–heterogeneous reactions. J Colloid Interface Sci 498:85–90CrossRefGoogle Scholar
  10. 10.
    Hayat T, Khan MI, Waqas M, Alsaedi A, Yasmeen T (2017) Diffusion of chemically reactive species in third grade fluid flow over an exponentially stretching sheet considering magnetic field effects. Chin J Chem Eng 25:257–263CrossRefGoogle Scholar
  11. 11.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2013) Mixed convection radiative flow of Maxwell fluid near a stagnation point with convective condition. J Mech 29:403–409CrossRefGoogle Scholar
  12. 12.
    Abbasbandy S, Naz R, Hayat T, Alsaedi A (2014) Numerical and analytical solutions for Falkner–Skan flow of MHD Maxwell fluid. Appl Math Comput 242:569–575MathSciNetzbMATHGoogle Scholar
  13. 13.
    Ramesh GK, Gireesha BJ (2014) Influence of heat source/sink on a Maxwell fluid over a stretching surface with convective boundary condition in the presence of nanoparticles. Ain Shams Eng J 5:991–998CrossRefGoogle Scholar
  14. 14.
    Hayat T, Bashir G, Waqas M, Alsaedi A, Ayub M, Asghar S (2016) Stagnation point flow of nanomaterial towards nonlinear stretching surface with melting heat. Neural Comput Appl. doi: 10.1007/s00521-016-2704-y Google Scholar
  15. 15.
    Sadiq MA, Hayat T (2016) Darcy–Forchheimer flow of magneto Maxwell liquid bounded by convectively heated sheet. Res Phys. doi: 10.1016/j.rinp.2016.10.019 Google Scholar
  16. 16.
    Hayat T, Qayyum S, Waqas M, Alsaedi A (2016) Thermally radiative stagnation point flow of Maxwell nanofluid due to unsteady convectively heated stretched surface. J Mol Liq 224:801–810CrossRefGoogle Scholar
  17. 17.
    Turkyilmazoglu M (2015) An analytical treatment for the exact solutions of MHD flow and heat over two–three dimensional deforming bodies. Int J Heat Mass Transf 90:781–789CrossRefGoogle Scholar
  18. 18.
    Turkyilmazoglu M (2016) Equivalences and correspondences between the deforming body induced flow and heat in two–three dimensions. Phys Fluids 28:043102CrossRefGoogle Scholar
  19. 19.
    Sarli VD, Benedetto AD (2015) Modeling and simulation of soot combustion dynamics in a catalytic diesel particulate filter. Chem Eng Sci 137:69–78CrossRefGoogle Scholar
  20. 20.
    Musto M, Bianco N, Rotondo G, Toscano F, Pezzella G (2016) A simplified methodology to simulate a heat exchanger in an aircraft’s oil cooler by means of a porous media model. Appl Therm Eng 94:836–845CrossRefGoogle Scholar
  21. 21.
    Fu J, Tang Y, Li J, Ma Y, Chen W, Li H (2016) Four kinds of the two-equation turbulence model’s research on flow field simulation performance of DPF’s porous media and swirl-type regeneration burner. Appl Therm Eng 93:397–404CrossRefGoogle Scholar
  22. 22.
    Qin L, Han J, Chen W, Yao X, Tadaaki S, Kim H (2016) Enhanced combustion efficiency and reduced pollutant emission in a fluidized bed combustor by using porous alumina bed materials. Appl Therm Eng 94:813–818CrossRefGoogle Scholar
  23. 23.
    Alrwashdeh SS, Markötter H, Haußmann J, Arlt T, Klages M, Scholta J, Banhart J, Manke I (2016) Investigation of water transport dynamics in polymer electrolyte membrane fuel cells based on high porous micro porous layers. Energy 102:161–165CrossRefGoogle Scholar
  24. 24.
    Darcy H (2004) Les Fontaines publiques de la ville de dijon (The Public Fountains of the City of Dijon) English translation by Patricia Bobeck, Kendall, in, Hunt Publishing Co.Google Scholar
  25. 25.
    Nield D, Bejan A (2013) Convection in porous media. Springer, New YorkCrossRefzbMATHGoogle Scholar
  26. 26.
    Malashetty MS, Dulal P, Premila K (2010) Double-diffusive convection in a Darcy porous medium saturated with a couple-stress fluid. Fluid Dyn Res 42:035502MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Malashetty MS, Pop I, Kollur P, Sidram W (2012) Soret effect on double diffusive convection in a Darcy porous medium saturated with a couple stress fluid. Int J Therm Sci 53:130–140CrossRefzbMATHGoogle Scholar
  28. 28.
    Zhu T, Manhart M (2015) Oscillatory Darcy flow in porous media. Transp Porous Media 111:521–539MathSciNetCrossRefGoogle Scholar
  29. 29.
    Kapoor S, Bera P, Kumar A (2012) Effect of Rayleigh thermal number in double diffusive non-Darcy mixed convective flow in vertical pipe filled with porous medium. Proc Eng 38:314–320CrossRefGoogle Scholar
  30. 30.
    Kumar BVR, Murthy SVSSNVGK (2010) Soret and Dufour effects on double-diffusive free convection from a corrugated vertical surface in a non-Darcy porous medium. Transp Porous Media 85:117–130CrossRefGoogle Scholar
  31. 31.
    Hayat T, Farooq S, Ahmad B, Alsaedi A (2017) Effectiveness of entropy generation and energy transfer on peristaltic flow of Jeffrey material with Darcy resistance. Int J Heat Mass Transf 106:244–252CrossRefGoogle Scholar
  32. 32.
    Siavashi M, Bordbar V, Rahnama P (2017) Heat transfer and entropy generation study of non-Darcy double-diffusive natural convection in inclined porous enclosures with different source configurations. Appl Therm Eng 110:1462–1475CrossRefGoogle Scholar
  33. 33.
    Umavathi JC, Ojjela O, Vajravelu K (2017) Numerical analysis of natural convective flow and heat transfer of nanofluids in a vertical rectangular duct using Darcy–Forchheimer–Brinkman model. Int J Therm Sci 111:511–524CrossRefGoogle Scholar
  34. 34.
    Merkin JH (1996) A model for isothermal homogeneous–heterogeneous reactions in boundary layer flow. Math Comput Model 24:125–136MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Abbas Z, Sheikh M, Pop I (2015) Stagnation-point flow of a hydromagnetic viscous fluid over stretching/shrinking sheet with generalized slip condition in the presence of homogeneous–heterogeneous reactions. J Taiwan Inst Chem Eng 55:69–75CrossRefGoogle Scholar
  36. 36.
    Hayat T, Khan MI, Waqas M, Alsaedi A (2017) Mathematical modeling of non-Newtonian fluid with chemical aspects: a new formulation and results by numerical technique. Colloids Surf A Phys Eng Aspect 518:263–272CrossRefGoogle Scholar
  37. 37.
    Farooq M, Anjum A, Hayat T, Alsaedi A (2016) Melting heat transfer in the flow over a variable thicked Riga plate with homogeneous–heterogeneous reactions. J Mol Liq. doi: 10.1016/j.molliq.2016.10.123 Google Scholar
  38. 38.
    Hayat T, Khan MI, Imtiaz M, Alseadi A, Waqas M (2016) Similarity transformation approach for ferromagnetic mixed convection flow in the presence of chemically reactive magnetic dipole. AIP Phys Fluids 28:102003CrossRefGoogle Scholar
  39. 39.
    Liao SJ (2012) Homotopic analysis method in nonlinear differential equations. Springer, HeidelbergCrossRefGoogle Scholar
  40. 40.
    Hayat T, Ali S, Farooq MA, Alsaedi A (2015) On comparison of series and numerical solutions for flow of Eyring–Powell fluid with Newtonian heating and internal heat generation/absorption. PLoS ONE 10:e0129613CrossRefGoogle Scholar
  41. 41.
    Shehzad SA, Hayat T, Alsaedi A, Chen B (2016) A useful model for solar radiation. Energy Ecol Environ 1:30–38CrossRefGoogle Scholar
  42. 42.
    Zheng L, Jiao C, Lin Y, Ma L (2016) Marangoni convection heat and mass transport of power-law fluid in porous medium with heat generation and chemical reaction. Heat Transf Eng. doi: 10.1080/01457632.2016.1200384 Google Scholar
  43. 43.
    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 102:1123–1129CrossRefGoogle Scholar
  44. 44.
    Turkyilmazoglu M (2016) An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method. Filomat 30:1633–1650MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) Mixed convection flow of a Burgers nanofluid in the presence of stratifications and heat generation/absorption. Eur Phys J Plus 131:253CrossRefGoogle Scholar
  46. 46.
    Khan WA, Khan M (2016) Impact of thermophoresis particle deposition on three-dimensional radiative flow of Burgers fluid. Res Phys 6:829–836Google Scholar
  47. 47.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) Mixed convection flow of viscoelastic nanofluid by a cylinder with variable thermal conductivity and heat source/sink. Int J Numer Methods Heat Fluid Flow 26:214–234MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Turkyilmazoglu M (2010) An optimal analytic approximate solution for the limit cycle of Duffing-van der Pol equation. J Appl Mech Trans ASME 78:021005CrossRefGoogle Scholar
  49. 49.
    Hayat T, Khan MI, Farooq M, Yasmeen T, Alsaedi A (2016) Stagnation point flow with Cattaneo–Christov heat flux and homogeneous–heterogeneous reactions. J Mol Liq 220:49–55CrossRefGoogle Scholar
  50. 50.
    Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) Mixed convection stagnation-point flow of Powell–Eyring fluid with Newtonian heating, thermal radiation, and heat generation/absorption. J Aerospace Eng 04016077Google Scholar
  51. 51.
    Hayat T, Khan MI, Waqas M, Alsaedi A (2017) Newtonian heating effect in nanofluid flow by a permeable cylinder. Res Phys 7:256–262Google Scholar
  52. 52.
    Waqas M, Alsaedi A, Shehzad SA, Hayat T, Asghar S (2017) Mixed convective stagnation point flow of Carreau fluid with variable properties. J Braz Soc Mech Sci Eng. doi: 10.1007/s40430-017-0743-7 Google Scholar
  53. 53.
    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 225:302–310CrossRefGoogle Scholar
  54. 54.
    Waqas M, Khan MI, Hayat T, Alsaedi A, Khan MI (2017) On Cattaneo–Christov double diffusion impact for temperature-dependent conductivity of Powell–Eyring liquid. Chin J Phys. doi: 10.1016/j.cjph.2017.02.003 Google Scholar
  55. 55.
    Hayat T, Zubair M, Waqas M, Alsaedi A, Ayub M (2017) Impact of variable thermal conductivity in doubly stratified chemically reactive flow subject to non-Fourier heat flux theory. J Mol Liq 234:444–451CrossRefGoogle Scholar
  56. 56.
    Tamoor M, Waqas M, Khan MI, Alsaedi A, Hayat T (2017) Magnetohydrodynamic flow of Casson fluid over a stretching cylinder. Results Phys 7:498–502CrossRefGoogle Scholar
  57. 57.
    Hayat T, Bashir G, Waqas M, Alsaedi A (2016) MHD 2D flow of Williamson nanofluid over a nonlinear variable thicked surface with melting heat transfer. J Mol Liq 223:836–844CrossRefGoogle Scholar
  58. 58.
    Hayat T, Mustafa M, Asghar S (2010) Unsteady flow with heat and mass transfer of a third grade fluid over a stretching surface in the presence of chemical reaction. Nonlinear Anal Real World Appl 11:3186–3197MathSciNetCrossRefzbMATHGoogle Scholar
  59. 59.
    Abbasbandy S, Hayat T, Alsaedi A, Rashidi MM (2014) Numerical and analytical solutions for Falkner–Skan flow of MHD Oldroyd-B fluid. Int J Numer Methods Heat Fluid Flow 24:390–401MathSciNetCrossRefzbMATHGoogle Scholar
  60. 60.
    Turkyilmazoglu M (2016) Determination of the correct range of physical parameters in the approximate analytical solutions of nonlinear equations using the Adomian decomposition method. Medit J Math 13:4019–4037MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of MathematicsDCC-KFUPMDhahranKingdom of Saudi Arabia
  2. 2.Department of MathematicsQuaid-I-Azam University 45320IslamabadPakistan
  3. 3.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahKingdom of Saudi Arabia

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