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

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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.

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References

  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 112:68–81

    Article  Google Scholar 

  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 223:1039–1147

    Article  Google Scholar 

  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 220:642–648

    Article  Google Scholar 

  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 3:330–336

    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, Shehzad SA, Alsaedi A (2016) A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid. J Mol Liq 215:704–710

    Article  Google Scholar 

  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 6:817–823

    Google Scholar 

  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 412:207–216

    Article  Google Scholar 

  9. Khan MI, Waqas M, Hayat T, Alsaedi A (2017) A comparative study of Casson fluid with homogeneous–heterogeneous reactions. J Colloid Interface Sci 498:85–90

    Article  Google Scholar 

  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 25:257–263

    Article  Google Scholar 

  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 29:403–409

    Article  Google Scholar 

  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 242:569–575

    MathSciNet  MATH  Google Scholar 

  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 5:991–998

    Article  Google Scholar 

  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. 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. 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 224:801–810

    Article  Google Scholar 

  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 90:781–789

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Sarli VD, Benedetto AD (2015) Modeling and simulation of soot combustion dynamics in a catalytic diesel particulate filter. Chem Eng Sci 137:69–78

    Article  Google Scholar 

  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 94:836–845

    Article  Google Scholar 

  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 93:397–404

    Article  Google Scholar 

  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 94:813–818

    Article  Google Scholar 

  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 102:161–165

    Article  Google Scholar 

  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.

  25. Nield D, Bejan A (2013) Convection in porous media. Springer, New York

    Book  MATH  Google Scholar 

  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 42:035502

    Article  MathSciNet  MATH  Google Scholar 

  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 53:130–140

    Article  MATH  Google Scholar 

  28. Zhu T, Manhart M (2015) Oscillatory Darcy flow in porous media. Transp Porous Media 111:521–539

    Article  MathSciNet  Google Scholar 

  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 38:314–320

    Article  Google Scholar 

  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 85:117–130

    Article  Google Scholar 

  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 106:244–252

    Article  Google Scholar 

  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 110:1462–1475

    Article  Google Scholar 

  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 111:511–524

    Article  Google Scholar 

  34. Merkin JH (1996) A model for isothermal homogeneous–heterogeneous reactions in boundary layer flow. Math Comput Model 24:125–136

    Article  MathSciNet  MATH  Google Scholar 

  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 55:69–75

    Article  Google Scholar 

  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 518:263–272

    Article  Google Scholar 

  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. 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 28:102003

    Article  Google Scholar 

  39. Liao SJ (2012) Homotopic analysis method in nonlinear differential equations. Springer, Heidelberg

    Book  Google Scholar 

  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:e0129613

    Article  Google Scholar 

  41. Shehzad SA, Hayat T, Alsaedi A, Chen B (2016) A useful model for solar radiation. Energy Ecol Environ 1:30–38

    Article  Google Scholar 

  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. 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 

  44. Turkyilmazoglu M (2016) An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method. Filomat 30:1633–1650

    Article  MathSciNet  MATH  Google Scholar 

  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 131:253

    Article  Google Scholar 

  46. Khan WA, Khan M (2016) Impact of thermophoresis particle deposition on three-dimensional radiative flow of Burgers fluid. Res Phys 6:829–836

    Google Scholar 

  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 26:214–234

    Article  MathSciNet  MATH  Google Scholar 

  48. Turkyilmazoglu M (2010) An optimal analytic approximate solution for the limit cycle of Duffing-van der Pol equation. J Appl Mech Trans ASME 78:021005

    Article  Google Scholar 

  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 220:49–55

    Article  Google Scholar 

  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 04016077

  51. Hayat T, Khan MI, Waqas M, Alsaedi A (2017) Newtonian heating effect in nanofluid flow by a permeable cylinder. Res Phys 7:256–262

    Google Scholar 

  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. 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 225:302–310

    Article  Google Scholar 

  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. 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 234:444–451

    Article  Google Scholar 

  56. Tamoor M, Waqas M, Khan MI, Alsaedi A, Hayat T (2017) Magnetohydrodynamic flow of Casson fluid over a stretching cylinder. Results Phys 7:498–502

    Article  Google Scholar 

  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 223:836–844

    Article  Google Scholar 

  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 11:3186–3197

    Article  MathSciNet  MATH  Google Scholar 

  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 24:390–401

    Article  MathSciNet  MATH  Google Scholar 

  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 13:4019–4037

    Article  MathSciNet  MATH  Google Scholar 

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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.

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Authors and Affiliations

  1. Department of Mathematics, DCC-KFUPM, Box 5084, Dhahran, 31261, Kingdom of Saudi Arabia

    M. Adil Sadiq

  2. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    T. Hayat

  3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Kingdom of Saudi Arabia

    T. Hayat

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Correspondence to M. Adil Sadiq.

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Sadiq, M.A., Hayat, T. Darcy–Forchheimer stretched flow of MHD Maxwell material with heterogeneous and homogeneous reactions. Neural Comput & Applic 31 (Suppl 2), 857–864 (2019). https://doi.org/10.1007/s00521-017-3037-1

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