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Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

  • T. Hayat
  • S. Naz
  • M. Waqas
  • A. Alsaedi
Article

Abstract

The effect of nonlinear mixed convection in stretched flows of rate-type non-Newtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

Key words

Maxwell nanomaterial nonlinear mixed convection thermal radiation double stratification convective condition 

Chinese Library Classification

O361 

2010 Mathematics Subject Classification

76A05 

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References

  1. [1]
    CHOI, S. U. S. and EASTMAN, J. A. Enhancing thermal conductivity of fluids with nanoparticles. The Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, 66, 99–105 (1995)Google Scholar
  2. [2]
    KUZNETSOV, A. V. and NIELD, D. A. Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences, 49, 243–247 (2010)CrossRefGoogle Scholar
  3. [3]
    KANDASAMY, R., MUHAIMIN, I., and MOHAMAD, R. Thermophoresis and Brownian motion effects on MHD boundary-layer flow of a nanofluid in the presence of thermal stratification due to solar radiation. International Journal of Mechanical Sciences, 70, 146–154 (2013)CrossRefGoogle Scholar
  4. [4]
    SANDEEP, N., KUMAR, B. R., and KUMAR, M. S. J. A comparative study of convective heat and mass transfer in non-Newtonian nanofluid flow past a permeable stretching sheet. Journal of Molecular Liquids, 212, 585–591 (2015)CrossRefGoogle Scholar
  5. [5]
    MAHANTHESH, B., GIREESHA, B. J., PRASANNAKUMARA, B. C., and KUMAR, P. B. S. Magneto-thermo-Marangoni convective flow of Cu-H2O nanoliquid past an infinite disk with particle shape and exponential space based heat source effects. Results in Physics, 7, 2990–2996 (2017)CrossRefGoogle Scholar
  6. [6]
    AHMED, S. E. Modeling natural convection boundary layer flow of micropolar nanofluid over vertical permeable cone with variable wall temperature. Applied Mathematics and Mechanics (English Edition), 38, 1171–1180 (2017) https://doi.org/10.1007/s10483-017-2231-9 MathSciNetCrossRefGoogle Scholar
  7. [7]
    NAGENDRAMMA, V., RAJU, C. S. K., MALLIKARJUNA, B., SHEHZAD, S. A., and LEE-LARATHNAM, A. 3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux. Applied Mathematics and Mechanics (English Edition), 39, 623–638 (2018) https://doi.org/10.1007/s10483-018-2331-6 MathSciNetCrossRefGoogle Scholar
  8. [8]
    GIREESHA, B. J., MAHANTHESH, B., and KRUPALAKSHMI, K. L. Hall effect on two-phase radiated flow of magneto-dusty-nanoliquid with irregular heat generation/consumption. Results in Physics, 7, 4340–4348 (2017)CrossRefGoogle Scholar
  9. [9]
    HAYAT, T., KHALID, H., WAQAS, M., and ALSAEDI, A. Homotopic solutions for stagnation point flow of third-grade nanoliquid subject to magnetohydrodynamics. Results in Physics, 7, 4310–4317 (2017)CrossRefGoogle Scholar
  10. [10]
    IRFAN, M., KHAN, M., and KHAN, W. A. Numerical analysis of unsteady 3D flow of Carreau nanofluid with variable thermal conductivity and heat source/sink. Results in Physics, 7, 3315–3324 (2017)CrossRefGoogle Scholar
  11. [11]
    MAHANTHESH, B., GIREESHA, B. J., and RAJU, C. S. K. Cattaneo-Christov heat flux on UCM nanofluid flow across a melting surface with double stratification and exponential space dependent internal heat source. Informatics in Medicine Unlocked, 9, 26–34 (2017)CrossRefGoogle Scholar
  12. [12]
    WAQAS, M., HAYAT, T., SHEHZAD, S. A., and ALSAEDI, A. Transport of magnetohydro-dynamic nanomaterial in a stratified medium considering gyrotactic microorganisms. Physica B: Condensed Matter, 529, 33–40 (2018)CrossRefGoogle Scholar
  13. [13]
    HAMID, A., HASHIM., and KHAN, M. Numerical simulation for heat transfer performance in unsteady flow of Williamson fluid driven by a wedge-geometry. Results in Physics, 9, 479–485 (2018)CrossRefGoogle Scholar
  14. [14]
    GIREESHA, B. J., MAHANTHESH, B., THAMMANNA, G. T., and SAMPATHKUMAR, P. B. Hall effects on dusty nanofluid two-phase transient flow past a stretching sheet using KVL model. Journal of Molecular Liquids, 256, 139–147 (2018)CrossRefGoogle Scholar
  15. [15]
    HAMID, H. A. and KHAN, M. Unsteady mixed convective flow of Williamson nanofluid with heat transfer in the presence of variable thermal conductivity and magnetic field. Journal of Molecular Liquids, 260, 436–446 (2018)CrossRefGoogle Scholar
  16. [16]
    DARCY, H. Les Fontaines Publiques de la Ville de Dijon, Hachette Livre Bnf, Paris (1856)Google Scholar
  17. [17]
    FORCHHEIMER, P. H. Wasserbewegung Durch Boden, Spielhagen & Schurich, Wien (1901)Google Scholar
  18. [18]
    SEDDEEK, M. A. Effects of magnetic field and variable viscosity on forced non-Darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and blowing. Journal of Applied Mechanics and Technical Physics, 43, 13–17 (2002)CrossRefMATHGoogle Scholar
  19. [19]
    SINGH, A. K., KUMAR, R., SINGH, U., SINGH, N. P., and SINGH, A. K. Unsteady hydromagnetic convective flow in a vertical channel using Darcy-Brinkman-Forchheimer extended model with heat generation/absorption: analysis with asymmetric heating/cooling of the channel walls. International Journal of Heat and Mass Transfer, 54, 5633–5642 (2011)CrossRefMATHGoogle Scholar
  20. [20]
    GIREESHA, B. J., MAHANTHESH, B., MANJUNATHA, P. T., and GORLA, R. S. R. Numerical solution for hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in non-Darcy porous medium with fluid-particle suspension. Journal of the Nigerian Mathematical Society, 34, 267–285 (2015)MathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    KHAN, M. I., WAQAS, M., HAYAT, T., KHAN, M. I., and ALSAEDI, A. Numerical simulation of nonlinear thermal radiation and homogeneous-heterogeneous reactions in convective flow by a variable thicked surface. Journal of Molecular Liquids, 246, 259–267 (2017)CrossRefGoogle Scholar
  22. [22]
    SADIQ, M. A., WAQAS, M., and HAYAT, T. Importance of Darcy-Forchheimer relation in chemically reactive radiating flow towards convectively heated surface. Journal of Molecular Liquids, 248, 1071–1077 (2017)CrossRefGoogle Scholar
  23. [23]
    HAYAT, T., SHAH, F., ALSAEDI, A., and WAQAS, M. Numerical simulation for magneto nanofluid flow through a porous space with melting heat transfer. Microgravity Science and Technology, 30, 265–275 (2018)CrossRefGoogle Scholar
  24. [24]
    WANG, S. and TAN, W. C. Stability analysis of Soret-driven double-diffusive convection of Maxwell fluid in a porous medium. International Journal of Heat and Fluid Flow, 32, 88–94 (2011)CrossRefGoogle Scholar
  25. [25]
    HAYAT, T., WAQAS, M., SHEHZAD, S. A., and ALSAEDI, A. Mixed convection radiative flow of Maxwell fluid near a stagnation point with convective condition. Journal of Mechanics, 29, 403–409 (2013)CrossRefGoogle Scholar
  26. [26]
    HAYAT, T., WAQAS, M., SHEHZAD, S. A., and ALSAEDI, A. Effects of Joule heating and thermophoresis on stretched flow with convective boundary conditions. Scientia Iranica Transaction B, Mechanical Engineering, 21, 682–692 (2014)Google Scholar
  27. [27]
    KHAN, M. I., KHAN, M. I., WAQAS, M., HAYAT, T., and ALSAEDI, A. Chemically reactive flow of Maxwell liquid due to variable thicked surface. International Communications in Heat and Mass Transfer, 86, 231–238 (2017)CrossRefGoogle Scholar
  28. [28]
    LIU, Y. and GUO, B. Effects of second-order slip on the flow of a fractional Maxwell MHD fluid. Journal of the Association of Arab Universities for Basic and Applied Sciences, 24, 232–241 (2017)CrossRefGoogle Scholar
  29. [29]
    KHAN, M., IRFAN, M., and KHAN, W. A. Impact of heat source/sink on radiative heat transfer to Maxwell nanofluid subject to revised mass flux condition. Results in Physics, 9, 851–857 (2018)CrossRefGoogle Scholar
  30. [30]
    CHRISTENSEN, R. M. Theory of Viscoelasticity, Academic Press, London (1971)Google Scholar
  31. [31]
    LIAO, S. J. An optimal homotopy-analysis approach for strongly nonlinear dixoerential equations. Communications in Nonlinear Science and Numerical Simulation, 15, 2003–2016 (2010)MathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    TURKYILMAZOGLU, M. Series solution of nonlinear two-point singularly perturbed boundary layer problems. Journal of Computational and Applied Mathematics, 60, 2109–2114 (2010)MathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    HAYAT, T., ALI, S., AWAIS, M., and ALHUTHALI, M. S. Newtonian heating in stagnation point flow of Burgers fluid. Applied Mathematics and Mechanics (English Edition), 36, 61–68 (2015) https://doi.org/10.1007/s10483-015-1895-9 MathSciNetCrossRefGoogle Scholar
  34. [34]
    HAYAT, T., ALI, S., FAROOQ, M. A., and ALSAEDI, A. 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 (2015)CrossRefGoogle Scholar
  35. [35]
    WAQAS, M., FAROOQ, M., KHAN, M. I., HAYAT, T., ALSAEDI, A., and YASMEEN, T. Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition. International Journal of Heat and Mass Transfer, 102, 766–772 (2016)CrossRefGoogle Scholar
  36. [36]
    HAYAT, T., ALI, S., ALSAEDI, A., and ALSULAMI, H. H. Influence of thermal radiation and Joule heating in the Eyring-Powell fluid flow with the Soret and Dufour effects. Journal of Applied Mechanics and Technical Physics, 57, 1051–1060 (2016)MathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    KHAN, M., IRFAN, M., and KHAN, W. A. Impact of nonlinear thermal radiation and gyrotactic microorganisms on the Magneto-Burgers nanofluid. International Journal of Mechanical Sciences, 130, 375–382 (2017)CrossRefGoogle Scholar
  38. [38]
    MUHAMMAD, T., ALSAEDI, A., SHEHZAD, S. A., and HAYAT, T. A revised model for Darcy-Forchheimer flow of Maxwell nanofluid subject to convective boundary condition. Chinese Journal of Physics, 55, 963–976 (2017)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia

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